essay about photosynthesis process

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Development of the idea

Overall reaction of photosynthesis.

• Basic products of photosynthesis
• Evolution of the process
• Light intensity and temperature
• Carbon dioxide
• Internal factors
• Energy efficiency of photosynthesis
• Structural features
• Light absorption and energy transfer
• The pathway of electrons
• Evidence of two light reactions
• Photosystems I and II
• Quantum requirements
• The process of photosynthesis: the conversion of light energy to ATP
• Elucidation of the carbon pathway
• Carboxylation
• Isomerization/condensation/dismutation
• Phosphorylation
• Regulation of the cycle
• Products of carbon reduction
• Photorespiration
• Carbon fixation in C 4 plants
• Carbon fixation via crassulacean acid metabolism (CAM)
• Differences in carbon fixation pathways
• The molecular biology of photosynthesis

Why is photosynthesis important?

What is the basic formula for photosynthesis, which organisms can photosynthesize.

photosynthesis

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• Khan Academy - Photosynthesis
• Biology LibreTexts - Photosynthesis
• University of Florida - Institute of Food and Agricultural Sciences - Photosynthesis
• Milne Library - Inanimate Life - Photosynthesis
• National Center for Biotechnology Information - Chloroplasts and Photosynthesis
• Roger Williams University Pressbooks - Introduction to Molecular and Cell Biology - Photosynthesis
• BCcampus Open Publishing - Concepts of Biology – 1st Canadian Edition - Overview of Photosynthesis
• photosynthesis - Children's Encyclopedia (Ages 8-11)
• photosynthesis - Student Encyclopedia (Ages 11 and up)
• Table Of Contents

Photosynthesis is critical for the existence of the vast majority of life on Earth. It is the way in which virtually all energy in the biosphere becomes available to living things. As primary producers, photosynthetic organisms form the base of Earth’s food webs and are consumed directly or indirectly by all higher life-forms. Additionally, almost all the oxygen in the atmosphere is due to the process of photosynthesis. If photosynthesis ceased, there would soon be little food or other organic matter on Earth, most organisms would disappear, and Earth’s atmosphere would eventually become nearly devoid of gaseous oxygen.

The process of photosynthesis is commonly written as: 6CO 2 + 6H 2 O → C 6 H 12 O 6 + 6O 2 . This means that the reactants, six carbon dioxide molecules and six water molecules, are converted by light energy captured by chlorophyll (implied by the arrow) into a sugar molecule and six oxygen molecules, the products. The sugar is used by the organism, and the oxygen is released as a by-product.

The ability to photosynthesize is found in both eukaryotic and prokaryotic organisms. The most well-known examples are plants, as all but a very few parasitic or mycoheterotrophic species contain chlorophyll and produce their own food. Algae are the other dominant group of eukaryotic photosynthetic organisms. All algae, which include massive kelps and microscopic diatoms , are important primary producers.  Cyanobacteria and certain sulfur bacteria are photosynthetic prokaryotes, in whom photosynthesis evolved. No animals are thought to be independently capable of photosynthesis, though the emerald green sea slug can temporarily incorporate algae chloroplasts in its body for food production.

photosynthesis , the process by which green plants and certain other organisms transform light energy into chemical energy . During photosynthesis in green plants, light energy is captured and used to convert water , carbon dioxide , and minerals into oxygen and energy-rich organic compounds .

It would be impossible to overestimate the importance of photosynthesis in the maintenance of life on Earth . If photosynthesis ceased, there would soon be little food or other organic matter on Earth. Most organisms would disappear, and in time Earth’s atmosphere would become nearly devoid of gaseous oxygen. The only organisms able to exist under such conditions would be the chemosynthetic bacteria , which can utilize the chemical energy of certain inorganic compounds and thus are not dependent on the conversion of light energy.

Energy produced by photosynthesis carried out by plants millions of years ago is responsible for the fossil fuels (i.e., coal , oil , and gas ) that power industrial society . In past ages, green plants and small organisms that fed on plants increased faster than they were consumed, and their remains were deposited in Earth’s crust by sedimentation and other geological processes. There, protected from oxidation , these organic remains were slowly converted to fossil fuels. These fuels not only provide much of the energy used in factories, homes, and transportation but also serve as the raw material for plastics and other synthetic products. Unfortunately, modern civilization is using up in a few centuries the excess of photosynthetic production accumulated over millions of years. Consequently, the carbon dioxide that has been removed from the air to make carbohydrates in photosynthesis over millions of years is being returned at an incredibly rapid rate. The carbon dioxide concentration in Earth’s atmosphere is rising the fastest it ever has in Earth’s history, and this phenomenon is expected to have major implications on Earth’s climate .

Requirements for food, materials, and energy in a world where human population is rapidly growing have created a need to increase both the amount of photosynthesis and the efficiency of converting photosynthetic output into products useful to people. One response to those needs—the so-called Green Revolution , begun in the mid-20th century—achieved enormous improvements in agricultural yield through the use of chemical fertilizers , pest and plant- disease control, plant breeding , and mechanized tilling, harvesting, and crop processing. This effort limited severe famines to a few areas of the world despite rapid population growth , but it did not eliminate widespread malnutrition . Moreover, beginning in the early 1990s, the rate at which yields of major crops increased began to decline. This was especially true for rice in Asia. Rising costs associated with sustaining high rates of agricultural production, which required ever-increasing inputs of fertilizers and pesticides and constant development of new plant varieties, also became problematic for farmers in many countries.

A second agricultural revolution , based on plant genetic engineering , was forecast to lead to increases in plant productivity and thereby partially alleviate malnutrition. Since the 1970s, molecular biologists have possessed the means to alter a plant’s genetic material (deoxyribonucleic acid, or DNA ) with the aim of achieving improvements in disease and drought resistance, product yield and quality, frost hardiness, and other desirable properties. However, such traits are inherently complex, and the process of making changes to crop plants through genetic engineering has turned out to be more complicated than anticipated. In the future such genetic engineering may result in improvements in the process of photosynthesis, but by the first decades of the 21st century, it had yet to demonstrate that it could dramatically increase crop yields.

Another intriguing area in the study of photosynthesis has been the discovery that certain animals are able to convert light energy into chemical energy. The emerald green sea slug ( Elysia chlorotica ), for example, acquires genes and chloroplasts from Vaucheria litorea , an alga it consumes, giving it a limited ability to produce chlorophyll . When enough chloroplasts are assimilated , the slug may forgo the ingestion of food. The pea aphid ( Acyrthosiphon pisum ) can harness light to manufacture the energy-rich compound adenosine triphosphate (ATP); this ability has been linked to the aphid’s manufacture of carotenoid pigments.

General characteristics

The study of photosynthesis began in 1771 with observations made by the English clergyman and scientist Joseph Priestley . Priestley had burned a candle in a closed container until the air within the container could no longer support combustion . He then placed a sprig of mint plant in the container and discovered that after several days the mint had produced some substance (later recognized as oxygen) that enabled the confined air to again support combustion. In 1779 the Dutch physician Jan Ingenhousz expanded upon Priestley’s work, showing that the plant had to be exposed to light if the combustible substance (i.e., oxygen) was to be restored. He also demonstrated that this process required the presence of the green tissues of the plant.

In 1782 it was demonstrated that the combustion-supporting gas (oxygen) was formed at the expense of another gas, or “fixed air,” which had been identified the year before as carbon dioxide. Gas-exchange experiments in 1804 showed that the gain in weight of a plant grown in a carefully weighed pot resulted from the uptake of carbon, which came entirely from absorbed carbon dioxide, and water taken up by plant roots; the balance is oxygen, released back to the atmosphere. Almost half a century passed before the concept of chemical energy had developed sufficiently to permit the discovery (in 1845) that light energy from the sun is stored as chemical energy in products formed during photosynthesis.

This equation is merely a summary statement, for the process of photosynthesis actually involves numerous reactions catalyzed by enzymes (organic catalysts ). These reactions occur in two stages: the “light” stage, consisting of photochemical (i.e., light-capturing) reactions; and the “dark” stage, comprising chemical reactions controlled by enzymes . During the first stage, the energy of light is absorbed and used to drive a series of electron transfers, resulting in the synthesis of ATP and the electron-donor-reduced nicotine adenine dinucleotide phosphate (NADPH). During the dark stage, the ATP and NADPH formed in the light-capturing reactions are used to reduce carbon dioxide to organic carbon compounds. This assimilation of inorganic carbon into organic compounds is called carbon fixation.

Van Niel’s proposal was important because the popular (but incorrect) theory had been that oxygen was removed from carbon dioxide (rather than hydrogen from water, releasing oxygen) and that carbon then combined with water to form carbohydrate (rather than the hydrogen from water combining with CO 2 to form CH 2 O).

By 1940 chemists were using heavy isotopes to follow the reactions of photosynthesis. Water marked with an isotope of oxygen ( 18 O) was used in early experiments. Plants that photosynthesized in the presence of water containing H 2 18 O produced oxygen gas containing 18 O; those that photosynthesized in the presence of normal water produced normal oxygen gas. These results provided definitive support for van Niel’s theory that the oxygen gas produced during photosynthesis is derived from water.

ENCYCLOPEDIC ENTRY

Photosynthesis.

Photosynthesis is the process by which plants use sunlight, water, and carbon dioxide to create oxygen and energy in the form of sugar.

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Learning materials, instructional links.

• Photosynthesis (Google doc)

Most life on Earth depends on photosynthesis .The process is carried out by plants, algae, and some types of bacteria, which capture energy from sunlight to produce oxygen (O 2 ) and chemical energy stored in glucose (a sugar). Herbivores then obtain this energy by eating plants, and carnivores obtain it by eating herbivores.

The process

During photosynthesis, plants take in carbon dioxide (CO 2 ) and water (H 2 O) from the air and soil. Within the plant cell, the water is oxidized, meaning it loses electrons, while the carbon dioxide is reduced, meaning it gains electrons. This transforms the water into oxygen and the carbon dioxide into glucose. The plant then releases the oxygen back into the air, and stores energy within the glucose molecules.

Chlorophyll

Inside the plant cell are small organelles called chloroplasts , which store the energy of sunlight. Within the thylakoid membranes of the chloroplast is a light-absorbing pigment called chlorophyll , which is responsible for giving the plant its green color. During photosynthesis , chlorophyll absorbs energy from blue- and red-light waves, and reflects green-light waves, making the plant appear green.

Light-dependent Reactions vs. Light-independent Reactions

While there are many steps behind the process of photosynthesis, it can be broken down into two major stages: light-dependent reactions and light-independent reactions. The light-dependent reaction takes place within the thylakoid membrane and requires a steady stream of sunlight, hence the name light- dependent reaction. The chlorophyll absorbs energy from the light waves, which is converted into chemical energy in the form of the molecules ATP and NADPH . The light-independent stage, also known as the Calvin cycle , takes place in the stroma , the space between the thylakoid membranes and the chloroplast membranes, and does not require light, hence the name light- independent reaction. During this stage, energy from the ATP and NADPH molecules is used to assemble carbohydrate molecules, like glucose, from carbon dioxide.

C3 and C4 Photosynthesis

Not all forms of photosynthesis are created equal, however. There are different types of photosynthesis, including C3 photosynthesis and C4 photosynthesis. C3 photosynthesis is used by the majority of plants. It involves producing a three-carbon compound called 3-phosphoglyceric acid during the Calvin Cycle, which goes on to become glucose. C4 photosynthesis, on the other hand, produces a four-carbon intermediate compound, which splits into carbon dioxide and a three-carbon compound during the Calvin Cycle. A benefit of C4 photosynthesis is that by producing higher levels of carbon, it allows plants to thrive in environments without much light or water. The National Geographic Society is making this content available under a Creative Commons CC-BY-NC-SA license . The License excludes the National Geographic Logo (meaning the words National Geographic + the Yellow Border Logo) and any images that are included as part of each content piece. For clarity the Logo and images may not be removed, altered, or changed in any way.

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Related Resources

• Biology Article

Photosynthesis

Photosynthesis is a process by which phototrophs convert light energy into chemical energy, which is later used to fuel cellular activities. The chemical energy is stored in the form of sugars, which are created from water and carbon dioxide.

Table of Contents

• What is Photosynthesis?
• Site of photosynthesis

What Is Photosynthesis in Biology?

The word “ photosynthesis ” is derived from the Greek words  phōs  (pronounced: “fos”) and σύνθεσις (pronounced: “synthesis “) Phōs means “light” and σύνθεσις   means, “combining together.” This means “ combining together with the help of light .”

Photosynthesis also applies to other organisms besides green plants. These include several prokaryotes such as cyanobacteria, purple bacteria and green sulfur bacteria. These organisms exhibit photosynthesis just like green plants.The glucose produced during photosynthesis is then used to fuel various cellular activities. The by-product of this physio-chemical process is oxygen.

A visual representation of the photosynthesis reaction

• Photosynthesis is also used by algae to convert solar energy into chemical energy. Oxygen is liberated as a by-product and light is considered as a major factor to complete the process of photosynthesis.
• Photosynthesis occurs when plants use light energy to convert carbon dioxide and water into glucose and oxygen. Leaves contain microscopic cellular organelles known as chloroplasts.
• Each chloroplast contains a green-coloured pigment called chlorophyll. Light energy is absorbed by chlorophyll molecules whereas carbon dioxide and oxygen enter through the tiny pores of stomata located in the epidermis of leaves.
• Another by-product of photosynthesis is sugars such as glucose and fructose.
• These sugars are then sent to the roots, stems, leaves, fruits, flowers and seeds. In other words, these sugars are used by the plants as an energy source, which helps them to grow. These sugar molecules then combine with each other to form more complex carbohydrates like cellulose and starch. The cellulose is considered as the structural material that is used in plant cell walls.

Where Does This Process Occur?

Chloroplasts are the sites of photosynthesis in plants and blue-green algae.  All green parts of a plant, including the green stems, green leaves,  and sepals – floral parts comprise of chloroplasts – green colour plastids. These cell organelles are present only in plant cells and are located within the mesophyll cells of leaves.

Also Read:  Photosynthesis Early Experiments

Photosynthesis Equation

Photosynthesis reaction involves two reactants, carbon dioxide and water. These two reactants yield two products, namely, oxygen and glucose. Hence, the photosynthesis reaction is considered to be an endothermic reaction. Following is the photosynthesis formula:

Unlike plants, certain bacteria that perform photosynthesis do not produce oxygen as the by-product of photosynthesis. Such bacteria are called anoxygenic photosynthetic bacteria. The bacteria that do produce oxygen as a by-product of photosynthesis are called oxygenic photosynthetic bacteria.

Structure Of Chlorophyll

The structure of Chlorophyll consists of 4 nitrogen atoms that surround a magnesium atom. A hydrocarbon tail is also present. Pictured above is chlorophyll- f,  which is more effective in near-infrared light than chlorophyll- a

Chlorophyll is a green pigment found in the chloroplasts of the  plant cell   and in the mesosomes of cyanobacteria. This green colour pigment plays a vital role in the process of photosynthesis by permitting plants to absorb energy from sunlight. Chlorophyll is a mixture of chlorophyll- a  and chlorophyll- b .Besides green plants, other organisms that perform photosynthesis contain various other forms of chlorophyll such as chlorophyll- c1 ,  chlorophyll- c2 ,  chlorophyll- d and chlorophyll- f .

Also Read:   Biological Pigments

Process Of Photosynthesis

At the cellular level,  the photosynthesis process takes place in cell organelles called chloroplasts. These organelles contain a green-coloured pigment called chlorophyll, which is responsible for the characteristic green colouration of the leaves.

As already stated, photosynthesis occurs in the leaves and the specialized cell organelles responsible for this process is called the chloroplast. Structurally, a leaf comprises a petiole, epidermis and a lamina. The lamina is used for absorption of sunlight and carbon dioxide during photosynthesis.

Structure of Chloroplast. Note the presence of the thylakoid

“Photosynthesis Steps:”

• During the process of photosynthesis, carbon dioxide enters through the stomata, water is absorbed by the root hairs from the soil and is carried to the leaves through the xylem vessels. Chlorophyll absorbs the light energy from the sun to split water molecules into hydrogen and oxygen.
• The hydrogen from water molecules and carbon dioxide absorbed from the air are used in the production of glucose. Furthermore, oxygen is liberated out into the atmosphere through the leaves as a waste product.
• Glucose is a source of food for plants that provide energy for  growth and development , while the rest is stored in the roots, leaves and fruits, for their later use.
• Pigments are other fundamental cellular components of photosynthesis. They are the molecules that impart colour and they absorb light at some specific wavelength and reflect back the unabsorbed light. All green plants mainly contain chlorophyll a, chlorophyll b and carotenoids which are present in the thylakoids of chloroplasts. It is primarily used to capture light energy. Chlorophyll-a is the main pigment.

The process of photosynthesis occurs in two stages:

• Light-dependent reaction or light reaction
• Light independent reaction or dark reaction

Stages of Photosynthesis in Plants depicting the two phases – Light reaction and Dark reaction

Light Reaction of Photosynthesis (or) Light-dependent Reaction

• Photosynthesis begins with the light reaction which is carried out only during the day in the presence of sunlight. In plants, the light-dependent reaction takes place in the thylakoid membranes of chloroplasts.
• The Grana, membrane-bound sacs like structures present inside the thylakoid functions by gathering light and is called photosystems.
• These photosystems have large complexes of pigment and proteins molecules present within the plant cells, which play the primary role during the process of light reactions of photosynthesis.
• There are two types of photosystems: photosystem I and photosystem II.
• Under the light-dependent reactions, the light energy is converted to ATP and NADPH, which are used in the second phase of photosynthesis.
• During the light reactions, ATP and NADPH are generated by two electron-transport chains, water is used and oxygen is produced.

The chemical equation in the light reaction of photosynthesis can be reduced to:

2H 2 O + 2NADP+ + 3ADP + 3Pi → O 2 + 2NADPH + 3ATP

Dark Reaction of Photosynthesis (or) Light-independent Reaction

• Dark reaction is also called carbon-fixing reaction.
• It is a light-independent process in which sugar molecules are formed from the water and carbon dioxide molecules.
• The dark reaction occurs in the stroma of the chloroplast where they utilize the NADPH and ATP products of the light reaction.
• Plants capture the carbon dioxide from the atmosphere through stomata and proceed to the Calvin photosynthesis cycle.
• In the Calvin cycle , the ATP and NADPH formed during light reaction drive the reaction and convert 6 molecules of carbon dioxide into one sugar molecule or glucose.

The chemical equation for the dark reaction can be reduced to:

3CO 2 + 6 NADPH + 5H 2 O + 9ATP → G3P + 2H+ + 6 NADP+ + 9 ADP + 8 Pi

* G3P – glyceraldehyde-3-phosphate

Calvin photosynthesis Cycle (Dark Reaction)

Also Read:  Cyclic And Non-Cyclic Photophosphorylation

Importance of Photosynthesis

• Photosynthesis is essential for the existence of all life on earth. It serves a crucial role in the food chain – the plants create their food using this process, thereby, forming the primary producers.
• Photosynthesis is also responsible for the production of oxygen – which is needed by most organisms for their survival.

Frequently Asked Questions

1. what is photosynthesis explain the process of photosynthesis., 2. what is the significance of photosynthesis, 3. list out the factors influencing photosynthesis., 4. what are the different stages of photosynthesis, 5. what is the calvin cycle, 6. write down the photosynthesis equation..

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Please What Is Meant By 300-400 PPM

PPM stands for Parts-Per-Million. It corresponds to saying that 300 PPM of carbon dioxide indicates that if one million gas molecules are counted, 300 out of them would be carbon dioxide. The remaining nine hundred ninety-nine thousand seven hundred are other gas molecules.

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Essay on Photosynthesis

Students are often asked to write an essay on Photosynthesis in their schools and colleges. And if you’re also looking for the same, we have created 100-word, 250-word, and 500-word essays on the topic.

Let’s take a look…

100 Words Essay on Photosynthesis

What is photosynthesis.

Photosynthesis is how plants make their own food using sunlight. It happens in the leaves of plants. Tiny parts inside the leaves, called chloroplasts, use sunlight to turn water and carbon dioxide from the air into sugar and oxygen. The sugar is food for the plant.

The Ingredients

The main things needed for photosynthesis are sunlight, water, and carbon dioxide. Roots soak up water from the soil. Leaves take in carbon dioxide from the air. Then, using sunlight, plants create food and release oxygen.

The Process

In the chloroplasts, sunlight energy is changed into chemical energy. This energy turns water and carbon dioxide into glucose, a type of sugar. Oxygen is made too, which goes into the air for us to breathe.

Why It’s Important

Photosynthesis is vital for life on Earth. It gives us food and oxygen. Without it, there would be no plants, and without plants, animals and people would not survive. It also helps take in carbon dioxide, which is good for the Earth.

250 Words Essay on Photosynthesis

Why is photosynthesis important.

This process is very important because it is the main way plants make food for themselves and for us, too. Without photosynthesis, plants could not grow, and without plants, animals and humans would not have oxygen to breathe or food to eat.

How Photosynthesis Works

Photosynthesis happens in two main stages. In the first stage, the plant captures sunlight with its leaves. The sunlight gives the plant energy to split water inside its leaves into hydrogen and oxygen. The oxygen is released into the air, and the hydrogen is used in the next stage.

In the second stage, the plant mixes the hydrogen with carbon dioxide from the air to make glucose, which is a type of sugar that plants use for energy. This energy helps the plant to grow, make flowers, and produce seeds.

The Cycle of Life

Photosynthesis is a key part of the cycle of life on Earth. By making food and oxygen, plants support life for all creatures. When animals eat plants, they get the energy from the plants, and when animals breathe, they use the oxygen that plants release. It’s a beautiful cycle that keeps the planet alive.

500 Words Essay on Photosynthesis

Photosynthesis is a process used by plants, algae, and some bacteria to turn sunlight, water, and carbon dioxide into food and oxygen. This happens in the green parts of plants, mainly the leaves. The green color comes from chlorophyll, a special substance in the leaves that captures sunlight.

The Ingredients of Photosynthesis

The photosynthesis recipe.

When sunlight hits the leaves, the chlorophyll captures it and starts the food-making process. The energy from the sunlight turns water and carbon dioxide into glucose, a type of sugar that plants use for energy, and oxygen, which is released into the air. This process is like a recipe that plants follow to make their own food.

The Importance of Photosynthesis

Photosynthesis is very important for life on Earth. It gives us oxygen, which we need to breathe. Plants use the glucose they make for growth and to build other important substances like cellulose, which they use to make their cell walls. Without photosynthesis, there would be no food for animals or people, and no oxygen to breathe.

The Benefits to the Environment

Photosynthesis and the food chain.

All living things need energy to survive, and this energy usually comes from food. Plants are at the bottom of the food chain because they can make their own food using photosynthesis. Animals that eat plants get energy from the glucose in the plants. Then, animals that eat other animals get this energy too. So, photosynthesis is the start of the food chain that feeds almost every living thing on Earth.

Photosynthesis in Our Lives

Photosynthesis affects our lives in many ways. It gives us fruits, vegetables, and grains to eat. Trees and plants also give us wood, paper, and other materials. Plus, they provide shade and help make the air fresh and clean.

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Photosynthesis

Reviewed by: BD Editors

Photosynthesis Definition

Photosynthesis is the biochemical pathway which converts the energy of light into the bonds of glucose molecules. The process of photosynthesis occurs in two steps. In the first step, energy from light is stored in the bonds of adenosine triphosphate (ATP), and nicotinamide adenine dinucleotide phosphate (NADPH). These two energy-storing cofactors are then used in the second step of photosynthesis to produce organic molecules by combining carbon molecules derived from carbon dioxide (CO 2 ). The second step of photosynthesis is known as the Calvin Cycle. These organic molecules can then be used by mitochondria to produce ATP, or they can be combined to form glucose, sucrose, and other carbohydrates. The chemical equation for the entire process can be seen below.

Photosynthesis Equation

Above is the overall reaction for photosynthesis. Using the energy from light and the hydrogens and electrons from water, the plant combines the carbons found in carbon dioxide into more complex molecules. While a 3-carbon molecule is the direct result of photosynthesis, glucose is simply two of these molecules combined and is often represented as the direct result of photosynthesis due to glucose being a foundational molecule in many cellular systems. You will also notice that 6 gaseous oxygen molecules are produced, as a by-produce. The plant can use this oxygen in its mitochondria during oxidative phosphorylation . While some of the oxygen is used for this purpose, a large portion is expelled into the atmosphere and allows us to breathe and undergo our own oxidative phosphorylation, on sugar molecules derived from plants. You will also notice that this equation shows water on both sides. That is because 12 water molecules are split during the light reactions, while 6 new molecules are produced during and after the Calvin cycle. While this is the general equation for the entire process, there are many individual reactions which contribute to this pathway.

Stages of Photosynthesis

The light reactions.

The light reactions happen in the thylakoid membranes of the chloroplasts of plant cells. The thylakoids have densely packed protein and enzyme clusters known as photosystems . There are two of these systems, which work in conjunction with each other to remove electrons and hydrogens from water and transfer them to the cofactors ADP and NADP + . These photosystems were named in the order of which they were discovered, which is opposite of how electrons flow through them. As seen in the image below, electrons excited by light energy flow first through photosystem II (PSII), and then through photosystem I (PSI) as they create NADPH. ATP is created by the protein ATP synthase , which uses the build-up of hydrogen atoms to drive the addition of phosphate groups to ADP.

The entire system works as follows. A photosystem is comprised of various proteins that surround and connect a series of pigment molecules . Pigments are molecules that absorb various photons, allowing their electrons to become excited. Chlorophyll a is the main pigment used in these systems, and collects the final energy transfer before releasing an electron. Photosystem II starts this process of electrons by using the light energy to split a water molecule, which releases the hydrogen while siphoning off the electrons. The electrons are then passed through plastoquinone, an enzyme complex that releases more hydrogens into the thylakoid space . The electrons then flow through a cytochrome complex and plastocyanin to reach photosystem I. These three complexes form an electron transport chain , much like the one seen in mitochondria. Photosystem I then uses these electrons to drive the reduction of NADP + to NADPH. The additional ATP made during the light reactions comes from ATP synthase, which uses the large gradient of hydrogen molecules to drive the formation of ATP.

The Calvin Cycle

With its electron carriers NADPH and ATP all loaded up with electrons, the plant is now ready to create storable energy. This happens during the Calvin Cycle , which is very similar to the citric acid cycle seen in mitochondria. However, the citric acid cycle creates ATP other electron carriers from 3-carbon molecules, while the Calvin cycle produces these products with the use of NADPH and ATP. The cycle has 3 phases, as seen in the graphic below.

During the first phase, a carbon is added to a 5-carbon sugar, creating an unstable 6-carbon sugar. In phase two, this sugar is reduced into two stable 3-carbon sugar molecules. Some of these molecules can be used in other metabolic pathways, and are exported. The rest remain to continue cycling through the Calvin cycle. During the third phase, the five-carbon sugar is regenerated to start the process over again. The Calvin cycle occurs in the stroma of a chloroplast. While not considered part of the Calvin cycle, these products can be used to create a variety of sugars and structural molecules.

Products of Photosynthesis

The direct products of the light reactions and the Calvin cycle are 3-phosphoglycerate and G3P, two different forms of a 3-carbon sugar molecule. Two of these molecules combined equals one glucose molecule, the product seen in the photosynthesis equation. While this is the main food source for plants and animals, these 3-carbon skeletons can be combined into many different forms. A structural form worth note is cellulose , and extremely strong fibrous material made essentially of strings of glucose. Besides sugars and sugar-based molecules, oxygen is the other main product of photosynthesis. Oxygen created from photosynthesis fuels every respiring organism on the planet.

Lodish, H., Berk, A., Kaiser, C. A., Krieger, M., Scott, M. P., Bretscher, A., . . . Matsudaira, P. (2008). Molecular Cell Biology 6th. ed . New York: W.H. Freeman and Company. Nelson, D. L., & Cox, M. M. (2008). Principles of Biochemistry . New York: W.H. Freeman and Company.

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• v.126(4); 2020 Sep 14

Photosynthesis: basics, history and modelling

Alexandrina stirbet.

1 Anne Burras Lane, Newport News, VA, USA

Dušan Lazár

2 Department of Biophysics, Center of the Region Haná for Biotechnological and Agricultural Research, Faculty of Science, Palacký University, Šlechtitelů 27, 783 71 Olomouc, Czech Republic

3 Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education), Jiangnan University, Wuxi, China

4 University of Missouri, Columbia, MO, USA

Govindjee Govindjee

5 Department of Biochemistry, Department of Plant Biology, and Center of Biophysics & Quantitative Biology, University of Illinois at Urbana-Champaign, Urbana, IL, USA

With limited agricultural land and increasing human population, it is essential to enhance overall photosynthesis and thus productivity. Oxygenic photosynthesis begins with light absorption, followed by excitation energy transfer to the reaction centres, primary photochemistry, electron and proton transport, NADPH and ATP synthesis, and then CO 2 fixation (Calvin–Benson cycle, as well as Hatch–Slack cycle). Here we cover some of the discoveries related to this process, such as the existence of two light reactions and two photosystems connected by an electron transport ‘chain’ (the Z-scheme), chemiosmotic hypothesis for ATP synthesis, water oxidation clock for oxygen evolution, steps for carbon fixation, and finally the diverse mechanisms of regulatory processes, such as ‘state transitions’ and ‘non-photochemical quenching’ of the excited state of chlorophyll a.

In this review, we emphasize that mathematical modelling is a highly valuable tool in understanding and making predictions regarding photosynthesis. Different mathematical models have been used to examine current theories on diverse photosynthetic processes; these have been validated through simulation(s) of available experimental data, such as chlorophyll a fluorescence induction, measured with fluorometers using continuous (or modulated) exciting light, and absorbance changes at 820 nm (ΔA 820 ) related to redox changes in P700, the reaction centre of photosystem I.

Conclusions

We highlight here the important role of modelling in deciphering and untangling complex photosynthesis processes taking place simultaneously, as well as in predicting possible ways to obtain higher biomass and productivity in plants, algae and cyanobacteria.

‘ Complexity is the prodigy of the world. Simplicity is the sensation of the universe. Behind complexity, there is always simplicity to be revealed. Inside simplicity, there is always complexity to be discovered.’ Gang Yu

INTRODUCTION

With limited agricultural land and increasing human population, it is essential to enhance photosynthetic activities. Oxygenic photosynthesis is a very important process, not only because it is the source of our food, fibre and many useful substances, but also because almost all life on the Earth depends on it, either directly or indirectly. Plants, algae and cyanobacteria are oxygenic photosynthetizers that use light energy to generate organic molecules [e.g. glucose (C 6 H 12 O 6 ), sugars, starch] from carbon dioxide (CO 2 ) and water (H 2 O), and release molecular oxygen (O 2 ) into the atmosphere (for a background on photosynthesis see, Eaton-Rye et al ., 2012 ; Blankenship, 2014 ; Shevela et al. , 2019 ):

Note that the above global equation of photosynthesis emphasizes that the oxygen molecules released into the atmosphere originate from water oxidation, not from carbon dioxide, as established using 18 O-labelled water ( Ruben et al. , 1941 ).

This process starts in the thylakoid membrane (TM) with two light reactions taking place simultaneously at photosystem (PS) II and PSI reaction centres (RCs; for PSII and PSI, see the review by Nelson and Junge, 2015 ). The light energy absorbed by pigment–protein antenna complexes of the PSs is converted, with very high efficiency, into redox chemical energy; a small part is, however, dissipated as heat (internal conversion), and as chlorophyll (Chl) fluorescence (2–10 %, Latimer et al. , 1956 ). Furthermore, water is oxidized to oxygen, and NADP + is reduced to NADPH, and, in addition, ATP is produced ( Rabinowitch and Govindjee, 1969 ; Blankenship, 2014 ; Shevela et al. , 2019 ). Both NADPH and ATP are then used for CO 2 assimilation in the stroma (for a historical background of the Calvin–Benson cycle, see, Bassham, 2005 ; Benson, 2005 ); here, Rubisco (ribulose 1,5-bisphosphate carboxylase/oxygenase) is a key enzyme, which catalyses the fixation of CO 2 on a five-carbon compound, RuBP (ribulose 1,5- bis phosphate). A diagram of the photosynthetic apparatus and the electron transport (ET) reactions is shown in Fig. 1 .

Diagram of the photosynthetic apparatus and electron transport (ET) pathways in plants and algae. Four major protein complexes in the thylakoid membrane (TM) participate in the production of ATP and nicotinamide adenine dinucleotide phosphate in reduced form (NADPH), needed for the Calvin–Benson cycle to fix CO 2 to produce sugars: two photosystems (PSII and PSI) connected in series via the cytochrome (Cyt) b 6 /f, and the ATP synthase. Light is absorbed simultaneously by pigments in the light harvesting complexes of PSI and PSII (LHCI and LHCII); excitation energy is transferred to reaction centre (RC) P700 (in PSI) and P680 (in PSII), where primary charge separation takes place, initiating a chain of redox reactions. PSII functions as a water/PQ (photo)-oxidoreductase, which has a manganese complex [Mn 4 O 5 Ca], and a tyrosine-161 (Y Z ), located on D1 protein on the electron donor side, as well as pheophytin (Pheo), plastoquinones Q A and Q B , and a non-haem (heme) iron binding a bicarbonate ion (HCO 3 ‒ ) on the electron acceptor side. By contrast, PSI is a plastocyanin (PC)/ferredoxin (Fd) (photo)-oxidoreductase; it uses reduced PC as an electron donor, and a particular Chl a molecule (A 0 ), vitamin K 1 (A 1 ), and three non-haem iron–sulfur centres (shown in the figure as Fe-S) are on the acceptor side of PSI. The Cyt b 6 /f complex includes a Cyt f, a Rieske iron–sulfur protein (Fe-S), two cytochromes b (Cyt b p and Cyt b n ) that participate in the oxidation and reduction of PQH 2 and PQ: PQH 2 is oxidized at the Q p -site by Cyt b p , while PQ is reduced at the Q n -site by Cyt b n . The Q p - and Q n -sides are also called Q o - and Q i -sides, respectively. Besides the linear ET flow from water to NADP + , there are several pathways leading to electron donation to alternative electron acceptors: cyclic electron flow (CEF) around PSI mediated by Fd (involving Fd-NADP + -reductase, FNR, and a proton gradient regulator, PGR5), or NADPH (via NADPH dehydrogenase, NDH); water–water cycle (WWC); chlororespiration (through the plastid terminal oxidase, PTOX); and the malate valve (through malate dehydrogenase, MDH). The proton motive force ( pmf ) [consisting of the proton concentration difference (ΔpH) and the electric potential (ΔΨ) across TM] is used by ATP synthase to produce ATP from ADP and phosphate (P i ); in the pmf formula, R is the gas constant, F is the Faraday constant, and T is the absolute temperature (in K). Modified from Alric (2010) .

The availability of high-performance computers and detailed knowledge of the various steps of photosynthesis have provided new opportunities to use mathematical modelling to better understand the dynamics of this process (see reviews by Lazár and Schansker, 2009 ; Jablonsky et al. , 2011 ; Stirbet et al. , 2014 ). In addition, several studies ( Zhu et al. , 2010 ; Long et al ., 2006 , 2015 ; Ort et al. , 2015 ; South et al. , 2018 ; Simkin et al. , 2019 ) strongly support the idea that the photosynthetic processes can be improved through genetic engineering to increase the yield potential of various crops (see also Rosenthal et al. , 2011 ; Simkin et al ., 2015 , 2017 ; Kromdijk et al. , 2016 ; McGrath and Long, 2016 ). Furthermore, mathematical modelling can be used to predict opportunities for specific genetic modifications and devise optimized engineering designs to improve photosynthesis ( Zhu et al. , 2007 ).

In this review, we first provide a background of oxygenic photosynthesis that forms the basis of its modelling. We then discuss a few selected studies on mathematical models describing photosynthetic processes. Partial reactions of photosynthesis have been often modelled separately, such as: (1) the primary photochemical reactions (e.g. Schatz et al. , 1988 ; Roelofs et al. , 1992 ); (2) water ‘splitting’ reactions (e.g. Kok et al. , 1970 ; Mar and Govindjee, 1972 ; Jablonsky and Lazár, 2008 ; Shen, 2015 ); (3) reduction of Q B , the secondary plastoquinone (PQ) acceptor of PSII (e.g. Velthuys and Amesz, 1974 ; Petrouleas and Crofts, 2005 ); and (4) the redox reactions of the PQ pool at the Cyt b 6 /f complex (which may include the Q-cycle; see e.g. Mitchell, 1975 ; Cramer et al. , 2011 ). However, in this review we mainly discuss larger models, which include several steps, providing information on complex photosynthetic processes.

PHOTOSYNTHESIS IN PLANTS, ALGAE AND CYANOBACTERIA: SOME BASICS

Early discoveries.

Not much was known about photosynthesis before the 20th century; for earlier discoveries in photosynthesis see chapter 2 in Rabinowitch (1945) and the timeline in Govindjee and Krogmann (2004) . The key discoveries were as follows (see chapter 1 in Rabinowitch and Govindjee, 1969 ): Jan van Helmont (1648) showed that plant growth was mainly from the water that plants had absorbed; it was only later that Nicolas Théodore de Saussure (1804) clearly showed that water was an essential reactant of photosynthesis. Joseph Priestley (1776) showed, in elegant experiments, that plants produced ‘oxygen’ (then called de-phlogisticated air) needed by a mouse to live, whereas Jan Ingen-Housz (1773) convincingly established that light was necessary for photosynthesis. The role of CO 2 in photosynthesis was shown by Jean Senebier (1782), whereas the synthesis of starch was shown by Julius von Sachs (1862, 1864). However, the involvement of chlorophyll (Chl) in this process has a long history. For some of the earliest concepts, we must remember to mention Pierre Joseph Pelletier and Joseph Bienaimé Caventou (1817, 1818), and René Joachim Henri Dutrochet (1837). However, Theodor Engelmann (1882) provided the first action spectrum of photosynthesis, showing that red and blue light, absorbed by Chl, produce oxygen (see figure 1.1 and its description in Shevela et al. , 2019 ).

Physiological and biochemical advances

An understanding of how photosynthesis functions began only after 1900, but by 1960 a basic model at the molecular level, including generation of NADPH and ATP as well as the steps leading to the assimilation of CO 2 to produce carbohydrates, was established (see Govindjee and Krogmann, 2004 ; Govindjee et al ., 2005; Nickelsen, 2016 ).

By measuring photosynthesis as a function of light intensity, Frederick Frost Blackman (1905) suggested that photosynthesis consists of two separate phases: a light-dependent phase (i.e. so-called ‘light’ reactions), and a temperature-dependent biochemical phase (so-called ‘dark’ reactions, or ‘Blackman reaction’; see Warburg and Uyesugi, 1924 ). However, because CO 2 fixation uses NADPH and ATP, formed in the light phase, these so-called ‘dark’ reactions are also light-dependent. Moreover, many enzymes, involved in CO 2 assimilation reactions, function only when they are ‘light-activated’, being controlled through the ferredoxin:thioredoxin reductase (FTR) system (see reviews by Buchanan et al. , 2002 ; Nikkanen and Rintamäki, 2019 ). Therefore, the term ‘dark phase’ is inappropriate; Buchanan (2016) has proposed the use of ‘carbon reactions’ for ‘dark reactions’. Furthermore, the true ‘light reactions’ end after the primary charge separation steps in the RCs; both the electron transfer and the proton transfer reactions, in principle, can occur in darkness.

Cornelis B. van Niel (1931, 1941) showed that certain photosynthetic bacteria use H 2 S instead of H 2 O as an electron donor, producing sulfur instead of oxygen, and the global reaction of photosynthesis is:

where A is sulfur in sulfur bacteria and oxygen in plants, algae and cyanobacteria. By analogy with photosynthetic bacteria, van Niel suggested that O 2 released by plants is derived from H 2 O rather than CO 2 . This was confirmed by Sam Ruben, Merle Randall, Martin Kamen and James Logan Hyde (see Ruben et al. , 1941 ), based on results using 18 O-labelled water.

Chlorophyll a fluorescence

As mentioned earlier, in addition to primary photochemistry, photosynthetic organisms lose some energy as heat (internal conversion) and as light (fluorescence). Fluorescence is radiative deactivation of (usually) the first singlet excited state of a molecule to the ground state. Kautsky and Hirsch (1931) discovered what others later called the ‘Kautsky effect’, which is Chl a fluorescence induction (ChlFI; see Govindjee, 1995 ). Kautsky and Hirsch observed (visually) transitory variations in Chl a fluorescence (ChlF) emitted by samples that were illuminated after a period of darkness; this ChlF has an increasing phase (peak, ~1 s) followed by a slower (5–10 min) decreasing phase. McAlister and Myers (1940) made an important observation by showing an inverse relationship between ChlF emission and CO 2 uptake. These ChlF transients were then studied, among other places, in the Photosynthesis Laboratory at the University of Illinois, Urbana-Champaign (beginning in the 1950s; see Govindjee and Papageorgiou, 1971 ; Papageorgiou, 1975 ; Govindjee and Satoh, 1986 ; Papageorgiou et al. , 2007 ). Because ChlF has been shown to be directly or indirectly affected by complex physical and biochemical processes taking place during photosynthesis, analysis of ChlFI curves is of importance in photosynthesis research (see reviews by Krause and Weis, 1991 ; Lazár, 1999 , 2015 ; Strasser et al. , 2004 ; Stirbet and Govindjee, 2011 ; Stirbet et al. , 2018 ).

Photosynthetic unit (antenna and reaction centres): excitation energy transfer

An essential concept related to the light phase of photosynthesis is ‘photosynthetic unit’. It was developed based on the crucial discovery by Emerson and Arnold (1932 a , b ) that ~2400 Chl molecules cooperate to evolve one molecule of O 2 , while the minimum quantum requirement for the evolution of one O 2 molecule was 8–10 ( Emerson, 1958 ; for the history of this discovery, see Nickelsen and Govindjee, 2011 ; Nickelsen, 2016 ). Gaffron and Wohl (1936) suggested the existence of ‘photosynthetic units’, where light energy absorbed by any antenna molecule is transferred as excitation energy among the pigment molecules, until finally it is trapped with high efficiency by a limiting enzyme (a ‘photoenzyme’, as implied by Emerson and Arnold, 1932 b ), which is equivalent to what we now call reaction centre (RC), a term introduced by Duysens (1952) . Here, the primary charge separation (i.e. photochemistry) takes place (see e.g. Myers, 1994 ; Govindjee and Krogmann, 2004 ). Experimental evidence for excitation energy transfer (EET) between photosynthetic pigments was initially obtained by comparing action spectra of photosynthesis and of sensitized ChlF in green, brown and red algae (see chapters 10–12 in Rabinowitch and Govindjee, 1969 ). We now have much more detailed knowledge on the molecular mechanisms of electronic EET in antenna, as well as on exciton trapping by the RCs (e.g. Croce and van Amerongen, 2013 ; van Amerongen and Croce, 2013 ; Roden et al. , 2016 ; Mirkovic et al. , 2017 ; Chan et al. , 2018 ).

Taking things apart

Robert Hill (1937) found that the ‘light phase’ of photosynthesis can operate independently from the ‘dark phase’ (the carbon reaction phase), since isolated chloroplasts can evolve O 2 in the presence of artificial electron acceptors [this reaction is called the ‘Hill-reaction’ in honor of Robert (Robin) Hill], even in the absence of CO 2 . This concept led to a ‘modularization’ in the study of photosynthesis ( Nickelsen, 2016 ), since even if these two partial processes are interrelated, the tendency after 1940 was to investigate them separately. Note that Mehler (1951) had found that molecular oxygen is also a Hill electron acceptor, and this reaction, called the ‘Mehler reaction’, has been shown to play an important role in photoprotection of photosynthetic organisms ( Miyake, 2010 ).

The carbon reactions

The long-lived form of radioactive carbon, 14 C, was discovered by Samuel Ruben and Martin Kamen (1941) . This radioactive isotope was used to decipher the major pathway of CO 2 reduction by photosynthetic organisms, by Andrew Benson (who did most of the early pioneering work, using 14 C), Melvin Calvin, James A. Bassham and co-workers (see Calvin et al. , 1950 ; Calvin, 1989 ; Bassham, 2005 ; Benson, 2005 ). For example, they found that ribulose 1,5-bisphosphate (RuBP; a 5-C sugar) was the acceptor of CO 2 ; the first stable product of CO 2 reduction was 3-phosphoglyceraldehyde (G3P; a triose phosphate); and that there was a cycle to regenerate the RuBP. Melvin Calvin received the Nobel Prize in Chemistry in 1961 for these discoveries; we are of the opinion that Andrew Benson should have been a co-recepient.

Photophosphorylation

Daniel Arnon et al . (1954 a , b ) showed that isolated chloroplasts can produce ATP in light; in addition, they showed that intact isolated chloroplasts can even perform complete photosynthesis (i.e. CO 2 fixation). Furthermore, Allen et al. (1958) found that photophosphorylation can be ‘cyclical’ (i.e. ATP is produced when there is a cyclic ET, which was shown to involve cyclic electron flow around PSI via Cyt b 6 /f, CEF-PSI), or when there is ‘non-cyclic’ [i.e. during linear electron flow (LEF) from PSII to PSI) (see also Arnon, 1984 ; Tagawa et al. , 1963 ). A third pathway, labelled as ‘pseudo-cyclic photophosphorylation’, was also established, in which molecular oxygen plays the role of a terminal electron acceptor (i.e. the Mehler reaction; Mehler, 1951 ; Heber, 2002 ). Furthermore, a coupling mechanism between ATP synthesis and the ET, also in chloroplasts, was demonstrated by Dave Krogmann, Mordhay Avron and André Jagendorf (see Krogmann et al. , 1959 ). Note that the chloroplast coupling factor (CF1) for photophosphorylation, today known as ATP synthase, was discovered by Avron (1963) .

The two-light reaction and the two-pigment system concept

The idea of two light reactions and two types of PSs had its beginning in the 1943 experiments of Robert Emerson and Charleton Lewis on the ‘red drop’ in the action spectrum of the quantum yield of photosynthesis ( Emerson and Lewis, 1943 ) and in the 1957 ‘Emerson enhancement’ effect, that is when the rate of photosynthesis in two lights given together was higher than the sum of the rates of photosynthesis measured when the two lights were given separately ( Emerson et al. , 1957 ; also see: Govindjee and Rabinowitch, 1960 ); this discovery led to the well-known ‘Z’-scheme of photosynthesis ( Hill and Bendall, 1960 ; for the evolution of the Z-scheme, see Govindjee et al. , 2017 ). The very first Chl electron donors in the two PSs are P700 for PSI (identified also by an absorbance change around 705 nm; see Kok, 1956 ; Govindjee and Renger, 1993 ), and P680 in PSII, first suggested by Krey and Govindjee (1964) and shown to exist by Döring et al. (1969) . Key experiments proving the Z-scheme were provided by Duysens et al. (1961) on the red alga Porphyridium cruentum , who showed the antagonistic effect of light 1 and light 2 on the redox state of cytochrome (Cyt). (Here, light absorbed by PSI was ~680 nm, and that absorbed by PSII was ~562 nm.) Furthermore, based on flashing light experiments, Witt et al . (1961 a , b ) provided evidence for the kinetics and on the existence of other intermediate steps in the Z-scheme; details of the ET components involved in the photosynthetic electron transport chain (PETC) are given in Fig. 1 . However, of course, the physical confirmation for the existence and organization of the two PSs was the isolation and characterization via X-ray crystallography of the high-resolution spatial structure of PSII (e.g. Zouni et al. , 2001 ) and PSI (e.g. Jordan et al. , 2001 ).

Evidence from Chl a fluorescence measurements

Additional evidence for the two-pigment-system/two-light-reaction scheme in oxygenic photosynthesis was obtained by Govindjee et al. (1960) on Chlorella cells, using ChlF measurements. They showed an antagonistic effect of light 1 (i.e. predominantly absorbed by PSI) and light 2 (i.e. predominantly absorbed by PSII) on ChlF: addition of far-red light (light 1) to a shorter wavelength light (light 2) caused a decline (rather than an enhancement) of ChlF yield, compared to that produced by the two beams separately. As an explanation of this effect, Duysens and Sweers (1963) proposed that light 2 reduces a quencher Q, while light 1 oxidizes Q ‒ back to Q. The quencher theory of Duysens and Sweers was based not only on ChlF data published by Govindjee et al. (1960) , but also by Butler (1962) , who showed that variable fluorescence is mostly from PSII, and far-red light, absorbed by PSI, gives a smaller amount of PSI fluorescence. The quencher Q (named X-320, but now labelled Q A ) was identified using single turnover flashes, and has an absorption spectrum with maximal spectral changes in the UV, at 270 and 320 nm ( Stiehl and Witt, 1968 ). In several experimental studies ( Stiehl and Witt, 1969 ; van Gorkom, 1974 ; see also Witt, 2004 ), plastoquinone difference spectra in the near UV (300–350 nm) were similar to light-minus-dark spectra of the first plastoquinone acceptor of PSII (i.e. Q A −• − Q A ). According to Duysens and Sweers (1963) , ChlF is proportional to the fraction of the reduced quencher ([Q A − ]/[Q A ] total ; see a discussion in Stirbet and Govindjee, 2012 ; for other views see, Schansker et al ., 2011 , 2014 ; Magyar et al. , 2018 ). Later, it was shown that several non-photochemical quenching (NPQ) processes take place in parallel with the photochemical quenching (i.e. by Q A ) during the so-called slow (~10 min) phase of the ChlF transient, and the proportionality of the fluorescence yield with [Q A − ]/[Q A ] total , observed during the initial (<1 s) Chl fluorescence rise, is lost (see below the section On NPQ of the excited state of Chl). Real advances in the study of these NPQ processes became possible only after Ulrich Schreiber developed a pulse-amplitude modulated (PAM) fluorescence instrument (Walz, Effeltrich, Germany) that could be used on leaves in the presence or the absence of actinic light ( Schreiber, 1986 ; Schreiber et al. , 1986 ).

Vredenberg and Duysens (1963) observed that closure of RCs is accompanied by an increase in fluorescence yield of bacteriochlorophyll in Rhodospirillum rubrum , a purple anoxygenic photosynthetic bacterium, and concluded that several RCs share the same antenna. In an oxygenic photosynthesizer, the green alga Chlorella , Anne and Pierre Joliot ( Joliot and Joliot, 1964 ) measured the rate of steady-state oxygen evolution, and correlated it with the fraction of active PSIIs (see also Joliot and Joliot, 2003 ). Joliot and Joliot (1964) observed that both the oxygen yield and the fluorescence yield are related, in a hyperbolic manner, to the fraction of closed PSII centres; this suggested that there is an energetic connectivity within PSIIs, that is an excitation visiting a closed PSII (i.e. with Q A reduced) is redirected to another PSII. In this manner, the trapping cross-section of the open PSIIs increases as their neighbouring PSIIs become closed (see a review on PSII excitonic connectivity by Stirbet, 2013 ). Joliot and Joliot (1964) also derived theoretical equations describing the dependence of the ChlF yield (Φ  F ) and the photochemical yield (Φ  P ) on the fraction of open PSIIs, which included a connectivity parameter ( p ) for the probability of excitation energy transfer from a closed PSII to a neighbouring PSII (either closed or open). This was followed by publication of detailed papers on PSII excitonic connectivity by Paillotin (1976) , Strasser (1978) and Butler (1980) , the last two describing the process, using bipartite and tripartite PSII models of Butler and co-workers ( Butler and Kitajima, 1975 ; Butler and Strasser, 1977 ). Later, Lavergne and Trissl (1995) and Trissl and Lavergne (1995) extended the concept of PSII excitonic connectivity, using an exciton–radical pair equilibrium model. The latter is equivalent to the reversible radical pair (RRP) model of Schatz et al. (1988) ; it assumes rapid exciton equilibration between all PSII pigments, including P680, and describes primary photochemistry (charge separation, recombination and stabilization) leading to closed PSII RCs. The major feature of the RRP model is equilibrium , i.e. reversibility of charge separation, meaning fast charge separation followed by fast charge recombination, in both the open and the closed PSII centres (see Fig. 2 ).

Scheme showing the RRP (reversible radical pair) model and related reactions. The original RRP model is represented by the reactions on lines I and II, which are reactions occurring in an open PSII RC (when Q A is initially oxidized) and a closed PSII RC (when Q A is initially reduced), respectively. (L–P680)* denotes Chls in the light harvesting antenna of PSII (L) plus P680, which are in ultrafast excitation kinetic equilibrium, the asterisk (*) indicating the excited state. The rates constants are: k L , overall rate constant of antenna excitation; k 3 , overall rate constant of the excited state deactivation through heat dissipation and ChlF emission; k 1 o and k 1 c , rate constants of the primary charge separation in open and closed PSIIs, respectively; k -1 o and k -1 c , rate constants of the radiative (i.e. to the excited state) charge recombination between P680 + and Pheo − in open and closed PSIIs, respectively; k 2 o , rate constant of charge stabilization in an open PSII, i.e. the ET from Pheo ‒ to Q A ; k 2 c , rate constant of non-radiative (i.e. to the ground state) charge recombination between P680 + and Pheo ‒ in a closed PSII. The scheme presented here also includes excitation energy transfer (the energetic connectivity) between open and closed PSIIs (rate constant k UU ) and reversible reduction of P680 + by Y Z (rate constants k Pred and k Pox ), as well as the reduction of Y Z + by the manganese cluster of the oxygen-evolving complex (OEC; rate constant k Yred ), which produces an S-state transition from S i to S i+1 , where S i and S i+1 represent particular S-states. Modified from Lazár and Schansker (2009) .

ATP synthesis

Peter Mitchell (1961 a , b ) proposed a chemiosmotic theory for phosphorylation, which suggests that a ‘proton motive force’ ( pmf ), i.e. the electrochemical potential of protons, couples the ET reactions with ATP synthesis (from ADP and inorganic phosphate, P i ). Mitchell received the Nobel Prize in Chemistry in 1978 for this hypothesis. Later, Paul Boyer and John E. Walker received the Nobel Prize in Chemistry in 1997 for their work on the structure of F1 mitochondrial ATPase and the mechanism of ATP synthesis (see e.g. Boyer, 2002 ). Hind and Jagendorf (1963) (see also Jagendorf and Uribe, 1966 ) showed how photosynthetic cells convert light energy into free energy stored in the ATP molecule on the basis of the chemiosmotic theory, particularly the ΔpH component. The pmf has two components, one due to the trans-thylakoid electric potential difference (i.e. the membrane potential, ΔΨ), and the other due to the trans-thylakoid difference in proton concentration (ΔpH), which builds up during water splitting reactions on the lumen side of PSII, and the translocation of stroma protons to the lumen during PQ pool reduction by PSII, and by Cyt b 6 /f (including the Q-cycle; Mitchell, 1975 ) in relation to both the linear and the cyclic photosynthetic ET (see Fig. 1 , and a historical review by Jagendorf, 2002 ). We remind the readers that just as André Jagendorf’s work proved the importance of the ΔpH component (of pmf ) for ATP synthesis, Wolfgang Junge’s work proved the importance of ΔΨ in making ATP (see mini-review by Junge, 2004 ). However, a high ∆Ψ component of the pmf was also shown to affect the equilibrium of redox reactions within PSII, and has been linked to higher rates of PSII charge recombination in vivo , and subsequent photodamage due to increased production of singlet oxygen ( Davis et al. , 2016 ). On the other hand, low pH has been shown to inactivate oxygen evolution ( Schlodder and Meyer, 1987 ); furthermore, release of Ca 2+ from the oxygen evolving complex (OEC) has also been suggested to be the cause of this inactivation ( Ono and Inoue, 1988 ; Krieger and Weis, 1993 ). For recent research (and reviews) on ΔΨ and ΔpH across the TM see, Strand and Kramer (2014) , Kaňa and Govindjee (2016) , and Lyu and Lazár (2017 a , b ).

Oxygen evolution

The key experiments that preceded the discovery of the water splitting mechanism, leading to O 2 evolution and P680 + reduction in PSII, were done by Pierre Joliot and co-workers ( Joliot, 1965 ; Joliot et al. , 1969 ). Joliot et al. (1969) discovered period 4 oscillations in oxygen evolution in algal suspensions when they were exposed to a sequence of single turnover (ST) saturating light flashes. These results were explained by Bessel Kok et al. (1970) , who proposed a model (now known as Kok’s oxygen clock model, or the Kok–Joliot model to many), in which the formation of oxygen requires sequential accumulation of four positive charges on the OEC, which cycles through five redox states, labelled as S 0 , S 1 , S 2 , S 3 and S 4 (see Fig. 3 ). For the history of this discovery, see Renger and Govindjee (1993) and Joliot (2003) . The first evidence for the participation of Mn in the S-states was obtained by Chuck Dismukes and Yona Siderer (1980) , who obtained electron paramagnetic resonance (EPR) signals for the same. For a review on the functioning of the OEC, see Najafpour et al . (2012) . For a recent review on oxygen evolution, see Lubitz et al. (2019) .

Highly simplified scheme of Kok’s oxygen clock model; misses and double hits are not shown. S i (i = 0, 1, 2, 3, 4) represent the particular S-states of the manganese cluster of OEC. The S 4 -state is assumed to be kinetically indistinguishable from the S 0 -state. During an S-state transition, Y Z + (formed through PSII reactions) is reduced (with rate constants k 01 , k 12 , k 23 and k 30 ). Modified from Lazár and Schansker (2009) . For a review, including the involvement of manganese, see Najafpour et al. (2012) .

Mechanistic models for early events in photosynthesis

Bay and Pearlstein (1963) provided one of the first mathematical models of the exciton kinetics and trapping in a photosynthetic system; it was based on electronic excitation transfer, FRET (Förster resonance energy transfer; see Förster 1946 , 1948 ; also see a historical review by Clegg, 2006 ). According to this model, the electronic excitation energy moves in a so-called ‘random walk’, hopping from one Chl to another Chl in the antenna, until it is trapped by an RC, or is dissipated as heat or fluorescence (also see: Govindjee, 2004 ). Starting from FRET, other more complex and elegant theories have now been developed to characterize the exciton dynamics in antenna (e.g. Engel et al ., 2007 ; Ishizaki and Fleming, 2009 ; Clegg et al. , 2010 ; Fassioli et al. , 2014 ).

On ‘state transition’ for regulation of balanced excitation in the two photosystems

State transition, a light-adaptive phenomenon that optimizes photosynthesis by synchronizing the turnover rates of PSII RCs and of PSI RCs, when there is an excitation imbalance between their antenna, was discovered by Cecilia Bonaventura and Jack Myers (1969) in Chlorella and, independently, by Norio Murata (1969 a , b ) in the red alga Porphyridium cruentum and spinach chloroplasts. The equilibration of PSII and PSI activities takes place through adjustment of the relative size of their antenna: During a transition from ‘state 1’ to ‘state 2’, the absorption cross-section (CS) of PSII antenna (which provides information on the PSII-specific rates of light absorption and represents an ‘apparent’ measure of PSII antenna size in situ , in units of Å  2 per PSII centre; see Osmond et al. , 2017 ) decreases and that of PSI antenna increases, while the opposite occurs during transition from ‘state 2’ to ‘state 1’. The result is: the overall ChlF yield decreases in ‘state 2’ and increases in ‘state 1’, because, at room temperature, PSI has a much lower ChlF yield than PSII ( Butler, 1962 ). State transitions have been shown by John Allen and collaborators to be regulated by the redox state of the PQ pool ( Allen et al. , 1981 ; see Allen, 2002 ): the transition from ‘state 1’ to ‘state 2’ is triggered by the reduction of the PQ pool, and the transition from ‘state 2’ to ‘state 1’ is triggered by the oxidation of the PQ pool. In plants and algae, the controlling events take place at the Qp site of Cyt b 6 /f (i.e. the binding site of PQH 2 ; see Zito et al. , 1999 ), where the PQ redox-state is sensed, which triggers the activation or inactivation of a protein kinase ( Allen et al. , 1981 ): PQ pool reduction activates the protein kinase, and thus induces phosphorylation of mobile light harvesting complex (LHC) II, followed by its attachment to PSI antenna, while PQ pool oxidation inhibits the protein kinase, followed by dephosphorylation of the mobile LHCIIs by a phosphatase, and their re-attachment to PSII antenna (see Fig. 4 and reviews by Papageorgiou and Govindjee, 2011 ; Rochaix, 2014 ). For background on PSII, see Wydrzynski and Satoh (2005) , on PSI, see Golbeck (2006) , and on the Cyt b6f complex, see Cramer and Kallas (2016) . Note that extensive dynamic changes in the organization and structure of the TMs are associated with state transitions, which include PSII antenna dissociation after LHCII phosphorylation by Stt7/STN7 kinases, or association with PSII after dephosphorylation by PPHI/TAP38 phosphatases (see above, and Iwai et al. , 2010 ). However, new research suggests that these protein kinases and phosphatases can also affect the likelihood of cyclic ET around PSI (see Wood et al. , 2019 ). On the other hand, Pribil et al. (2018) have shown that the changes in the shape of grana stacks are mediated by the CURVATURE THYLAKOID1 (CURT1) protein complexes, which were shown to facilitate adjustments in membrane curvature at the grana margins in a dose-dependent manner.

Diagram of the mechanism of state transitions in plants and algae. In the diagram, the system is shown to be initially in ‘state 1’, with the absorption cross section (CS) of photosystem (PS) II being larger than that of PSI (it will have high Chl fluorescence yield because Chl in PSII is much more fluorescent than in PSI). During illumination, the plastoquinone (PQ) pool will be reduced by PSII because of higher absorption there. This is sensed by the Cyt b 6 /f (via its PQH 2 -oxidizing site, Q p ), and leads to activation of a kinase ( Stt7/STN7 ) and phosphorylation of the mobile light harvesting complexes of PSII (LHCII), which then associate with the PSI antenna. The reverse occurs when the system is in ‘state 2’ initially, with the absorption CS of PSI being larger than that of PSII. Here, oxidation of the PQ pool by PSI during illumination will be sensed by the Cyt b 6 /f, which leads to the inactivation of kinases, followed by de-phosphorylation of the mobile LHCIIs (by the phosphatases Pph1/TAB38 ) and their relocation to PSII. Abbreviations: A 0 and A 1 , a particular Chl a molecule and a vitamin K1 molecule, respectively; Fe-S, three non-haem (heme) iron–sulfur centres; Fd, ferredoxin; Q A and Q B , plastoquinone electron acceptors of PSII; NADP + and NADPH, nicotinamide adenine dinucleotide phosphate in oxidized and reduced state; P680 and P700, reaction centre chlorophylls/primary electron donors of PSII and PSI; PC, plastocyanin. Figure modified from Allen (2003) and Rochaix (2014) .

Two-electron gate on the electron acceptor side of PSII, and the requirement of bicarbonate

Bernadette Bouges-Bocquet (1973) and Bruno Velthuys and Jan Amesz (1974) independently discovered the two-electron gate (TEG) mechanism on the electron acceptor side of PSII in plants; it describes ET from Q A to Q B (see also Robinson and Crofts, 1983 ). As mentioned above, both Q A and Q B are PQs, but Q A is a one-electron acceptor, and is permanently bound to the D2 protein of PSII. By contrast, Q B is a two-electron acceptor that is bound to the D1 protein of PSII; it is strongly bound only when it is in Q B − -state, but is weakly bound in its fully oxidized state (Q B ), and very weakly bound when in the fully reduced state (Q B H 2 ). Following the primary charge separation: (1) Q A is reduced to Q A − (via pheophytin, Pheo; discovered by Vyacheslav Klimov et al. , 1977 ); (2) Q A − then reduces Q B to Q B − , and the latter remains tightly bound to D1; (3) after another light reaction, Q B − is then further reduced by Q A − , becoming fully reduced to Q B H 2 (PQH 2 ), after the addition of two protons; and finally (4) because Q B H 2 is loosely bound to D1, it is released in the membrane and replaced by another PQ molecule from the PQ pool (see Fig. 5 , and reviews discussing light-induced PQ pool reduction by PSII by Cardona et al. , 2012 ; Müh et al. , 2012 ). A bicarbonate ion has been shown to have a very important role in the functioning of the TEG and Q B H 2 formation ( Wydrzynski and Govindjee, 1975 ; see reviews by Govindjee and van Rensen, 1978 ; van Rensen, 2002 ; Shevela et al. , 2012 ). A similar TEG was also discovered in bacteria, independently by Colin Wraight and André Vermeglio (see Vermeglio, 2002 ), but there is no bicarbonate effect there (see Wang et al. , 1992 , and references therein). Note that the TEG model, the Kok model and the RRP model are important partial models that are used in more complex (or complete) models describing the photosynthetic ET (e.g. Nedbal et al. , 2009 ).

Scheme of the two-electron gate (TEG) model and related reactions. The two-electron gate mechanism, by which electrons are transferred from Q A to Q B , is represented by the reactions on line II. The rate constants are: k L , overall rate constant of Q A reduction; k AB1 and k AB2 , rate constants of ET from the reduced Q A to Q B and Q B ‒ , respectively; k BA1 and k BA2 , rate constants of backward ET from Q B ‒ and Q B 2‒ to Q A , respectively. The reactions above and below line II describe the reversible exchange of doubly reduced Q B (after its double protonation, which is implicitly assumed) with a PQ molecule from the PQ pool (rate constants k (B/PQ)exch and k (PQ/B)exch ); the reversible oxidation of the plastoquinol (rate constants k ox and k red ) is implicitly assumed to be the result of chlororespiration and cyclical electron flow around PSI. Modified from Lazár and Schansker (2009) .

On NPQ of the excited state of Chl

In general, NPQ processes can be defined as processes that decrease ChlF through mechanisms other than photochemical quenching (i.e. Q A quenching; e.g. Müller et al. , 2001 ; for a time line, see Papageorgiou and Govindjee, 2014 ). In this sense, the avoidance movement of chloroplasts in the leaf under high light conditions (i.e. qM; Dall’Osto et al. , 2014 ; Baránková et al. , 2016 ; Semer et al ., 2018 , 2019 ), the state 1 to state 2 transition (qT 12 ; see above), as well as the photoinhibition (qI), initiated by the photodamage of PSII ( Tyystjärvi et al. , 2005 ; Murata et al. , 2012 ; Tyystjärvi, 2013 ), would all be considered to be NPQ processes. However, according to Papageorgiou and Govindjee (2014) , it is preferable to consider as NPQ processes only those in which the excess energy accumulated as singlet excited Chl a ( 1 Chl a *) in PSII antenna is dissipated as heat (see Kitajima and Butler, 1975 ), such as the quickly reversible ‘high-energy non-photochemical quenching’ (qE), which develops in a few seconds and relaxes in 1–2 min (see Jahns and Holzwarth, 2012 ; and chapters in Demmig-Adams et al ., 2014 ), or other less clearly elucidated sustained forms of ChlF quenching processes (such as qH; Malnoë, 2018 ). This type of NPQ is induced by low lumen pH, being fully activated only after the pmf is established across the TM, when the TM is in a ‘high-energy’ state; it regulates the utilization of the light energy in PSII antenna in order to reduce photo-oxidative events that can damage the RCs. The exact relationship between lumen pH and NPQ is not fully understood; however, see discussions by Johnson (2011) and Zaks et al. (2013) . There are three main requirements for qE activation: (1) a trans-thylakoid ΔpH formed in light ( Wraight and Crofts, 1970 ; Briantais et al. , 1979 ); (2) the xanthophyll (VAZ) cycle, particularly the conversion of the carotenoid violaxanthin (V) to antheraxanthin (A) and zeaxanthin (Z) ( Yamamoto et al. , 1962 ; Yamamoto and Higashi, 1978 ); and (3) the PSII protein subunit S (PsbS) ( Li et al. , 2000 ; Brooks et al. , 2014 ). Barbara Demmig-Adams et al. (1989) (see also a historical review by Demmig-Adams, 2003 ) were the first to demonstrate that the extent of qE is proportional to the Z content of leaves; Demmig et al. (1987) further showed a correlation between Z and a form of qI manifested as a dark-sustained NPQ. Thus, they proposed that Z, which is derived from V in the xanthophyll cycle, is the link between the high energy state of the membrane and the heat dissipation of excess excitation energy of Chl a (see also Rees et al. , 1989 , 1992 ). In the xanthophyll cycle, the content of V decreases during illumination and is restored in darkness: Light ↝V⇄A⇄Z⇐ Dark . Violaxanthin deepoxidase (VDE) has a higher affinity for A than for V ( Yamamoto and Higashi 1978 ), and binds on the lumen side of the membrane, at pH ≈ 5.0 ( Hager and Holocher, 1994 ), which induces qE. Also, the NPQ kinetics was shown to depend on [Z], its induction being faster and its relaxation being slower when Z is present (see Johnson et al. , 2008 ). Adam Gilmore made an important contribution to the field, which included a successful collaboration with one of us (G) on the effects of intrathylakoid pH and VAZ cycle pigments on Chl a lifetime distributions and intensity in thylakoids ( Gilmore et al ., 1995 , 1998 ; Gilmore, 1997 ). On the other hand, the role of PsbS protein in qE is that of a pH sensor and quenching amplifier, as its amount in plant modulates the maximal qE level, but the underlying event is not yet fully understood ( Horton et al. , 2008 ; Holzwarth et al. , 2009 ; Brooks et al. , 2014 ). However, there is also evidence that qE can be induced in the absence of PsbS ( Johnson et al. , 2011 ), or even xanthophylls ( Johnson et al. , 2012 ), if the lumenal pH is sufficiently low (i.e. lower than the value assumed by the ‘moderate lumen pH paradigm’; see Kramer et al. , 1999 ). Finally, qE in algae is much more species-dependent than in plants. In unicellular green algae, or other algal groups (e.g. diatoms), the qE extent depends on the Light-Harvesting Complex Stress-Related (LHCSR) proteins ( Peers et al. , 2009 ). In most organisms, the LHCSR level is strongly light-dependent, and in some species, such as Chlamydomonas reinhardtii , acclimation to low light leads to very low NPQ levels ( Peers et al. , 2009 ).

Recently, Schreiber et al. (2019) have described a rapidly induced NPQ process during a pulse of high-light intensity in a dilute suspension of Chlorella vulgaris ; they called this process HIQ [high (light) intensity quenching]. The amplitude of the HIQ increases linearly with the effective rate of quantum absorption by PSII, reaching ~8 % of F M (i.e. the maximum Chl fluorescence measured in dark-adapted samples). This quenching rapidly relaxed after the pulse, and was shown to be caused by annihilation of 1 Chl* a by 3 Car* (excited state of a carotenoid in triplet state).

MODELLING CHL FLUORESCENCE INDUCTION IN PLANTS, ALGAE AND CYANOBACTERIA

ChlF emitted by plants and algae has little involvement in the process of photosynthesis, being one of the pathways in which excess excitation energy is dissipated by photosynthetic organisms. However, ChlFI kinetics is well recognized to have an intricate connection with many processes taking place during the conversion of light energy into a stable chemical form. Because it is a non-destructive measurement, although indirect, the ChlFI has numerous applications in the study of photosynthesis (see chapters in Papageorgiou and Govindjee, 2004 ), while its modelling is a straightforward way to verify various theories regarding different photosynthetic processes. Note that ChlFI in cyanobacteria is in part affected in different ways by the activity of the photosynthetic apparatus than in plants and algae, and this is due to their structural differences (see Stirbet et al. , 2019 ), but its modelling is not described in this review.

The ChlFI curve has been labeled O-J-I-P-S-(M)-T, where O-J-I-P represents the first fast (<1 s) phase, also known as the fast ChlF rise, and P-S-(M)-T the slower (5–10 min) phase (see Fig. 6 , and a review by Govindjee, 1995 ). Level O (origin) is the first measured minimum fluorescence level; J and I are intermediate inflections; P is the peak; S is the semi-steady state; M is a maximum, which, in plants, at room temperature is often seen only at low light intensities, but has been observed in Arabidopsis thaliana under low (freezing) temperature conditions ( Mishra et al. , 2019 ); and T is a terminal steady state level.

Chlorophyll a fluorescence induction curves measured in leaves of 10-d-old barley ( Hordeum vulgare L.) plants kept in darkness for 20 min before the measurement, shown on a logarithmic time scale (A), and on a linear time scale (B); a.u., arbitrary units. The O, J, I, P, S, M and T steps marked in the figure represent: O, the origin (minimum fluorescence F O ); J and I, intermediary fluorescence levels at 2 and 30 ms (F J and F I ); P, the peak (F P ); S, a semi-steady state level; M, a maximum; and T, the terminal steady state. Measurements were made under continuous red (650 nm) light of 2500 μmol photons m –2 s –1 with a Plant Efficiency Analyser (Hansatech, UK). Modified from Stirbet et al. (2018) .

The fast phase was labelled OIDP ( Munday and Govindjee, 1969 ), as OI 1 I 2 P ( Schreiber, 1986 ) and then OJIP ( Strasser and Govindjee, 1991 ); the O-J-I-P curves are measured only under a high intensity of excitation light. At low light the J step is missing, so that only an O-I-P curve is observed ( Strasser et al. , 1995 ; Tomek et al. , 2001 ). Below, we briefly discuss several models for the O-J-I-P fluorescence rise, as well as for the entire O-J-I-P-S-(M)-T transient or just the slow P-S-(M)-T phase (see also reviews by Lazár, 1999 ; Lazár and Schansker, 2009 ; Stirbet et al. , 2014 ).

Modelling strategy, definition of the Chl fluorescence signal, and some selected partial models of PSII

Mathematical modelling is an essential part of modern biology and can have several purposes. In any experimental study, the measured data provide information about how the explored system works, and based on these, we formulate hypotheses about how the explored system is functioning. By converting the hypotheses into a mathematical model, running the model and comparing the calculated results with experimental data, we can judge if the model describes the data well or not. In this case, the structure of the model (i.e. the hypotheses as such) and also the values of model parameters can cause agreement/disagreement between the results obtained with the model and the measured data. Regarding the values of the model parameters, we can run the model with fixed parameter values, taken from the literature, or we can fit the values to get the best agreement between the model results and experimental data. However, in the latter case, we may find a perfect agreement, but only by using unrealistic values of the model parameters (based on the literature), which usually rules out the correctness of the model. On the other hand, when values of system variables are not known from the litrrature and/or are not directly accessible from experiments, the fitting can provide this information, assuming the model structure is correct.

Furthermore, a so-called metabolic control analysis (MCA) can be performed, which quantifies the extent to which a given process (hypothesis) affects a given result (for a review see Visser and Heijnen, 2002 ). Sometimes, this quantification can be made easy only by using modelling rather than by doing experiments, because it is not always possible to infer the desired (initial) state of the experimental system, or to experimentally modify the parameters of the system, as needed to perform MCA.

Finally, if we have a robust model that describes well the various measured data, we can modify the model parameters and track the results, or in other words, we can perform ‘experiments’ without measuring anything – i.e. biological experiments in silico . These in silico experiments are very useful in making predictions that allow us to determine the role of model parameters, or to design experiments to prove or refute certain predictions. Concerning the modelling of ChlFI discussed below, it is important to keep in mind that a qualitative agreement between experiment and theory is a useful goal. The ChlFI is a manifestation of a very complex biological system, and therefore describing it correctly and comprehensively is difficult – this is quite different from modelling technical systems, which can be described correctly, and where a quantitative agreement between experiments and theory is strictly required.

Several approaches have been used for the formulation of a fast ChlF rise model, or for the entire ChlFI. The variable ChlF is emitted mostly from PSII (reviewed by Krause and Weis, 1991 ; Dau, 1994 ; Govindjee, 1995 ; Lazár, 1999 , 2006 ; Stirbet and Govindjee, 2011 , 2012 ). The basic strategy for modelling the fast ChlF rise has been to first use a model of the ET reactions occurring only in PSII, but then later add ET reactions beyond PSII, especially for the modelling of the entire ChlFI. The formulation of a ChlFI model also depends on the specific ET components considered, and then, on the way, the variable ChlF emitted during the transient is defined. The basic approach in the definition of the variable ChlF is based on the early work of Duysens and Sweers (1963) and the quencher theory defined there, later identified to be due to Q A (see above the subsection Evidence from Chl a fluorescence measurements). According to this theory, if Q A is oxidized, ChlF is low and if Q A is reduced, ChlF is high, and the variable ChlF is proportional to the fraction of Q A − . Moreover, the energetic PSII connectivity (mentioned earlier) can be also considered in modelling the variable ChlF.

Taken together, the most basic approach used to model the fast ChlF rise has been to define a PSII model that describes the redox changes of Q A during reduction of the PQ pool. These redox changes are modulated by Q B , the second PQ electron acceptor of PSII, which unlike Q A is a two-electron PQ acceptor of the PSII RC; originally, it came from the PQ pool, transiently binding to the Q B -site. The reduction of Q B to plastoquinol is described by the TEG model ( Bouges-Bocquet, 1973 ; Velthuys and Amesz, 1974 ), which is the fundamental partial model used in ChlFI modelling (see discussion earlier, and Fig. 5 ). Thus, one group of models describing the fast ChlF rise, including the first ever models (see below the subsection Modelling the fast Chl fluorescence rise by using only models of PSII reactions), are based on the TEG model. The charge stabilization on Q A (i.e. the reduction of Q A by Pheo − ) means that the PSII RC is closed and thus the ChlF is high. However, this charge stabilization is preceded by the formation of P680 + Pheo − (see Fig. 2 ). Thus, when either P680 + and/or Pheo − are present, the PSII RC is closed, but the ChlF decreases in their presence, as both P680 + and Pheo − are quenchers of ChlF (for P680 + , see Okayama and Butler, 1972 ; Shinkarev and Govindjee, 1993 ; Steffen et al ., 2001 , 2005 ; for Pheo − , see Klimov et al. , 1977 ). Quenching of Chl fluorescence by P680 + accumulation has been considered in several models of the fast ChlF rise (e.g. Lazár, 2003 ; Laisk and Oja, 2018 ). Accumulation of reduced Pheo was shown to take place only under illumination at 200–220 K ( Klimov et al. , 1980 ; Breton, 1982 ). Nonetheless, Vredenberg (2000 , 2008 , 2011 ) has assumed, in his O-J-I-P model, not only that Pheo ‒ accumulates at room temperature, but also that ChlF is higher when both Q A and Pheo are reduced than when only Q A is reduced. Strasser and Stirbet (2001) have also simulated and fitted a fast ChlF rise with a simple TEG-based model, but considering three different PSII redox states that contribute to the fluorescence signal: (1) with Q A ‒ ; (2) with Pheo ‒ ; and (3) with PheoQ A ‒ and Pheo ‒ Q A ‒ ; ChlF in the presence of Pheo ‒ Q A ‒ was considered to be two-fold larger than that when PheoQ A ‒ was present. The experimental O-J-I-P curve was fitted quite well by all three models, but the parameters of the models and the kinetics of the PSII redox states were different in each case. Thus, overparametrized models cannot be validated by fitting one experimental curve, and other approaches must be also used to reach firm conclusions. These can be, for example, measurements of the kinetics of the redox states of PSII during the ChlF transient, as well as through in silico experiments, in which the basic parameters of the model are kept constant.

On the other hand, ChlF yield during ChlFI has also been defined by using ratios of the rate constants related to fluorescence emission, heat dissipation and photochemistry ( Goltsev and Yordanov, 1997 ; Laisk et al. , 2006 ; Ebenhöh et al. , 2014 ; Stirbet and Govindjee, 2016 ). A better estimation of the ChlF signal, in models used to simulate the ChlFI, is obtained by considering fluorescence as a radiative deactivation of the singlet excited state of Chl (i.e. 1 Chl*); this was used in the modelling of the fast ChlF rise by Baake and Schlöder (1992) (see also Lebedeva et al. , 2002 ; Lazár, 2003 ; Belyaeva, 2004 ). If the ChlF signal is defined by the redox states of Q A or by the concentration of 1 Chl*, the model must include these entities. The reactions among the excited states of Chl a in PSII antenna that include P680 and Pheo, besides Q A , have been described by the RRP model of Schatz et al. (1988) ; it was based on measurements of ChlF decay in the picosecond range after excitation by a short laser pulse. In the RRP model, charge separation between P680 and Pheo is reversible and is followed by charge stabilization (ET from Pheo − to Q A ) in the open PSII RCs, and by non-radiative charge recombination (to the ground state) in closed PSII RCs (see Fig. 2 ). Thus, the RRP model is the second fundamental partial model, in addition to the TEG model, which must be considered in modelling the ChlFI.

If the formation of P680 + is considered in a model, then the reduction of P680 + must be also included, i.e. reactions on the donor side of PSII, as well as the recombination reactions between P680 + and Pheo ‒ or Q A ‒ . The P680 + is reduced by tyrosine 161 (i.e. Y Z ; Debus et al. , 1988 ), which is, in turn, reduced by OEC. Electrons are donated to Y Z + , by OEC, as it undergoes the S-state cycle ( Kok et al. , 1970 ; Fig. 3 ). Kok’s model of OEC is the third fundamental partial model for the description of PSII function. This model also includes parameters called ‘misses’ (when the light flash used does not lead to an S-state advancement) and ‘double hits’ (when the flash leads to an advancement by two S-states). Kok’s model has been modified by Jablonsky and Lazar (2008) by including the so-called intermediate S-states, which enable omission of the misses and double hits in the model.

Modelling of the fast Chl fluorescence rise measured after treatment with a herbicide

Because many photosynthetic processes affect ChlFI, herbicides that interrupt the ET from Q A to Q B have been used to simplify the observed curves. Note that many different herbicides are employed to kill weeds, and this can be achieved by using different substances that operate through various other mechanisms, but here we discuss only those that block the Q B -pocket of PSII. DCMU (3-(3′,4′-dichlorophenyl)-1,1-dimethylurea) is a herbicide that has been frequently used in such studies; it binds to the Q B -pocket, blocking ET beyond PSII (e.g. Oettmeier et al. , 1980 ), which leads to a faster closure of PSII RCs during illumination and to a faster accumulation of Q A ‒ . Binding of DCMU at the Q B -pocket results in a faster sigmoidal ChlF rise to its maximal value (F M ), which is reached approximately at the J step (~2 ms) of the ChlF rise, measured (under saturating light) with an untreated sample. The gradual binding of DCMU to the Q B -pocket of PSII, and thus the gradual closure of PSII, as reflected in changes in the O-J-I-P transient, was modelled by Lazár et al. (1998) . Here, the diffusion of DCMU was described using Fick’s laws, and the reaction of DCMU at the Q B -binding site of PSII, by second-order kinetics. From this work, Lazár et al. (1998) provided values of the diffusion coefficient of DCMU, and the second-order rate constant of DCMU binding to the Q B -pocket of PSII.

The sigmoidal shape of the fast ChlF rise measured with DCMU has been suggested to reflect energetic connectivity ( p ) between the PSII units ( Joliot and Joliot, 1964 ; also see above for discussion). This concept is tightly connected with a type of PSII heterogeneity, namely PSII α/β antenna heterogeneity ( Melis and Homann, 1975 ). The PSIIα units, the main PSIIs, have a large and energetically connected light-harvesting antenna. The size of the antenna is reflected in the rate constant of the fast ChlF rise, measured with DCMU, and PSII connectivity is reflected in the value of the parameter p ; the PSIIβ units have smaller antenna and a lower energetic connectivity. Several different procedures have been used to obtain quantitative information on this PSII heterogeneity (see Hsu et al. , 1989 ). To increase the reliability and accuracy in the determination of PSII antenna heterogeneity, Lazár et al. (2001) have fitted the values of rate constants, the parameter p and the fractions of particular PSII types to several curves of fast ChlF rise in the presence of DCMU, measured at different light intensities, by using just one fitting procedure; results from this work were in good agreement with those in the literature.

The fast ChlF rise measured with DCMU has also been explored using the RRP model by Trissl et al. (1993) , Lavergne and Trissl (1995) , and Trissl and Lavergne (1995) , with PSII energetic connectivity included. The RRP model has been further improved by Lazár and Pospíšil (1999) by the addition of P680 + reduction step(s) on the (electron) donor side of PSII; for this, they had used the fast ChlF rise in the presence of DCMU measured at high temperatures. Decreases in PSII energetic connectivity and in the rate of P680 + reduction by Y Z were suggested to occur in the photosynthetic samples kept at high temperatures (e.g. 47 °C for 5 min; Guissé et al. , 1995 ; Srivastava et al. , 1997 ), but these conclusions were based on results on samples, without DCMU. By contrast, Lazár and Pospíšil (1999) have simulated the fast ChlF rise, in the presence of DCMU, at high temperatures by omitting PSII energetic connectivity, and by decreasing the rate constants related to the electron donation to P680 + .

To study photoinhibition in DCMU-treated samples, Vavilin et al. (1998) and Lazár et al. (2005) have simulated fast ChlF rise curves by using the RRP model. Lazár et al. (2005) further extended the RRP model by considering a possible protective function of Cyt b 559 against photoinhibition, as proposed by Thompson and Brudvig (1988) and by Nedbal et al. (1992) . Cyt b 559 is indeed reduced by Pheo − , which then donates electrons to P680 + , involving a CEF around PSII. However, an argument against such an ET may be in the crystal structure of PSII (e.g. Zouni et al. , 2001 ; Kamiya and Shen, 2003 ), which shows that the distance from the Pheo in the active D1 branch of PSII and the Cyt b 559 is too long (~45 Å) to allow an ET between them. However, the distance between Pheo in the inactive D2 branch of PSII and the Cyt b 559 is shorter (22 Å), and ET by tunnelling has been reported for such distances ( Page et al. , 1999 ). Thus, the Pheo in the model of Lazár et al. (2005) could be Pheo in the D2 branch of PSII.

Modelling the fast Chl fluorescence rise by using only models of PSII reactions

Mathematical analyses of the fast ChlF rise were published in the 1960s ( Malkin and Kok, 1966 ; Malkin, 1966 ; Munday and Govindjee 1969 ). Munday and Govindjee (1969) measured the O-I-D-P (where D is for a dip) ChlF rise curve in Chlorella pyrenoidosa and related it successfully to variations in the fraction of reduced Q A . In their paper, the dip was analysed by studying the transient oxidation of Q A − by PSI.

In all likelihood, the first ‘real’ model of the fast ChlF rise [i.e. a scheme of ET reactions and a related set of coupled ordinary differential equations (ODEs)] was that of Holzapfel and Bauer (1975) . This model was rather complex: it described the complete ET chain in the TM, including the formation of NADPH and ATP. On the other hand, some details of the photosynthetic ET were not included in the model, due to limited knowledge of the photosynthesis process at that time. In this model, the ChlF was assumed to be proportional to the amount of Q A − . Holzapfel and Bauer (1975) were able to qualitatively simulate the rate of oxygen evolution at different light intensities, the fast ChlF rise of control samples, and of those treated with DCMU and/or 2,5-dibromo-3-methyl-6-isopropyl-p-benzoquinone (DBMIB, which blocks the electron flow between PQ and Cyt b 6 /f; cf. Trebst and Reimer, 1973 ), as well as of samples that were dark-adapted under anaerobic conditions. This model was further used by Holzapfel (1978) , where the effect of ΔΨ across the TM was included. It is unclear why these models were missed by others. However, several models on the fast O-I-P ChlF rise, measured using light intensities lower than 1200 µmol photons m −2 s −1 , are available ( Renger and Schulze, 1985 ; Hsu, 1992 a , b ; Goltsev and Yordanov, 1997 ; Tomek et al. , 2003 ); these models were based on the TEG model, where ChlF signal was assumed to be proportional to the amount of reduced Q A (for an exception, see Goltsev and Yotdanov, 1997). Tomek et al. (2003) have further used the amplitude of the I step to estimate the fraction of ‘Q B -non-reducing centres’ (i.e. PSIIs which cannot reduce Q B ).

Different TEG models, and PSII redox states with reduced Q A to calculate the ChlF signal, were also used in modelling the O-J-I-P ChlF rise measured under saturating light (~3000 µmol photons m −2 s −1 ; Stirbet and Strasser, 1995 , 1996 ; Lazár et al. , 1997 ; Stirbet et al. , 1998 , 2001 ; Strasser and Stirbet, 2001 ; Tomek et al. , 2001 ; Sušila et al. , 2004 ). In these studies, the authors mainly showed how selected parameters of the models (e.g. initial concentrations and values of the rate constants) affect the shape of the O-J-I-P curves. However, Stirbet and Strasser (1996) showed that consideration of second-order kinetics for the reactions between Q A and Q B in the TEG model gives different simulated O-J-I-P curves compared to those obtained in the simulation where first-order kinetics is used. Strasser and Stirbet (1998) have also simulated O-J-I-P ChlF transients with a TEG model, by taking into account the heterogeneity of the PSII population in relation to PSII antenna, PSII energetic connectivity, and the ability of PSII to reduce Q B (‘Q B -reducing’ vs. ‘Q B -non-reducing’ RCs).

Sušila et al. (2004) considered a hypothetical sample divided into ten layers of the same thickness, and calculated the light intensity in each layer, based on the Lambert–Beer attenuation law, in order to determine the light gradient inside the sample. They then simulated the fast ChlF rise curve for each layer, by using the same model as in Lazár et al. (1997) and Tomek et al. (2001) , and summed the ChlF signal from all the layers to obtain the total ChlF signal. Their results showed that the light gradient inside a sample can significantly affect the shape of the fast ChlF transient. We note that in all the above models for the O-J-I-P ChlF rise, with the exception of those used by Stirbet et al . (1998 , 2001 ) and Strasser and Stirbet (1998, 2001 ), the presence of an unknown component X that accepts electrons from the Q B ‒ was assumed to exist.

Guo and Tan (2011) have extended the TEG model by taking in account the existence of a light-harvesting antenna system. Later, Feng et al. (2018) extended the above model by including the pH-dependent NPQ process, which allows the fitting of the decrease of the ChlF signal from the peak ‘P’ to ‘S’ and/or the ‘T’ level. To fit the O-J-I-P ChlF curves measured at different temperatures (20, 25, 30 °C), the rate constants in the model of Guo and Tan (2011) were assumed to be dependent on the temperature according to the Arrhenius law ( Xia et al. , 2018 ). Because the formation of 1 Chl* during illumination was included in the models used in all three studies above, the ChlF signal was defined as radiative deactivation of 1 Chl* in the PSII antenna.

In some of the models just mentioned, the function of the PSII donor side was implicitly included. By contrast, in the models of Stirbet et al . (1998 , 2001 ), Chernev et al. (2006) , Lazár and Jablonský (2009) , and Laisk and Oja (2018) , the function of the PSII donor side was included explicitly, and that too in combination with the TEG model. Stirbet et al . (1998 , 2001 ) not only included the S-states of OEC, but also the PSII energetic connectivity, and the quenching of the ChlF signal by P680 + and by the oxidized PQ molecules. Stirbet et al . (1998 , 2001 ) then simulated (or fitted) the O-J-I-P ChlF transient by defining the ChlF signal to be proportional to the amount of reduced Q A , and by considering different initial fractions of Q B and Q B ‒ , or of the S 1 and S 0 states of OEC. In the model of Lazár and Jablonský (2009) , all the S-state transitions of OEC were taken into account, as well as the redox states of P680 + that were explicitly considered in combination with the TEG model, which was then used for simulation of the O-J-I-P ChlF transient. In their study, the effect on the simulated fast ChlF curve was described by using (1) first- or second-order reaction kinetics for electron donation from the OEC to P680 + ; (2) one second-order reaction or two subsequent reactions for the Q B 2‒ /PQ exchange; and (3) all possible reactions between the ET components, or of fewer ‘logical’ reactions.

Other models used for simulation of the fast ChlF rise are those that include, in addition to the TEG model, the description of the fast events in the PSII RC (i.e. charge separation, recombination and stabilization) described by the RRP model. Models by Baake and Schlőder (1992) and Belyaeva et al. (2011) belong to this group, where reduction of P680 + by Y Z (via OEC) was implicitly included. Other authors ( Lazár, 2003 ; Zhu et al. , 2005 ; Matsuoka et al. , 2015 ) have explicitly included Y Z and the S-state transitions of OEC.

Lazár (2003) provided a detailed analysis of how values of particular rate constants and initial conditions affect the simulated fast O-J-I-P ChlF curves. An important aspect of the ChlFI curves analysed by simulations in this work is the origin of the minimal ChlF level (F O ) which is the initial ChlF, when all PSII RCs have all Q A in the oxidized state; F O originates from the radiative deactivation of the excited PSII state [(antenna-P680)*PheoQ A Q B ; see Fig. 7 ]. Interestingly, although the model of Lazár (2003) is one of the most detailed models of PSII reactions (consisting of a set of 44 coupled ODEs), yet it was not able to simulate typical O-J-I-P ChlF transients, as the ChlF signal increased from the J step to a maximum, which was reached at the I step position in the experimental curves ( Fig. 7 ).

Simulations of the O-J-I(=P) ChlF rise (see text) and of the model forms of photosystem (PS) II in the excited state, which mainly contribute to the (chlorophyll a ) fluorescence transient, are shown on a logarithmic time scale. Abbreviations: (L-P)*, the excited state of the PSII antenna, which is equilibrated among all light harvesting Chls, including P680; Ph, pheophytin; A and B, the first and second plastoquinone acceptors of PSII (Q A and Q B ). The time course of the PSII model form (L-P)*PhAB at the beginning of the transient, which represents excited open PSII RCs (i.e. with oxidized Q A ), is at the origin of the minimal ChlF, F O . Modified from Lazár (2003) .

The inability to simulate the proper time-dependence of the ChlF signal by the detailed model based only on PSII redox states is one of the arguments that a proper model for the O-J-I-P ChlF rise should also describe ET reactions occurring beyond the PQ pool, as already inferred by Munday and Govindjee (1969) and later confirmed in other studies (i.e. Schreiber et al. , 1989 ; Schansker et al ., 2003 , 2005 ).

Modelling the fast Chl a fluorescence rise with models that consider electron transport in and around the TM

The last group of models used in simulation of the O-J-I-P ChlF transients are those that include ET reactions occurring in and around the TM ( Lebedeva et al. , 2002 ; Kroon and Thoms, 2006 ; Lazár, 2009 ; Makarov et al. , 2012 ; Belyaeva et al ., 2016 , 2019 ), or even the metabolic reactions in the stroma (e.g. the Calvin–Benson cycle; see Laisk et al ., 2006 , 2009 ; Zhu et al. , 2013 ). Given the all-inclusive nature of these models, some of them were also used for modelling of the the entire ChlFI (see below). A diagram of the reactions considered in the model proposed by Lazár (2009) is shown in Fig. 8 . This model consists of a set of 42 coupled ODEs, and the ChlF emission is defined as being proportional to the amount of reduced Q A . In addition, the ΔA 820 signal, describing redox changes of P700 and plastocyanin (PC), was also modelled. To show that the ET reactions beyond the PQ pool affect the shape of the simulated fast ChlF transients, Lazár (2009) also analysed in silico the effects of DBMIB and MV [methylviologen, which accepts electrons from both the iron–sulfur cluster of PSI and ferredoxin (Fd); Sétif, 2015 ]. The shapes of the simulated fast ChlF transients and of ΔA 820 signal were qualitatively in agreement with the experimental curves (see Fig. 8 ). This model is also a part of e-photosynthesis.org ( Šafránek et al. , 2011 ), which is a web-based platform for modelling complex photosynthetic processes.

Diagram of the ET reactions used in the model of Lazár (2009) (A), the O-J-I-P ChlF transients measured on control (= untreated) leaves, as well as on leaves treated with 2,5-dibromo-3-methyl-6-isopropyl-p-benzoquinone (DBMIB, which inhibits ET in the cytochrome b 6 /f, see A) or with methyl-viologen (MV, which accepts electrons from the iron–sulfur cluster of PSI and ferredoxin, Fd, see A) (B), and the respective curves simulated with the model (C), the Δ A 820 curves measured under the same conditions (D), and the respective curves simulated by the model (E). The curves are shown on a logarithmic time scale. Abbreviations: S i , the S-states of the oxygen-evolving complex (OEC); f, b L , b H … c, cytochrome f, low/potential cytochrome b 6 , and high-potential cytochrome b 6 in kinetic equilibrium with the haem c of cytochrome b 6 /f complex; PC, plastocyanin. Modified from Lazár (2009) .

In all the models mentioned above, the variable ChlF signal was assumed to originate from the PSII antenna. The problem with direct measurement of the variable ChlF from PSI in vivo (not from isolated PSI complexes) is that it overlaps spectrally with the PSII ChlF. However, some experimental results, presented in the literature (see Lazár, 2013 ), show the existence of a variable ChlF originating in PSI, at least under certain conditions. Lazár (2013) presented a very detailed model of the ET reactions in PSI (i.e. a set of 106 coupled ODEs), and simulated fast ChlF transients originating only from PSI. The ChlF signal was defined as the radiative deactivation of 1 Chl*. PSI was further shown to emit variable ChlF, and its contribution to the total maximal variable ChlF signal from the two PSI and PSII was ~8–17 % ( Lazár, 2013 ). Future studies are needed to quantitatively assess these findings.

Rule-based modelling of the fast Chl fluorescence rise

All the models of the fast ChlF rise discussed thus far have described the photosynthetic processes by using sets of coupled ODEs. Each ODE was used to describe the time-change of a particular PSII redox form (i.e. state variable) of the model. This approach is deterministic, because in any run of the model, the same solution is obtained.

If too many state variables (coupled ODEs) are considered in a model, it becomes difficult to obtain model results, due to high requirements of computational time and hardware; this is because all ODEs must be solved simultaneously at each time of system evolution. While there are ways (specific for each model) to decrease the number of equations, this problem can be better overcome by employing a rule-based modelling approach, where rules are defined that are equivalent to the particular ET reactions. Furthermore, random numbers are generated, and these determine (using internal decision process) which rules should be considered in each particular step of the model run, i.e. in each ‘evolvement’ of the system in time. Thus, a time course of the system behaviour would be described by a sequence of particular rules, which are slightly different in different model runs, i.e. small differences between solutions are obtained after different runs of the model. Thus, this approach would be stochastic (i.e. random). The rule-based stochastic approach by means of kinetic Monte Carlo simulations has been applied for modelling of the O-J-I-P ChlF transient by Xin et al. (2013) , Guo and Tan (2014) , Maslakov et al. (2016) and Antal et al. (2018) . However, in all these cases, the shapes of simulated ChlFI curves were the same (except for the noise) as when using the deterministic approach. Similarly, the O-J-I-P curve was also simulated using stochastic π-calculus ( Tokarčík, 2012 ) and rule-based language-simplified Kappa ( Nižnan, 2014 ). Much further work is needed to obtain conclusive results from this approach.

Modelling the slow PS(M)T phase of the Chl a fluorescence induction curve

The nomenclature of P-S-(M)-T for the slow phase of the ChlFI was first used by Papageorgiou and Govindjee (1968 a , b ). Compared with the fast ChlF rise, this phase is much more complex and less well understood, as the fluorescence yield is modulated by an increasing number of processes triggered during this phase, besides the photochemical quenching by Q A (see above), such as: (1) the NPQ of excited singlet 1 Chl* a in PSII antenna, induced by low pH in the lumen (i.e. the high-energy NPQ qE; Horton et al. , 1996 ; Rochaix, 2014 ); (2) state transitions (i.e. qT 12 or qT 21 ) that regulate the absorption CS of PSI and PSII (with ‘state 1’ being more fluorescent than ‘state 2’; see Papageorgiou and Govindjee, 2011 , 2014 ); (3) photoinactivation processes (qI) due to the photodamage of PSII (e.g. Tyystjärvi, 2013 ); (4) cyclic electron flow around PSI (e.g. Miyake, 2010 ; Buchert et al. , 2018 ), chlororespiration ( Bennoun, 1982 ) and electron flow to molecular oxygen ( Mehler, 1951 ; Asada, 1999 ); as well as (5) activation of the Calvin–Benson cycle. Therefore, besides the partial models necessary for modelling the fast ChlF rise discussed in the previous section (e.g. RRP, Kok’s oxygen clock, TEG, the Q-cycle at the Cyt b 6 /f complex), the processes listed above are fundamental for modelling the whole ChlFI; however, qT and qI, with a few exceptions, have been usually neglected by most authors.

Laisk et al. (1997) were the first to model the qE process, which they used later to simulate successfully the slow PS(M)T phase of ChlFI ( Laisk et al. , 2006 ). This qE model was later adapted by Zhu et al. (2013) for C 3 photosynthesis, but the descending M-T phase is missing in their simulated ChlFI curve. Note that these two papers were centred on the detailed description of metabolic reactions.

The transmembrane pmf , i.e. both ΔpH and ΔΨ, was modelled by Lebedeva et al. (2002) , which predicts that a sufficiently large transmembrane electric potential (positive inside) would slow the rate of PQH 2 oxidation by the Cyt b 6 /f (the so-called backpressure effect; see van Kooten et al. , 1986 ), and consequently the ET rate from PSII to PSI (see also comments in Stirbet et al. , 2014 ). This pmf model was further used by, for example, Rubin et al. (2009) and Belyaeva et al . (2016 , 2019 ) to model the complete ChlFI curve, with a TM model that describes the electron/proton transfer reactions between membrane protein complexes: PSII, PSI, Cyt b 6 /f, mobile PQ pool in the TM, PC in lumen and Fd in stroma, CEF-PSI, and reduction of NADP + via Fd-NADP + -oxidoreductase (FNR) (see Fig. 1 ). Belyaeva et al. (2016) used the TM model to fit both ChlFI data and P700 redox changes (Δ A 810 ), measured in pea leaves, from 20 μs to 20 s. Belyaeva et al. (2019) added to their earlier TM model partial models for the light-induced activation of FNR and qE, with the goal to simulate the ChlFI and Δ A 810 kinetics on the time scale from 40 μs to 30 s. Their results showed that the time-dependent rate constants changed substantially upon the release of ET on the (electron) acceptor side of PSI and during qE induction. Belyaeva et al. (2019) also discussed differences between the parameters related to FNR activation and qE induction evaluated for dark-adapted and pre-illuminated pea leaves, and also analysed the transition between CEF-PSI and LEF modes.

Because the photosynthetic organisms are exposed continuously to fluctuations in the environmental conditions, the activity of their photosynthetic apparatus is dynamic, being feedback-regulated by several processes that reduce imbalances between the rate of energy trapping by the PSs and CO 2 assimilation. These serve to optimize the photosynthetic ET to, for example, light-induced pH changes in the lumen and in the stroma (see Tikhonov, 2013 ; Rochaix, 2014 ; Strand and Kramer, 2014 ), or changes in the PQ pool redox state, as modulated by variations in light irradiance, ATP/ADP ratio and the ambient CO 2 level ( Rochaix, 2014 , 2016 ). Light-induced acidification of the lumen slows down PQH 2 oxidation by the Cyt b 6 /f (the backpressure effect), and also decreases PSII activity by inducing excitonic energy dissipation as heat in PSII antenna through qE ( Jahns and Holzwarth, 2012 ; Rochaix, 2014 , 2016 ). This reduces the excess of input energy in the system, and thus oxidative damage ( Nishiyama et al. , 2006 ), which occurs when singlet excited 1 Chl* forms triplet-state Chl ( 3 Chl) ( Durrant et al. , 1990 ) that interacts with ground state oxygen, generating ‘noxious’ reactive oxygen species (ROS), such as singlet oxygen ( 1 O 2 ). Furthermore, the alkalization of stroma activates the Calvin–Benson cycle, which stimulates the consumption of NADPH and ATP ( Werdan et al. , 1975 ; Noctor and Foyer, 2000 ). As shown earlier, state transitions re-equilibrate PSI and PSII activities through changes in their absorption CS, which are triggered by PQ pool redox state changes (for plants and algae, see reviews by Rochaix, 2014 , 2016 ; Goldschmidt-Clermont and Bassi, 2015 ), and involve phosphorylation/dephosphorylation of the PSII mobile antenna by kinases and phosphatases (i.e. STN7/TAP38 in Arabidopsis thaliana , or Stt7/Pph1 in Chlamydomonas reinhardtii ; Rochaix et al. , 2012 ). Furthermore, during induction of the Calvin–Benson cycle, changes in illumination, or anaerobiosis, photosynthetic electron fluxes are optimally redistributed between the linear electron transport (LET) from water to NADP + , and alternative electron pathways, i.e. cyclic electron flows, pseudocyclic O 2 -dependent electron flows and the malate valve ( Backhausen et al. , 2000 ; Miyake, 2010 ; Hemschemeier and Happe, 2011 ).

Modelling the state transition process

Ebenhöh et al. (2014) were the first to model state transitions in plants and algae based on a mechanism, described by Allen et al. (1981) ; they investigated the dynamics and regulation of state transitions by simulating experimental PAM-SP curves from Chlamydomonas reinhardtii cells, grown under dim light, and thus with little capacity for qE, having a low LHCSR3 content ( Peers et al. , 2009 ). Here, a simplified mathematical model (based on eight coupled ODEs) was used, where the most relevant ET routes, necessary for modelling state transitions in this green alga, were used: LEF, CEF-PSI, and chlororespiration through the plastid terminal oxidase PTOX (see Fig. 1 ; and Bennoun, 1982 ; McDonald et al. , 2011 ). Individual reactions of the Calvin–Benson cycle were treated implicitly, using steady-state consumption of NADPH and ATP, and a quasi-steady state approximation for the dynamics of oxygen evolution and charge separation in PSII. For simplicity, in the partial model of state transitions, it was assumed that the PSII mobile antennas phosphorylated by the kinase Stt7 (activated by the PQ pool reduction) are relocated directly to PSI (i.e. state 1 to state 2 transition, qT 12 ); also, after the Stt7 inhibition (triggered by the PQ pool oxidation), the PSII mobile antennas are dephosphorylated by the phosphatase Pph1, and directly re-associate with PSII (i.e. state 2 to state 1 transition, qT 21 ) (see Fig. 4 ). Finally, the ChlF signal is defined by the ratios of rate constants related to fluorescence emission, heat dissipation and photochemistry, which include changes in the absorption CS of PSI and PSII (due to state transition). Ebenhöh et al. (2014) successfully simulated with their model the main features of the experimental fluorescence signal measured with a PAM instrument from dark-adapted wild-type Chlamydomonas cells illuminated for 10 min with low light (100 μmol photons m −2 s −1 ). The saturating F M ′ peaks during illumination reflect changes in the antenna CS of PSII (i.e. a partial state transition to ‘state 2’), which take place in parallel with the establishment of a stationary redox poise of the PQ pool.

State transitions were also modelled by Stirbet and Govindjee (2016) , with the goal to simulate the slow PS(M)T phase of the ChlFI, in order to determine the origin of the S–M rise of Chlamydomonas reinhardtii cells (see Kodru et al. , 2015 ; Zhou et al. , 2015 ). Here, the photosynthesis model of Ebenhöh et al. (2014) was adapted for the simulation of ChlF data obtained by using a Plant Efficiency Analyser (PEA; Hansatech, UK). Stirbet and Govindjee (2016) confirmed that, under anaerobic conditions, in darkness, the PQ pool reduction through chlororespiration triggers a state 1 to state 2 transition (see Fig. 9A ), when the relative CS of PSII (CSII) is lower than that of PSI (see Bulté et al. , 1990 ). Next, it was shown that, during the subsequent illumination, the hypothetical sample undergoes a transition from this ‘state 2’ to a ‘state 1’, which is the origin of the slow S-M fluorescence rise (see Fig. 9B ). However, if the dark-adaptation period is too short, and the transition to ‘state 2’ in darkness is not complete, the subsequent illumination triggers a state 1 to state 2 transition (see Fig. 9C ). We note, however, that the M-T fluorescence decline observed experimentally ( Kodru et al. , 2015 ; see also Fig. 6B ) is missing in the simulated curves, and, thus, further research is needed to determine its origin.

Simulated kinetics of the fraction of the oxidized plastoquinone (PQ) pool (i.e. PQ/PQ tot ) and the relative absorption cross-section of photosystem (PS) II (i.e. CSII) during dark adaptation under anoxic conditions of a hypothetical sample of Chlamydomonas reinhardtii cells (see A), as well as simulated time courses of PQ/PQ tot , CSII and Chl fluorescence induction (F) during illumination in the presence of oxygen of the hypothetical sample after 600 s (see B) and 200 s (see C) anoxic dark adaptation. Note that a decrease in CSII reflects a state 1 to state 2 transition, while an increase reflects a state 2 to state 1 transition. Modified from Stirbet and Govindjee (2016) .

Stirbet and Govindjee (2016) also examined in silico the influence of different factors on the amplitude of the S-M fluorescence rise under low light conditions (~100 to 300 μmol photons m −2 s −1 ). For example, they found that, under conditions that trigger a qT 21 during a dark-to-light transition (i.e. reduced PQ pool, and CSII < 0.5 at the beginning of illumination), an increase in the CEF-PSI rate leads to a lower CSII increase at the end of the state transition, and a smaller amplitude of the S-M fluorescence rise (see Fig. 10A ). This simulation also confirmed that, when the CEF-PSI is much more rapid, the ATP level increases, while the NADPH level decreases. When the light intensity is higher, the simulations also showed a decrease in the S-M fluorescence rise. This result is in agreement with the experimental ChlFI data on Chlorella published by Papageorgiou and Govindjee (1968 a ), who showed that the slow S-M fluorescence rise is larger at lower exciting light intensities. By contrast, under other conditions taken into account by Stirbet and Govindjee (2016) , such as the increase in NADPH and ATP consumption by the Calvin–Benson cycle, or an increase in the rate of the Mehler reaction, the S-M amplitude increased, due to a larger increase in the PSII CS during the qT 21 (see Fig. 10B ). However, the increase in the S-M rise becomes saturated by further increasing these rate constants. The conclusion is that the factors reducing the PQ pool (e.g. higher light intensity, or more rapid CEF-PSI) decrease the S-M amplitude, and those that oxidize further the PQ pool (e.g. more rapid NADPH consumption or Mehler reaction) increase the S-M amplitude.

Simulated kinetics of the fraction of the oxidized plastoquinone (PQ) pool (i.e. PQ/PQ tot ), the relative absorption cross-section of photosystem (PS) II (i.e. CSII), and of chlorophyll (Chl) fluorescence induction (F) during illumination in the presence of oxygen of a hypothetical sample of Chlamydomonas reinharditii cells dark-adapted for 600 s under anoxic conditions, by considering that: (1) the illumination is equivalent to 100 μmol photons m −2 s −1 , and the rate constant of the cyclic electron flow (CEF) around PSI is k Cyc = 1 or 5 s −1 (see A); and (2) the illumination is equivalent to 300 μmol photons m −2 s −1 , the rate constant of CEF-PSI is 1 s −1 , and that of the Mehler reaction (i.e. ET from ferredoxin to O 2 ) k O2 = 0 or 11 s −1 (see B). Note that an increase in CSII reflects a state 2 to state 1 transition. These simulations show that the S-M fluorescence rise decreases when light intensity increases or when CEF-PSI is faster, but increases when the Mehler reaction is also functioning. Modified from Stirbet and Govindjee (2016) .

Modelling the qE component of NPQ

Because NPQ in plants and algae is associated with LHCs of PSII (see Horton et al. , 1996 ; Tian et al. , 2017 ), models simulating qE usually include reactions around PSII, and focus on describing the ChlFI (see reviews by Zaks et al. , 2013 ; Matuszyńska and Ebenhöh, 2015 ). Different photosynthesis models have been used to simulate either ChlFI curves measured with instruments using direct light (e.g. PEA), or with PAM-SP fluorometers (for a review see Stirbet et al. , (2014) . But, of course, the main phenomenon under analysis with either of these instruments is the same. Besides measurements of ChlF lifetime (e.g. Gilmore et al ., 1995 , 1998 ; Sylak-Glassman et al. , 2016 ), measurements of Chl fluorescence yield with PAM-SP fluorometers are especially suitable for the study of NPQ processes ( Müller et al. , 2001 ). It is clear that models that simulate experimental PAM data are valuable tools to analyse the qE component of NPQ.

Several original qE models have been proposed by, for example, Ebenhöh et al. (2011) and Zaks et al. (2012) ; these have been used for the simulation of the dynamics of ChlF quenching, as measured by PAM-SP instruments (see review by Stirbet et al. , 2014 ). Now, photosynthesis models that include qE are available ( Ebenhöh et al. , 2014 ; Matuszyńska et al ., 2016 , 2019 ; Snellenburg et al. , 2017 ; Morales et al ., 2018 a , b ).

The qE model of Ebenhöh et al. (2014) takes into account the induction of qE by low pH in the lumen (see above), but it is based on the simplifying assumption that the xanthophyll cycle is the only component involved in qE-dependent quenching. Thus, it was assumed that the decrease in lumenal pH leads directly to the formation of ‘Z’ through the xanthophyll cycle (i.e. the de-epoxidation of V via A), which then acts as a fluorescence quencher in the PSII antenna; the quencher acts by increasing the rate constant of the non-radiative deactivation of the 1 Chl*. Furthermore, the qE is reversed in darkness as Z is epoxidized to V by an active epoxidase. The results of the simulations, obtained with this qE model, showed that high light illumination leads to a plateau of the PQ pool redox state, which is relatively constant for a range of CSII values. Based on these theoretical results, Ebenhöh et al. (2014) concluded that, due to qE induction, the requirement to adjust the antenna CS through state transition under high light is much lower than under low light conditions. Indeed. Allorent et al. (2013) showed that the phosphorylation of LHCII antenna, mainly mediated by the STN7/Stt7 kinase in low light, is inhibited by high light, due either to a negative regulation of the kinase through the thioredoxin pathway under high light (see e.g. Lemeille and Rochaix, 2010 ), or to a conformational change in the PSII antenna ( Vink et al. , 2004 ).

To avoid the harmful effects of over-excitation, plants optimize their photosynthetic performance based on their illumination history through a process in which Z seems to play a key role (e.g. Ruban et al. , 2012 ). Matuszyńska et al. (2016) used a combined experimental and theoretical approach in the study of qE, particularly designed to determine if plants have a ‘memory’ of their recent (minutes to hours) light exposure, similar to what occurs after really long (days, months) periods of stress ( Demmig et al. , 1987 ; Adams and Demmig-Adams, 2004 ). In these studies, fluorescence measurements were made on Epipremnum aureum (a shadow (shade)-tolerant, ornamental plant) by PAM-SP. Here, F M ′ was used instead of NPQ, as suggested by Holzwarth et al. (2013) , to avoid mathematical distortion of the ChlF quenching kinetics. Additionally, the pigment composition was measured at the end of each phase of the experiment, in order to determine the contribution of Z to the ‘memory’ effect. These data confirmed the presence of a short-term ‘memory’ effect, which is influenced by both light intensity and the period of dark-relaxation between two light exposures. Matuszyńska et al. (2016) concluded that the ‘memory’ of recent light exposure related to qE can be assigned to dynamic changes in pigment composition, being due to a slower conversion of Z to V, as observed by, for example, Demmig et al. (1987) and Reinhold et al. (2008) . By implementing a qE model based on the ‘4 state-2-site quenching’ system ( Holzwarth and Jahns, 2014 ) in the photosynthesis model of Ebenhöh et al. (2014) (but without state transitions), Matuszyńska et al. (2016) were able to simulate successfully changes in the quantum yield of ChlF during the PAM-SP experiments, discussed above. In these simulations, the ChlF signal was also calculated using ratios of rate constants related to fluorescence emission, heat dissipation and photochemistry, where the rate constant of the heat dissipation was assumed to be modulated by the concentration of a quencher (Q), which was, in turn, calculated by taking into account the concentrations at any time of both Z and the protonated PsbS protein. [Note that Snellenburg et al. (2017) and Morales et al . (2018 a , b ) have used similar qE models, depending on the relative concentrations of Z and protonated PsbS.]

Modelling alternative electron flows

Besides LEF, which provides the Calvin–Benson cycle with NADPH and ATP, other ET routes function during oxygenic photosynthesis (see Fig. 1 ; Alric and Johnson, 2017 ; Shikanai and Yamamoto, 2017 ): (1) CEF-PSI via ferredoxin-plastoquinone reductase, or NADPH dehydrogenase (NDH); and (2) ‘alternative’ non-cyclic pathways that involve reduction of electron acceptors such as O 2 [the water–water cycle (WWC); see a model by Valero et al. (2009) ], or oxaloacetate [by malate dehydrogenase (MDH); see a model by Fridlyand et al. (1998) ]. The main role of CEF-PSI is to increase the ATP/NADPH ratio, as ‘required’ by the metabolic reactions in stroma or other energy-dependent processes in the chloroplast; furthermore, the pH difference, which induces qE, protects PSI and PSII against photoinhibition ( Strand et al , 2016 , 2017 ). The electron pathway to molecular oxygen (Mehler reaction, WWC), besides contributing to the acidification of the lumen and to the reduction of the excitation pressure on PSs, is also important in chloroplast redox signalling during abiotic stress, and in the regulation of CEF-PSI ( Miyake, 2010 ). The respective contributions of alternative electron pathways to the total ET is strictly regulated, depending on environmental conditions, but further research is needed to understand how these diverse pathways and their regulatory mechanisms function (see Yamori et al. , 2016 ; Nawrocki et al. , 2019 ).

Comprehensive dynamic C 3 photosynthesis models, such as those by Laisk et al . (2006 , 2009 ) and Zhu et al. (2013) , include light reactions, proton and electron transport, detailed carbon metabolism reactions, exchange of intermediates between cytosol and stroma, photorespiration, amino acid synthesis, and regulatory mechanisms. However, because these models involve a large number of model parameters, simplified photosynthesis models are much more suitable, and practical, for the study of dynamic responses of the photosynthetic apparatus to diverse changes of environmental factors. Indeed, a number of simplified photosynthesis models have been used in several studies to analyse PETC regulation in silico , through simulation of experimental data measured with a variety of methods ( Ebenhöh et al. , 2011 ; Zaks et al. , 2013 ; Tikhonov and Vershubskii, 2014 ; Stirbet and Govindjee, 2016 ; Snellenburg et al. , 2017 ; Morales et al ., 2018 a , b ; Matuszyńska et al ., 2016 , 2019 ). According to Morales et al. (2018 b ), the term ‘regulation’ means: reaching simultaneously, during environmental fluctuations, a suitable redox state of PETC, dissipation of excess excitation energy and ATP/NADPH ratio through adjustments of NPQ processes, CEF-PSI and reduction of alternative electron acceptors (also including the reduction of NO 2 ‒ during NH 4 + assimilation, NiR), as well as pmf optimization through changes in ATP synthase activity.

We have reviewed above results obtained in studies of photosynthesis regulation through state transitions and qE, based on simulations of ChlFI data. By contrast, Morales et al. (2018 b ) used, for simulations, several types of experimental data on Arabidopsis thaliana , such as PAM-SP ChlF data (for effective quantum yield of PSII and NPQ), Δ A 820 (for the P700 redox state, which is related to LET and alternative ET pathways), the electrochromic shift in A 520 (for pmf and its components), and net CO 2 assimilation ( A n , for the Calvin–Benson cycle and CO 2 diffusion). The results of these simulations have shown that CEF-PSI and alternative ET pathways are strongly interacting, and, thus, changes in FQR- or NDH-dependent CEF-PSI kinetics indirectly influence WWC, NiR and MDH activities, due to changes in the redox state of Fd. It is also known that the steady-state pH in the lumen cannot be controlled only by CEF-PSI and alternative ET, because it is also greatly affected by the pH sensitivity of qE, Cyt b 6 /f and ATP synthase. Additionally, Morales et al. (2018 b ) have examined the influence of the ADP/ATP ratio in stroma on the metabolic regulation of ATP synthesis, and their simulations showed that there is a coordination between the regulation of Rubisco, NPQ and PETC over a large range of light intensities and CO 2 concentrations. These are important observations for programming plants for better productivity.

MODELLING THE REGULATORY DEPENDENCE BETWEEN THE LIGHT REACTIONS AND THE CARBON REACTIONS

The slow part of the ChlFI induction also reflects changes due to the induction of the Calvin–Benson cycle during a dark to light transition. The activation and gradual increase in CO 2 assimilation during this phase leads to a parallel activation of ATP synthesis and an increase in the rate of LEF, which decreases the initial excitation pressure. As a result: (1) the level of Q A reduction decreases and photochemical quenching increases; and (2) qE decreases, because, due to a faster synthesis of ATP, the ΔpH decreases. Therefore, only models that include the induction of the Calvin–Benson cycle are suitable for correctly modelling the slow part of the ChlFI induction (see Laisk et al ., 2006 , 2009 ; Zhu et al. , 2013 ).

The Calvin–Benson cycle is one of the best-studied plant metabolic processes. Besides photosynthesis models, which include both the light and carbon reactions (e.g. Laisk et al ., 2006 , 2009 ; Zhu et al. , 2013 ; Belassio, 2019 ; Matuszyńska et al. , 2019 ), the carbon assimilation was often modelled separately, by considering a simplified relationship for NADPH and ATP supply (see review by Jablonsky et al. , 2011 ). In these models, carbon metabolism was analysed either by taking into account the kinetic properties of the enzymes involved, i.e. dynamic modelling ( Pettersson and Ryde-Pettersson, 1988 ; Zhu et al. , 2007 ), or without the need to use these, i.e. stoichiometric modelling ( Boyle and Morgan, 2009 ). In addition, a combination of both the above approaches has also been used ( Fleming et al. , 2010 ). In many models for the Calvin–Benson cycle, the steady-state behaviour of the photosynthetic apparatus has been analysed based on the equations of Farquhar et al . (1980) . Here we briefly mention some recent results on (short-term) regulation of photosynthesis obtained with the photosynthesis models of Morales et al. (2018 a ), Belassio (2019) and Matuszyńska et al. (2019) .

Fluctuating irradiances, which were shown to limit the performance of photosynthesis ( Pearcy, 1990 ), can be due to transient sun exposure, penumbra effects, shading by clouds, gaps in the canopy that produce ‘light (sun) flecks’, or movements of the leaves in the wind. Morales et al. (2018 a ) used a simplified dynamic model of CO 2 assimilation in a leaf to analyse the effects of fluctuating irradiances. In this study, they extended the canonical steady-state model by adding original empirical (phenomenological) partial models for the effects of chloroplast movement (qM; Dall’Osto et al. , 2014 ; Baránková et al. , 2016 ; Semer et al ., 2018 , 2019 ), qE, qI, regulation of enzyme activity in the Calvin–Benson cycle, metabolite concentrations, and the dynamic CO 2 diffusion through different leaf compartments. Changes in qE were assumed to follow PsbS protonation and Z generation, as was the case with the approach used by Matuszyńska et al. (2016) . With their model, Morales et al. (2018 a ) analysed potential improvements in CO 2 assimilation that may result after removing the kinetic limitation of different regulatory processes. Their simulations predicted that the most limiting steps in the carbon reactions are the activation rates of the Calvin–Benson cycle enzymes and stomatal opening (up to 17 % improvement), followed by the rate of qE relaxation and chloroplast movement (up to 10 % improvement), depending on the frequency of light fluctuations. However, up to 32 % improvement in CO 2 assimilation has been predicted, when all the kinetic limitations were simultaneously removed. Belassio (2019) has presented a dynamic photosynthesis model which also includes both light and carbon reactions, coupled to a mechanistic hydro-mechanical partial model for stomatal behaviour. This model successfully simulates responses to rapid changes in light intensity (light flecks), as well as in atmospheric CO 2 and O 2 concentrations. This model is freely available (as a supplement to the paper), and runs as a stand-alone workbook in Microsoft Excel.

Finally, Matuszyńska et al. (2019) have proposed a dynamic photosynthetic model describing the light reactions and the Calvin–Benson cycle in C 3 plants, for which they have used their earlier models [for light reactions: Ebenhöh et al. (2014) and Matuszyńska et al. (2016) ; for carbon reactions: Pettersson and Ryde-Pettersson (1988) and Poolman et al. (2000) ]. This newly merged model is based on nine coupled ODEs for the PETC, and 15 coupled ODEs for the carbon reactions. Analysis of this model shows the need for a ‘stand-by’ mode of the Calvin–Benson cycle in darkness, so that it can be restarted after prolonged dark periods; in this sense, the oxidative pentose phosphate pathway can play this function. Matuszyńska et al. (2019) have also used MCA (e.g. Visser and Heijnen, 2002 ) and metabolic supply–demand analysis ( Hofmeyr and Cornish-Bowden, 2000 ) to investigate the regulatory dependence between the PETC and the Calvin–Benson cycle, and to quantify the ‘control distribution’ of supply and demand under different light conditions and CO 2 assimilation rates. Th results obtained with MCA have indicated that, when CO 2 is saturating, the demand reactions control the flux under light-saturating conditions (with seduheptulose-1,7- bis phosphatase maintaining the highest overall flux control; see Poolman et al. , 2000 ), while the supply reactions display higher overall flux control under light-limited conditions, with PSII and PSI activities sustaining the highest overall flux control.

CONCLUSIONS

In this review, we have shown the important role played by models in deciphering and untangling different less well-understood and complex processes of photosynthesis, emphasizing the necessity and importance of modelling in the analysis of hypotheses developed from experimental studies. One major example, used in this review, is the ChlFI, which is simultaneously influenced by various photosynthetic processes affecting different segments of the fluorescence transient. As shown here, this process has been simulated by many modellers, who were focused either on understanding the dynamics of the redox states of different PETC components (see also reviews by Lazár, 1999 ; Lazár and Schansker, 2009 ; Stirbet et al. , 2014 ), or that of more complex, regulatory mechanisms involved in processes such as state transitions and qE, or of the relative contributions of alternative ET pathways, as well as their relationship with the CO 2 assimilation (the Calvin–Benson cycle) (see also Stirbet et al ., 2014 ). From the examples discussed in this review, it is evident that correctly simplified but complete dynamic models of photosynthesis are well suited to obtaining information about how the photosynthetic organisms cope with variable environmental conditions (see also Matuszyńska and Ebenhöh, 2015 ). Indeed, modelling is a very efficient method to identify important morphological and physiological parameters of a biological system and to find their optimal values. In addition, by using a larger variety of experimental data to verify such models, the simulations can lead to much more meaningful information about the organizational principles of the photosynthetic apparatus, which can also reveal original ways and means to improve the photosynthetic efficiency of plant crops ( Zhu et al. , 2007 ; Rosenthal et al. , 2011 ; Kromdijk et al. , 2016 ), besides being of theoretical interest. Moreover, multi-scale plant models (also known as plant system models), which quantitatively integrate physical, biochemical and physiological processes at different organizational levels (e.g. molecular, cell, organ, plant, population, or ecosystem), are able to predict physiological and growth properties of plants beyond photosynthetic metabolism, and they represent the future challenge in plant modelling (see Zhu et al. , 2016 ; Marshall-Colón et al. , 2017 ; Chang et al. , 2019 ; Marshall-Colón and Kliebenstein, 2019 ).

D.L. was supported by European Regional Development Fund project ‘Plants as a tool for sustainable global development’ [No. CZ.02.1.01/0.0/0.0/16_019/0000827].

ACKNOWLEDGEMENTS

Govindjee is grateful for IT support provided by the UIUC Life Sciences Office of Information Technology (Andrew Debevec, Karl Schlipf, Thomas Uebele, Jeffrey Haas), and the staff of the Department of Plant Biology and of the Department of Biochemistry, University of Illinois at Urbana-Champaign; he encourages all readers to visit his web site ( http://www.life.illinois.edu/govindjee/ ) to download available educational material on photosynthesis for personal use.

LITERATURE CITED

• Adams WW III, Demmig-Adams B. 2004. Chlorophyll fluorescence as a tool to monitor plant response to the environment. In: George C, Papageorgiou GC, Govindjee eds: Chlorophyll a fluorescence: a signature of photosynthesis. Advances in photosynthesis and respiration . Vol. 19 Dordrecht: Springer, 583–604. [ Google Scholar ]
• Allen JF. 2002. Plastoquinone redox control of chloroplast thylakoid protein phosphorylation and distribution of excitation energy between photosystems: discovery, background, implications . Photosynthesis Research 73 : 139–148. [ PubMed ] [ Google Scholar ]
• Allen JF. 2003. State transitions – a question of balance . Science 299 : 1530–1532. [ PubMed ] [ Google Scholar ]
• Allen JF, Bennett J, Steinback KE, Arntzen CJ. 1981. Chloroplast protein phosphorylation couples plastoquinone redox state to distribution of excitation-energy between photosystems . Nature 291 : 25–29. [ Google Scholar ]
• Allen MB, Whatley FR, Arnon DI. 1958. Photosynthesis with isolated chloroplasts. VI. Rates of conversion of light into chemical energy in photosynthetic phosphorylation . Biochimica et Biophysica Acta 27 : 16–23. [ PubMed ] [ Google Scholar ]
• Allorent G, Tokutsu R, Roach T, et al.. 2013. A dual strategy to cope with high light in Chlamydomonas reinhardtii . Plant Cell 25 : 545–557. [ PMC free article ] [ PubMed ] [ Google Scholar ]
• Alric J. 2010. Cyclic electron flow around photosystem I in unicellular green algae , Photosynthesis Research 106 : 47–56. [ PubMed ] [ Google Scholar ]
• Alric J, Johnson X. 2017. Alternative electron transport pathways in photosynthesis: a confluence of regulation . Current Opinion in Plant Biology 37 : 78–86. [ PubMed ] [ Google Scholar ]
• Antal TK, Maslakov A, Yakovleva OV, Krendeleva TE, Riznichenko GY, Rubin AB. 2018. Simulation of chlorophyll fluorescence rise and decay kinetics, and P 700 -related absorbance changes by using a rule-based kinetic Monte-Carlo method . Photosynthesis Research 138 : 191–206. [ PubMed ] [ Google Scholar ]
• Arnon DI. 1984. The discovery of photosynthetic phosphorylation . Trends in Biochemical Sciences 9 : 258–262. [ Google Scholar ]
• Arnon DI, Allen MB, Whatley FR. 1954 a Photosynthesis by isolated chloroplasts . Nature 174 : 394–396. [ PubMed ] [ Google Scholar ]
• Arnon DI, Whatley FR, Allen MB. 1954 b Photosynthesis by isolated chloroplasts. II. Photosynthetic phosphorylation, the conversion of light energy into phosphate bond energy . Journal of the American Chemical Society 76 : 6324–6329. [ Google Scholar ]
• Asada K. 1999. The water–water cycle in chloroplasts: scavenging of active oxygens and dissipation of excess photons . Annual Review of Plant Physiology and Plant Molecular Biology 50 : 601–639. [ PubMed ] [ Google Scholar ]
• Avron M. 1963. A coupling factor in photophosphorylation . Biochimica et Biophysica Acta 77 : 699–702. [ Google Scholar ]
• Baake E, Schlöder JP. 1992. Modelling the fast fluorescence rise of photosynthesis . Bulletin of Mathematical Biology 54 : 999–1021. [ Google Scholar ]
• Backhausen JE, Kitzmann C, Horton P, Scheibe R. 2000. Electron acceptors in isolated intact spinach chloroplasts act hierarchically to prevent over-reduction and competition for electrons . Photosynthesis Research 64 : 1–13. [ PubMed ] [ Google Scholar ]
• Baránková B, Lazár D, Nauš J. 2016. Analysis of the effect of chloroplast arrangement on optical properties of green tobacco leaves . Remote Sensing of Environment 174 : 181–196. [ Google Scholar ]
• Bassham JA. 2005. Mapping the carbon reduction cycle: a personal perspective. In: Govindjee, Beatty JT, Gest H, Allen JF, eds. Discoveries in photosynthesis. Advances in photosynthesis and respiration . Dordrecht: Springer, 815–832. [ Google Scholar ]
• Bay Z, Pearlstein RM. 1963. A theory of energy transfer in the photosynthetic unit . Proceedings of the National Academy of Sciences of the USA 50 : 1071–1078. [ PMC free article ] [ PubMed ] [ Google Scholar ]
• Belassio C. 2019. A generalised dynamic model of leaf-level C3 photosynthesis combining light and dark reactions with stomatal behavior . Photosynthesis Research 141 : 99–118. [ PubMed ] [ Google Scholar ]
• Belyaeva NE. 2004. Generalized model of primary photosynthetic processes in chloroplasts . PhD thesis, Lomonosov Moscow State University. [ Google Scholar ]
• Belyaeva NE, Bulychev AA, Riznichenko GYu, Rubin AB. 2011. A model of photosystem II for the analysis of fast fluorescence rise in plant leaves . Biophysics 56 : 464–477. [ PubMed ] [ Google Scholar ]
• Belyaeva NE, Bulychev AA, Riznichenko GYu, Rubin AB. 2016. Thylakoid membrane model of the Chl a fluorescence transient and P700 induction kinetics in plant leaves . Photosynthesis Research 130 : 491–515. [ PubMed ] [ Google Scholar ]
• Belyaeva NE, Bulychev AA, Riznichenko GYu, Rubin AB. 2019. Analyzing both the fast and the slow phases of chlorophyll a fluorescence and P700 absorbance changes in dark-adapted and preilluminated pea leaves using a thylakoid membrane model . Photosynthesis Research 140 : 1–19. [ PubMed ] [ Google Scholar ]
• Benson AA. 2005. Following the path of carbon in photosynthesis: a personal story. In: Govindjee, Beatty JT, Gest H, Allen JF, eds. Discoveries in photosynthesis. Advances in photosynthesis and respiration . Dordrecht: Springer, 793–813. [ PubMed ] [ Google Scholar ]
• Bennoun P. 1982. Evidence for a respiratory chain in the chloroplast . Proceedings of the National Academy of Sciences of the USA 79 : 4352–4356. [ PMC free article ] [ PubMed ] [ Google Scholar ]
• Blackman FF. 1905. Optima and limiting factors . Annals of Botany 19 : 281–295. [ Google Scholar ]
• Blankenship RE. 2014. Molecular Mechanisms of Photosynthesis , 2nd edn.Oxford: Wiley-Blackwell. [ Google Scholar ]
• Bonaventura C, Myers J. 1969. Fluorescence and oxygen evolution from Chlorella pyrenoidosa . Biochimica et Biophysica Acta 189 : 366–383. [ PubMed ] [ Google Scholar ]
• Bouges-Bocquet B. 1973. Electron transfer between two photosystems in spinach chloroplasts . Biochimica et Biophysica Acta 31 : 250–256. [ PubMed ] [ Google Scholar ]
• Boyer PD. 2002. A research journey with ATP synthase . The Journal of Biological Chemistry 277 : 39045–39061. [ PubMed ] [ Google Scholar ]
• Boyle NR, Morgan JA. 2009. Flux balance analysis of primary metabolism in Chlamydomonas reinhardtii . BMC Systems Biology 3 : 4. [ PMC free article ] [ PubMed ] [ Google Scholar ]
• Breton J. 1982. The 692 nm fluorescence (F695) of chloroplasts at low temperature is emitted from the primary acceptor of photosystem II . FEBS Letters 147 : 16–20. [ Google Scholar ]
• Briantais J-M, Vernotte C, Picaud M, Krause GH. 1979. A quantitative study of the slow decline of chlorophyll a fluorescence in isolated chloroplasts . Biochimica et Biophysica Acta 548 : 128–138. [ PubMed ] [ Google Scholar ]
• Brooks MD, Jansson S, Niyogi KK. 2014. PsbS-dependent non-photochemical quenching. In: Demmig-Adams B, Garab G, Adams WW III, Govindjee, Sharkey TD, eds. Nonphotochemical quenching and energy dissipation in plants, algae and cyanobacteria. Advances in photosynthesis and respiration , vol. 40. Dordrecht: Springer, 297–314. [ Google Scholar ]
• Buchanan BB, 2016. The carbon (formerly dark) reactions of photosynthesis . Photosynthesis Research 128 : 215–217. [ PubMed ] [ Google Scholar ]
• Buchanan BB, Schürmann P, Wolosiuk RA, Jacquot JP. 2002. The ferredoxin/thioredoxin system: from discovery to molecular structures and beyond . Photosynthesis Research 73 : 215–222. [ PubMed ] [ Google Scholar ]
• Buchert F, Hamon M, Gäbelein P, Scholz M, Hippler M, Wollman F. 2018. The labile interactions of cyclic electron flow effector proteins . Journal of biological chemistry 293 : 17559–17573. [ PMC free article ] [ PubMed ] [ Google Scholar ]
• Bulté L, Gans P, Rebeillé F, Wollman FA. 1990. ATP control on state transitions in vivo in Chlamydomonas reinhardtii . Biochimica et Biophysica Acta 1020 : 72–80. [ Google Scholar ]
• Butler WL. 1962. Effects of red and far-red light on the fluorescence yield of chlorophyll in vivo . Biochimica et Biophysica Acta 64 : 309–317. [ PubMed ] [ Google Scholar ]
• Butler WL. 1980. Energy transfer between photosystem II units in a connected package model of the photochemical apparatus of photosynthesis (photochemical model) . Proceedings of the National Academy of Sciences of the USA 77 : 4697–4701. [ PMC free article ] [ PubMed ] [ Google Scholar ]
• Butler WL, Kitajima M. 1975. Fluorescence quenching in photosystem II of chloroplasts . Biochimica et Biophysica Acta 376 : 116–125. [ PubMed ] [ Google Scholar ]
• Butler WL, Strasser RJ. 1977. Tripartite model for the photochemical apparatus of green plant photosynthesis . Proceedings of the National Academy of Sciences of the USA 74 : 3382–3385. [ PMC free article ] [ PubMed ] [ Google Scholar ]
• Calvin M. 1989. Forty years of photosynthesis and related activities . Photosynthesis Research 23 : 3–16. [ PubMed ] [ Google Scholar ]
• Calvin M, Bassham JA, Benson AA. 1950. Chemical transformations in photosynthesis . Federation Proceedings 9 : 524–534. [ PubMed ] [ Google Scholar ]
• Cardona T, Sedoud A, Cox N, Rutherford AW. 2012. Charge separation in Photosystem II: a comparative and evolutionary overview . Biochimica et Biophysica Acta 1817 : 26–43. [ PubMed ] [ Google Scholar ]
• Chan HCH, Gamel OE, Fleming GR, Whaley KB. 2018. Single-photon absorption by single photosynthetic light-harvesting complexes . Journal of Physics B: Atomic, Molecular and Optical Physics 51 : 054002. [ Google Scholar ]
• Chang TG, Chang S, Song QF, Perveen S, Zhu XG. 2019. Systems models, phenomics and genomics: three pillars for developing high-yielding photosynthetically efficient crops . In silico Plants 1 : diy003. [ PMC free article ] [ PubMed ] [ Google Scholar ]
• Chernev P, Goltsev V, Zaharieva I, Strasser RJ. 2006. A highly restricted model approach quantifying structural and fuctional parameters of photosystem II probed by the chlorophyll a fluorescence rise . Ecological Engineering and Environment Protection 2 : 19–29. [ Google Scholar ]
• Clegg RM. 2006. The history of FRET. In: Geddes CD, Lakowicz JR, eds. Reviews in fluorescence . New York: Springer, 1–45. [ Google Scholar ]
• Clegg RM, Sener M, Govindjee. 2010. From Forster resonance energy transfer (FRET) to coherent resonance energy transfer (CRET) and back – A wheen o’mickles mak’s a muckle. In: Alfano RR, eds. Optical biopsy VII , vol. 7561. Proceedings of SPIE, 7561–7572. [ Google Scholar ]
• Cramer WA, Kallas T, eds. 2016. Cytochrome complexes: evolution, structures, energy transduction, and signaling. Advances in photosynthesis and respiration , Vol. 41. Dordrecht: Springer. [ Google Scholar ]
• Cramer WA, Hasan SS, Yamashita E. 2011. The Q cycle of cytochrome bc complexes: a structure perspective . Biochimica et Biophysica Acta 1807 : 788–802. [ PMC free article ] [ PubMed ] [ Google Scholar ]
• Croce R, van Amerongen H. 2013. Light-harvesting in photosystem I . Photosynthesis Research 116 : 153–166. [ PMC free article ] [ PubMed ] [ Google Scholar ]
• Dall’Osto L, Cazzaniga S, Wada M, Bassi R. 2014. On the origin of a slowly reversible fluorescence decay component in the Arabidopsis npq4 mutant . Philosophical Transactions of the Royal Society B: Biological Sciences 369 , 20130221. [ PMC free article ] [ PubMed ] [ Google Scholar ]
• Dau H. 1994. Molecular mechanism and quantitative models of variable photosystem II fluorescence . Photochemistry and Photobiology 60 : 1–23. [ Google Scholar ]
• Davis GA, Kanazawa A, Schöttler MA, et al.. 2016. Limitations to photosynthesis by proton motive force-induced photosystem II photodamage . eLife 5 , e16921. [ PMC free article ] [ PubMed ] [ Google Scholar ]
• Debus RJ, Barry BA, Sithole I, Babcock GT, McIntosh L. 1988. Direct mutagenesis indicates that the donor to P680+ in photosystem II is tyrosine-161 of the D1 polypeptide . Biochemistry 27 : 9071–9074. [ PubMed ] [ Google Scholar ]
• Demmig-Adams B. 2003. Linking the xanthophyll cycle with thermal energy dissipation . Photosynthesis Research 76 : 73–80. [ PubMed ] [ Google Scholar ]
• Demmig B, Winter K, Krüger A, Czygan F-C. 1987. Photoinhibition and zeaxanthin formation in intact leaves: a possible role of the xanthophyll cycle in the dissipation of excess light energy . Plant Physiology 84 : 218–224 [ PMC free article ] [ PubMed ] [ Google Scholar ]
• Demmig-Adams B, Winter K, Krüger A, Czygan F-C. 1989. Zeaxathin and the induction and relaxation kinetics of the dissipation of excess excitation energy in leaves in 2% O 2 , 0% CO 2 . Plant Physiology 90 : 887–893. [ PMC free article ] [ PubMed ] [ Google Scholar ]
• Demmig-Adams B, Garab G, Adams WW III, Govindjee, Sharkey TD, eds. 2014. Nonphotochemical quenching and energy dissipation in plants, algae and cyanobacteria. Advances in photosynthesis and respiration , vol. 40. Dordrecht: Springer. [ Google Scholar ]
• Dismukes GC, Siderer Y. 1980. EPR spectroscopic observations of a manganese center associated with water oxidation in spinach chloroplasts . FEBS Letters 121 : 78–80. [ Google Scholar ]
• Döring G, Renger G, Vater J. Witt HT. 1969. Properties of the photoactive chlorophyll-aII in photosynthesis . Zeitschrift für Naturforschung 24 : 1139–1143. [ PubMed ] [ Google Scholar ]
• Durrant J, Giorgi L, Barber J, Klug D, Porter G. 1990. Characterisation of triplet states in isolated photosystem II reaction centres: oxygen quenching as a mechanism for photodamage . Biochimica et Biophysica Acta 1017 : 167–175. [ Google Scholar ]
• Duysens LNM. 1952. Transfer of excitation energy in photosynthesis . PhD Thesis, Leiden University. [ Google Scholar ]
• Duysens LMN, Amesz J, Kamp BM. 1961. Two photochemical systems in photosynthesis . Nature 190 : 510–511. [ PubMed ] [ Google Scholar ]
• Duysens LMN, Sweers HT. 1963. Mechanism of the two photochemical reactions in algae as studied by means of fluorescence. In: Japanese Society of Plant Physiologists, ed. Studies on microalgae and photosynthetic bacteria . Tokyo: University of Tokyo Press, 353–372. [ Google Scholar ]
• Eaton-Rye JJ, Tripathy BC, Sharkey TD, eds. 2012. Photosynthesis: plastid biology, energy conversion and carbon assimilation . Dordrecht: Springer. [ Google Scholar ]
• Ebenhöh O, Houwaart T, Lokstein H, Schlede S, Tirok K. 2011. A minimal mathematical model of nonphotochemical quenching of chlorophyll fluorescence . Biosystems 103 : 196–204. [ PubMed ] [ Google Scholar ]
• Ebenhöh O, Fucile G, Finazzi GG, Rochaix J-D, Goldschmidt-Clermont M. 2014. Short-term acclimation of the photosynthetic electron transfer chain to changing light: a mathematical model . Philosophical Transactions of the Royal Society B: Biological Sciences 369 : 20130223. [ PMC free article ] [ PubMed ] [ Google Scholar ]
• Edwards GE, Black CC Jr. 1971. Isolation of mesophyll cells and bundle sheath cells from Digitaria sanguinalis (L.) Scop. leaves and a scanning microscopy study of the internal leaf cell morphology . Plant Physiology 47 : 149–156. [ PMC free article ] [ PubMed ] [ Google Scholar ]
• Emerson R. 1958. The quantum yield of photosynthesis . Annual Review of Plant Physiology 9 : 124. [ Google Scholar ]
• Emerson R, Arnold W. 1932 a A separation of the reactions in photosynthesis by means of intermittent light . Journal of General Physiology 15 : 391–420. [ PMC free article ] [ PubMed ] [ Google Scholar ]
• Emerson R, Arnold W. 1932 b The photochemical reaction in photosynthesis . The Journal of General Physiology 16 : 191–205. [ PMC free article ] [ PubMed ] [ Google Scholar ]
• Emerson R, Lewis CM. 1943. The dependence of the quantum yield of Chlorella photosynthesis on wavelength of light . American Journal of Botany 30 : 165–178. [ Google Scholar ]
• Emerson R, Chalmers RV, Cederstrand CN. 1957. Some factors influencing the long wave limit of photosynthesis . Proceedings of the National Academy of Sciences of the USA 43 : 133–143. [ PMC free article ] [ PubMed ] [ Google Scholar ]
• Engel GS, Calhoun TR, Read EL. et al.. 2007. Evidence for wavelike energy transfer through quantum coherence in photosynthetic systems . Nature 446 : 782–786 [ PubMed ] [ Google Scholar ]
• Farquhar GD, von Caemmerer S, Berry JA. 1980. A biochemical model of photosynthetic CO 2 assimilation in leaves of C3 species . Planta 149 : 78–90. [ PubMed ] [ Google Scholar ]
• Fassioli F, Dinshaw R, Arpin PC, Scholes GD. 2014. Photosynthetic light harvesting: excitons and coherence . Journal of the Royal Society Interface 11 : 20130901. [ PMC free article ] [ PubMed ] [ Google Scholar ]
• Feng S, Fu L, Xia Q, Tan J, Jiang Y, Guo Y. 2018. Modelling and simulation of photosystem II chlorophyll fluorescence transition from dark-adapted state to light-adapted state . IET Systems Biology 12 : 289–293. [ PMC free article ] [ PubMed ] [ Google Scholar ]
• Fleming RMT, Thiele I, Provan G, Nasheuer HP. 2010. Integrated stoichiometric, thermodynamic and kinetic modelling of steady state metabolism . Journal of Theoretical Biology 264 : 683–692. [ PMC free article ] [ PubMed ] [ Google Scholar ]
• Förster T. 1946. Energiewanderung und fluoreszenz . Naturwissenschaften 6 : 166–175. [ Google Scholar ]
• Förster T. 1948. Zwischenmolekulare energiewanderung und fluoreszenz . Annalen der Physik 2 : 55–75. [ Google Scholar ]
• Fridlyand LE, Backhausen JE, Scheibe R. 1998. Flux control of the malate valve in leaf cells . Archives of Biochemistry and Biophysics 349 : 290–298. [ PubMed ] [ Google Scholar ]
• Gaffron H, Wohl K. 1936. Zür theorie der assimilation . Naturwissenschaften 24 : 103–107. [ Google Scholar ]
• Gilmore AM. 1997. Mechanistic aspects of xanthophyll cycle dependent energy dissipation in higher plant chloroplasts and leaves . Physiologia Plantarum 99 : 197–209. [ Google Scholar ]
• Gilmore AM, Hazlett TL, Govindjee. 1995. Xanthophyll cycle dependent quenching of Photosystem II chlorophyll a fluorescence: formation of a quenching complex with a short fluorescence lifetime . Proceedings of the National Academy of Sciences of the USA 92 : 2273–2277. [ PMC free article ] [ PubMed ] [ Google Scholar ]
• Gilmore AM, Shinkarev VP, Hazlett TL, Govindjee. 1998. Quantitative analysis of the effects of intra-thylakoid pH and xanthophylls cycle pigments on chlorophyll a lifetime distributions and intensity in thylakoids . Biochemistry 37 : 13582–13593. [ PubMed ] [ Google Scholar ]
• Golbeck JH, ed. 2006. Photosystem I. The light-driven plastocyanin:ferredoxin oxidoreductase. Advances in photosynthesis and respiration , Vol. 24. Dordrecht: Springer. [ Google Scholar ]
• Goldschmidt-Clermont M, Bassi R. 2015. Sharing light between two photosystems: mechanism of state transitions . Current Opinion in Plant Biology 25 : 71–78. [ PubMed ] [ Google Scholar ]
• Goltsev V, Yordanov I. 1997. Mathematical model of prompt and delayed chlorophyll fluorescence induction kinetics . Photosynthetica 33 : 571–586. [ Google Scholar ]
• Govindjee 1995. Sixty-three years since Kautsky: chlorophyll a fluorescence . Australian Journal of Plant Physiology 22 : 131–160. [ Google Scholar ]
• Govindjee 2004. Chlorophyll a fluorescence: a bit of basics and history. In: Papageorgiou GC, Govindjee, eds. Chlorophyll a fluorescence: a signature of photosynthesis . Advances in photosynthesis and respiration , Vol 19. Dordrecht: Springer, 1–41. [ Google Scholar ]
• Govindjee, Krogmann DW. 2004. Discoveries in oxygenic photosynthesis (1727–2003): a perspective: dedicated to the memories of Martin Kamen (1920–2002) and William A. Arnold (1904–2001) . Photosynthesis Research 80 : 15–57. [ PubMed ] [ Google Scholar ]
• Govindjee, Papageorgiou GC. 1971. Chlorophyll fluorescence and photosynthesis: fluorescence transients. In: Giese AC, ed. Photophysiology . New York: Academic Press, 1–46. [ Google Scholar ]
• Govindjee, Rabinowitch EI. 1960. Two forms of chlorophyll a in vivo with distinct photochemical function . Science 132 : 355–356. [ PubMed ] [ Google Scholar ]
• Govindjee, Renger G. 1993. In appreciation of Bessel Kok . Photosynthesis Research 38 : 211–213. [ Google Scholar ]
• Govindjee, Satoh K. 1986. Fluorescence properties of chlorophyll b- and chlorophyll c-containing algae. In: Govindjee, Amesz J, Fork DC eds. Light emission by plants and bacteria . Orlando: Academic Press, 497–537. [ Google Scholar ]
• Govindjee, van Rensen JJS. 1978. Bicarbonate effects on the electron flow in isolated broken chloroplasts . Biochimica et Biophysica Acta 505 : 183–213. [ PubMed ] [ Google Scholar ]
• Govindjee, Ichimura S, Cederstrand C, Rabinowitch EI. 1960. Effect of combining far-red light with shorter wave light on the excitation of fluorescence in Chlorella . Archives of Biochemistry and Biophysics 89 : 322–323. [ PubMed ] [ Google Scholar ]
• Govindjee, Barber J, Cramer WA, et al. , eds. 1986. Excitation and electron transfer in photosynthesis – special issue dedicated to Warren L Butler . Photosynthesis Research 10 : 147–518. [ Google Scholar ]
• Govindjee, Beatty JT, Gest H, Allen JF, eds. 2005. Discoveries in photosynthesis. Advances in photosynthesis and respiration . Dordrecht: Springer. [ Google Scholar ]
• Govindjee, Kern JF, Messinger J, Whitmarsh J. 2010. Photosystem II. In: Encyclopedia of Life Sciences (ELS) . Chichester: John Wiley & Sons, Ltd, 1–15. [ Google Scholar ]
• Govindjee, Shevela D, Björn L. 2017. Evolution of the Z-scheme of photosynthesis: a perspective . Photosynthesis Research 133 : 5–15. [ PubMed ] [ Google Scholar ]
• Guissé B, Srivastava A, Strasser RJ. 1995. The polyphasic rise of the chlorophyll a fluorescence (O-K-J-I-P) in heat stressed leaves . Archives des Sciences - Université de Genève 48 : 147–160. [ Google Scholar ]
• Guo Y, Tan J. 2011. Modeling and simulation of the initial phases of chlorophyll fluorescence from photosystem II . BioSystems 103 : 152–157. [ PubMed ] [ Google Scholar ]
• Guo Y, Tan J. 2014. Kinetic Monte Carlo simulation of the initial phases of chlorophyll fluorescence from photosystem II . BioSystems 115 : 1–4. [ PubMed ] [ Google Scholar ]
• Hager A, Holocher K. 1994. Localization of the xanthophyll-cycle enzyme violaxanthin de-epoxidase within the thylakoid lumen and abolition of its mobility by a (light-dependent) pH decrease . Planta 192 : 581–589. [ Google Scholar ]
• Harbinson J, Woodward FI. 1987. The use of light-induced absorbance changes at 820 nm to monitor the oxidation state of P-700 in leaves . Plant, Cell & Environment 10 : 131–140. [ Google Scholar ]
• Heber U. 2002. Irrungen, Wirrungen? The Mehler reaction in relation to cyclic electron transport in C3 plants . Photosynthesis Research 73 : 223–231. [ PubMed ] [ Google Scholar ]
• Hemschemeier A, Happe T. 2011. Alternative photosynthetic electron transport pathways during anaerobiosis in the green alga Chlamydomonas reinhardtii . Biochimica et Biophysica Acta 1807 : 919–926. [ PubMed ] [ Google Scholar ]
• Hill R. 1937. Oxygen evolution by isolated chloroplasts . Nature 139 : 881–882. [ Google Scholar ]
• Hill R, Bendall F. 1960. Function of the two cytochrome components in chloroplasts: a working hypothesis . Nature 186 : 136–140. [ Google Scholar ]
• Hind G, Jagendorf AT. 1963. Separation of light and dark stages in photophosphorylation . Proceedings of the National Academy of Sciences of the USA 49 : 715–722. [ PMC free article ] [ PubMed ] [ Google Scholar ]
• Hofmeyr JHS, Cornish-Bowden A. 2000. Regulating the cellular economy of supply and demand . FEBS Letters 476 : 47–51. [ PubMed ] [ Google Scholar ]
• Holzapfel C. 1978. Analysis of the prompt fluorescence induction by means of computer simulation of the primary photosynthetic reactions . Zeitschrift für Naturforschung 33c : 402–407. [ Google Scholar ]
• Holzapfel C, Bauer R. 1975. Computer simulation of primary photosynthetic reactions – Compared with experimental results on O 2 -exchange and chlorophyll fluorescence of green plants . Zeitschrift für Naturforschung 30c : 489–498. [ Google Scholar ]
• Holzwarth A, Jahns P. 2014. Non-photochemical quenching mechanisms in intact organisms as derived from ultrafast-fluorescence kinetic studies. In: Demmig-Adams B, Garab G, Adams WW III, Govindjee, Sharkey TD, eds. Nonphotochemical quenching and energy dissipation in plants, algae and cyanobacteria. Advances in photosynthesis and respiration , vol. 40. Dordrecht: Springer, 129–156. [ Google Scholar ]
• Holzwarth AR, Miloslavina Y, Nilkens M, Jahns P. 2009. Identification of two quenching sites active in the regulation of photosynthetic light-harvesting studied by time-resolved fluorescence . Chemical Physics Letters 483 : 262–267. [ Google Scholar ]
• Holzwarth AR, Lenk D, Jahns P. 2013. On the analysis of non-photochemical chlorophyll fluorescence quenching curves: I. Theoretical considerations . Biochimica et Biophysica Acta 1827 : 786–792. [ PubMed ] [ Google Scholar ]
• Horton P, Ruban A, Rees D, Pascal A, Noctor G, Young A. 1991. Control of the light-harvesting function of chloroplast membranes by aggregation of the LHCII chlorophyll protein complex . FEBS Letters 292 : 1–4. [ PubMed ] [ Google Scholar ]
• Horton P, Ruban V, Walters RG. 1996. Regulation of light harvesting in green plants . Annual Review of Plant Physiology and Plant Molecular Biology 47 : 655–684. [ PubMed ] [ Google Scholar ]
• Horton P, Johnson MP, Perez-Bueno ML, Kiss AZ, Ruban AV. 2008. Photosynthetic acclimation: does the dynamic structure and macro-organisation of photosystem II in higher plant grana membranes regulate light harvesting states? The FEBS Journal 275 : 1069–1079. [ PubMed ] [ Google Scholar ]
• Hsu B-D. 1992 a A theoretical study on the fluorescence induction curve of spinach thylakoids in the absence of DCMU . Biochimica et Biophysica Acta 1140 : 30–36. [ Google Scholar ]
• Hsu B-D. 1992 b The active photosystem II centers can make a significant contibution to the initial fluorescence rise from F 0 to F i . Plant Science 81 : 169–174. [ Google Scholar ]
• Hsu B-D, Lee Y-S, Jang Y-R. 1989. A method for analysis of fluorescence induction curve from DCMU-poisoned chloroplasts . Biochimica et Biophysica Acta 975 : 44–49. [ Google Scholar ]
• Ishizaki A, Fleming GR. 2009. United treatment of quantum coherent and incoherent hopping dynamics in electronic energy transfer: reduced hierarchy equation approach . The Journal of Chemical Physics 130 : 234111. [ PubMed ] [ Google Scholar ]
• Iwai M, Yokono M, Inada N, Minagawa J. 2010. Live-cell imaging of photosystem II antenna dissociation during state transitions . Proceedings of the National Academy of Sciences of the USA 107 : 2337–2342. [ PMC free article ] [ PubMed ] [ Google Scholar ]
• Jablonsky J, Lazar D. 2008. Evidence for intermediate S-states as initial phase in the process of oxygen-evolving complex oxidation . Biophysical Journal 94 : 2725–2736. [ PMC free article ] [ PubMed ] [ Google Scholar ]
• Jablonsky J, Bauwe H, Wolkenhauer O. 2011. Modeling the Calvin–Benson cycle . BMC Systems Biology 5 : 185. [ PMC free article ] [ PubMed ] [ Google Scholar ]
• Jagendorf AT. 2002. Photophosphorylation and the chemiosmotic perspective . Photosynthesis Research 73 : 233–241. [ PubMed ] [ Google Scholar ]
• Jagendorf AT, Uribe E. 1966. ATP formation caused by acid-base transition of spinach chloroplasts . Proceedings of the National Academy of Sciences of the USA 55 : 170–177. [ PMC free article ] [ PubMed ] [ Google Scholar ]
• Jahns P, Holzwarth AR. 2012. The role of the xanthophyll cycle and of lutein in photoprotection of photosystem II . Biochimica et Biophysica Acta 1817 : 182–193. [ PubMed ] [ Google Scholar ]
• Johnson MP, Ruban AV. 2011. Restoration of rapidly reversible photoprotective energy dissipation in the absence of PsbS protein by enhanced ΔpH . Journal of Biological Chemistry 286 : 19973–19981. [ PMC free article ] [ PubMed ] [ Google Scholar ]
• Johnson MP, Davison P, Ruban A, Horton P. 2008. The xanthophyll cycle pool size controls the kinetics of non-photochemical quenching in Arabidopsis thaliana . FEBS Letters 582 : 259–263. [ PubMed ] [ Google Scholar ]
• Johnson MP, Zia A, Ruban AV. 2012. Elevated ΔpH restores rapidly reversible photoprotective energy dissipation in Arabidopsis chloroplasts deficient in lutein and xanthophyll cycle activity . Planta 235 : 193–204. [ PubMed ] [ Google Scholar ]
• Joliot A, Joliot P. 1964. Étude cinétique de la réaction photochimique libérant l’oxygène au cours de la photosynthèse . Comptes Rendus de l’Académie des Sciences (Paris) 258 : 4622–4625. [ PubMed ] [ Google Scholar ]
• Joliot P. 1965. Cinétiques de réactions liées à l’émission d’oxygène photosynthétique . Biochimica et Biophysica Acta 102 : 116–134. [ PubMed ] [ Google Scholar ]
• Joliot P. 2003. Period-four oscillations of the flash-induced oxygen formation in photosynthesis . Photosynthesis Research 76 : 65–72. [ PubMed ] [ Google Scholar ]
• Joliot P, Joliot A. 2003. Excitation transfer between photosynthetic units: the 1964 experiment . Photosynthesis Research 76 : 241–245. [ PubMed ] [ Google Scholar ]
• Joliot P, Barbieri G, Chabaud R. 1969. Un nouveau modèle des centres photochimiques du système II . Photochemistry and Photobiology 10 : 309–329. [ Google Scholar ]
• Jordan P, Fromme P, Witt HT, Klukas O, Saenger W, Krauss N. 2001. Three dimensional structure of cyanobacterial photosystem I at 2.5 Å resolution . Nature 411 : 909–917. [ PubMed ] [ Google Scholar ]
• Junge W. 2004. Protons, proteins and ATP . Photosynthesis Research 80 : 197–221. [ PubMed ] [ Google Scholar ]
• Kaiser E, Morales A, Harbinson J, Kromdijk J, Heuvelink E, Marcelis LFM. 2015. Dynamic photosynthesis in different environmental conditions . Journal of Experimental Botany 66 : 2415–2426. [ PubMed ] [ Google Scholar ]
• Kaiser E, Kromdijk J, Harbinson J, Heuvelink E, Marcelis LFM. 2017. Photosynthetic induction and its diffusional, carboxylation and electron transport processes as affected by CO 2 partial pressure, temperature, air humidity and blue irradiance . Annals of Botany 119 : 191–205. [ PMC free article ] [ PubMed ] [ Google Scholar ]
• Kamen MD. 1947. Radioactive tracers in biology . New York: Academic Press. [ Google Scholar ]
• Kamiya N, Shen R-J. 2003. Crystal structure of oxygen-evolving photosystem II from Thermosynechococcus vulcanus at 3.7-Å resolution . Proceedings of the National Academy of Sciences of the USA 100 : 98–103. [ PMC free article ] [ PubMed ] [ Google Scholar ]
• Kaňa R, Govindjee. 2016. Role of ions in the regulation of light harvesting . Frontiers in Plant Science 7 : 1849. [ PMC free article ] [ PubMed ] [ Google Scholar ]
• Kautsky H, Hirsch A. 1931. Neue versuche zur kohlensaureassimilation . Naturwissenschaften 19 : 964. [ Google Scholar ]
• Kitajima M, Butler WL. 1975. Quenching of chlorophyll fluorescence and primary photochemistry in chloroplasts by dibromothymoquinone . Biochimica et Biophysica Acta 723 : 105–115. [ PubMed ] [ Google Scholar ]
• Klimov VV, Klevanik AV, Shuvalov VA, Krasnovsky AA. 1977. Reduction of pheophytin in primary light reaction of photosystem II . FEBS Letters 82 : 183–186. [ PubMed ] [ Google Scholar ]
• Klimov VV, Dolan E, Ke B. 1980. EPR properties of an intermediary electron acceptor (pheophytin) in photosystem II reaction centers at cryogenic temperatures . FEBS Letters 112 : 97–100. [ Google Scholar ]
• Klughammer C, Schreiber U. 1994. An improved method, using saturating light pulses, for the determination of photosystem I quantum yield via P700+-absorbance changes at 830 nm . Planta 192 : 261–268. [ Google Scholar ]
• Kodru S, Malavath T, Devadasu E, et al.. 2015. The slow S to M rise of chlorophyll a fluorescence induction reflects transition from state 2 to state 1 in the green alga Chlamydomonas reinhardtii . Photosynthesis Research 125 : 219–231. [ PubMed ] [ Google Scholar ]
• Kok B. 1956. On the reversible absorption change at 705 μm in photosynthetic organisms . Biochimica et Biophysica Acta 22 : 399–401. [ PubMed ] [ Google Scholar ]
• Kok B, Forbush B, McGloin M. 1970. Cooperation of charges in photosynthetic O 2 evolution. 1. A linear four step mechanism . Photochemistry and Photobiology 11 : 457–475. [ PubMed ] [ Google Scholar ]
• Kramer DM, Sacksteder CA, Cruz JA. 1999. How acidic is the lumen? Photosynthesis Research 60 : 151–163. [ Google Scholar ]
• Krause H, Weis W. 1991. Chlorophyll fluorescence and photosynthesis: the basics . Annual Review of Plant Physiology and Plant Molecular Biology 42 : 313–349. [ Google Scholar ]
• Krey A, Govindjee 1964. Fluorescence changes in Porphyridium exposed to green light of different Intensity: A new emission band at 693 nm and its significance to photosynthesis . Proceedings of the National Academy of Sciences of the USA 52 : 1568–1572. [ PMC free article ] [ PubMed ] [ Google Scholar ]
• Krieger A, Weis E. 1993. The role of calcium in the pH-dependent control of photosystem II . Photosynthesis Research 37 : 117–130. [ PubMed ] [ Google Scholar ]
• Krogmann DW, Jagendorf AT, Avron M. 1959. Uncouplers of spinach chloroplast photosynthetic phosphorylation . Plant Physiology 34 : 272–277. [ PMC free article ] [ PubMed ] [ Google Scholar ]
• Kromdijk J, Głowacka K, Leonelli L, et al.. 2016. Improving photosynthesis and crop productivity by accelerating recovery from photoprotection . Science 354 : 857–861. [ PubMed ] [ Google Scholar ]
• Kroon BMA, Thoms S. 2006. From electron to biomass: a mechanistic model to describe phytoplankton photosynthesis and steady-state growth mates . Journal of Phycology 42 : 593–609. [ Google Scholar ]
• Kuvykin IV, Vershubskii AV, Priklonskii VI, Tikhonov AN. 2009. Computer simulation study of pH-dependent regulation of electron transport in chloroplasts . Biophysics 54 : 455–464. [ PubMed ] [ Google Scholar ]
• Laisk A, Oja V. 2018. Kinetics of photosystem II electron transport: a mathematical analysis based on chlorophyll fluorescence induction . Photosynthesis Research 136 : 63–82. [ PubMed ] [ Google Scholar ]
• Laisk A, Oja V, Rasulov B, Eichelmann H, Sumberg A. 1997. Quantum yields and rate constants of photochemical and nonphotochemical excitation quenching. Experiment and model . Plant Physiology 115 : 803–815. [ PMC free article ] [ PubMed ] [ Google Scholar ]
• Laisk A, Eichelmann H, Oja V. 2006. C3 photosynthesis in silico . Photosynthesis Research 90 : 45–66. [ PubMed ] [ Google Scholar ]
• Laisk A, Eichelmann H, Oja V. 2009. Leaf C 3 photosynthesis in silico : Integrated carbon/nitrogen metabolism. In: Laisk A, Nedbal AL, Govindjee, eds. Photosynthesis in silico: understanding complexity from molecules to ecosystems. Advances in photosynthesis and respiration , Vol. 29. Dordrecht: Springer, 295–322. [ Google Scholar ]
• Latimer P, Bannister TT, Rabinowitch E. 1956. Quantum yields of fluorescence of plant pigments . Science 124 : 585–586. [ PubMed ] [ Google Scholar ]
• Lavergne J, Trissl H-W. 1995. Theory of fluorescence induction in photosystem II: Derivation of analytical expressions in a model including exciton-radical-pair equilibrium and restricted energy transfer between photosynthetic units . Biophysical Journal 68 : 2474–2492. [ PMC free article ] [ PubMed ] [ Google Scholar ]
• Lazár D. 1999. Chlorophyll a fluorescence induction . Biochimica et Biophysica Acta 1412 : 1–28. [ PubMed ] [ Google Scholar ]
• Lazár D. 2003. Chlorophyll a fluorescence rise induced by high light illumination of dark-adapted plant tissue studied by means of a model of photosystem II and considering photosystem II heterogeneity . Journal of Theoretical Biology 220 : 469–503. [ PubMed ] [ Google Scholar ]
• Lazár D. 2006. The polyphasic chlorophyll a fluorescence rise measured under high intensity of exciting light . Functional Plant Biology 33 : 9–30. [ PubMed ] [ Google Scholar ]
• Lazár D. 2009. Modelling of light-induced chlorophyll a fluorescence rise (O-J-I-P transient) and changes in 820 nm-transmittance signal of photosynthesis . Photosynthetica 47 : 483–498. [ Google Scholar ]
• Lazár D. 2013. Simulations show that a small part of variable chlorophyll a fluorescence originates in photosystem I and contributes to overall fluorescence rise . Journal of Theoretical Biology 335 : 249–264. [ PubMed ] [ Google Scholar ]
• Lazár D. 2015. Parameters of photosynthetic energy partitioning . Journal of Plant Physiology 175 : 131–147. [ PubMed ] [ Google Scholar ]
• Lazár D, Jablonský J. 2009. On the approaches applied in formulation of a kinetic model of photosystem II: different approaches lead to different simulations of the chlorophyll a fluorescence transients . Journal of Theoretical Biology 257 : 260–269. [ PubMed ] [ Google Scholar ]
• Lazár D, Pospíšil P. 1999. Mathematical simulation of chlorophyll a fluorescence rise measured with 3-(3′,4′-dichlorophenyl)-1,1-dimethylurea-treated barley leaves at room and high temperatures . European Biophysics Journal 28 : 468–477. [ PubMed ] [ Google Scholar ]
• Lazár D, Schansker G. 2009. Models of chlorophyll a fluorescence transients. In: Laisk A, Nedbal L, Govindjee, eds. Photosynthesis in silico: understanding complexity from molecules to ecosystems. Advances in photosynthesis and respiration , Vol. 29. Dordrecht: Springer, 85–123. [ Google Scholar ]
• Lazár D, Nauš J, Matoušková M, Flašarová M. 1997. Mathematical modeling of changes in chlorophyll fluorescence induction caused by herbicides . Pesticide Biochemistry and Physiology 57 : 200–210. [ Google Scholar ]
• Lazár D, Brokeš M, Nauš J, Dvořák L. 1998. Mathematical modelling of 3-(3′,4′-dichlorophenyl)-1,1-dimethylurea action in plant leaves . Journal of Theoretical Biology 191 : 79–86. [ PubMed ] [ Google Scholar ]
• Lazár D, Tomek P, Ilík P, Nauš J. 2001. Determination of the antenna heterogeneity of Photosystem II by direct simultaneous fitting of several fluorescence rise curves measured with DCMU at different light intensities . Photosynthesis Research 68 : 247–257. [ PubMed ] [ Google Scholar ]
• Lazár D, Ilík P, Kruk J, Strzalka K, Nauš J. 2005. A theoretical study on effect of the initial redox state of cytochrome b559 on maximal chlorophyll fluorescence level (F M ). Implications for photoinhibition of photosystem II . Journal of Theoretical Biology 233 : 287–300. [ PubMed ] [ Google Scholar ]
• Lebedeva GV, Belyaeva NE, Demin OV, Riznichenko GYu, Rubin AB. 2002. Kinetic model of primary photosynthetic processes in chloroplasts. Description of the fast phase of chlorophyll fluorescence induction under different light intensities . Biophysics (Russia) 47 : 968–980. [ Google Scholar ]
• Lemeille S, Rochaix JD. 2010. State transitions at the crossroad of thylakoid signalling pathways . Photosynthesis Research 106 : 33–46. [ PubMed ] [ Google Scholar ]
• Li X-P, Björkman O, Shih C, et al.. 2000. A pigment-binding protein essential for regulation of photosynthetic light harvesting . Nature 403 : 391–395. [ PubMed ] [ Google Scholar ]
• Long SP, Zhu XG, Naidu SL, Ort DR. 2006. Can improvement in photosynthesis increase crop yields? Plant, Cell and Environment 29 : 315–330. [ PubMed ] [ Google Scholar ]
• Long SP, Marshall-Colon A, Zhu XG. 2015. Meeting the global food demand of the future by engineering crop photosynthesis and yield potential . Cell 161 : 56–66. [ PubMed ] [ Google Scholar ]
• Lubitz W, Chrysina M, Cox N. 2019. Water oxidation in photosystem II . Photosynthesis Research 142 : 105–125. [ PMC free article ] [ PubMed ] [ Google Scholar ]
• Lyu H, Lazár D. 2017 a Modeling the light-induced electric potential difference (ΔΨ), the pH difference (ΔpH) and the proton motive force across the thylakoid membrane in C3 leaves . Journal of Theoretical Biology 413 : 11–23. [ PubMed ] [ Google Scholar ]
• Lyu H, Lazár D. 2017 b Modeling the light-induced electric potential difference ΔΨ across the thylakoid membrane based on the transition state rate theory . Biochimica et Biophysica Acta 1858 : 239–248. [ PubMed ] [ Google Scholar ]
• Magyar M, Sipka G, Kovács L, et al.. 2018. Rate-limiting steps in the dark-to-light transition of Photosystem II - revealed by chlorophyll- a fluorescence induction . Scientific Reports 8 : 2755. [ PMC free article ] [ PubMed ] [ Google Scholar ]
• Makarov S, Grachev EA, Antal TK. 2012. Mathematical modeling of photosynthetic electron transport chain considering spatial heterogeneity of the thylakoid membrane . Mathematical Biology and Bioinformatics 7 : 508–528. [ Google Scholar ]
• Malkin S. 1966. Fluorescence induction studies in isolated chloroplasts. II. Kinetic analysis of the fluorescence intensity dependence on time . Biochimica et Biophysica Acta 123 : 433–442. [ PubMed ] [ Google Scholar ]
• Malkin S, Kok B. 1966. Fluorescence induction studies in isolated chloroplasts. I. Number of components involved in the reaction and quantum yields . Biochimica et Biophysica Acta 123 : 413–432. [ PubMed ] [ Google Scholar ]
• Malnoë A. 2018. Photoinhibition or photoprotection of photosynthesis? Update on the (newly termed) sustained quenching component qH . Environmental and Experimental Botany 154 : 123–133. [ Google Scholar ]
• Mar T, Govindjee. 1972. Kinetic models of oxygen evolution in photosynthesis . Journal of Theoretical Biology 36 : 427–446. [ PubMed ] [ Google Scholar ]
• Marshall-Colón A, Kliebenstein DJ. 2019. Plant networks as traits and hypotheses: moving beyond description . Trends of Plant Science 24 : 840–852. [ PubMed ] [ Google Scholar ]
• Marshall-Colón A, Long SP, Douglas K, et al.. 2017. Crops in silico: generating virtual crops using an integrative and multi-scale modeling platform . Frontiers in Plant Science 8 : 786. [ PMC free article ] [ PubMed ] [ Google Scholar ]
• Maslakov AS, Antal TK, Riznichenko GY, Rubin AB. 2016. Modeling of primary photosynthetic processes using the kinetic Monte Carlo method . Biophysics 61 : 387–399. [ Google Scholar ]
• Matsuoka T, Tanaka S, Ebina K. 2015. Systems approach to excitation-energy and electron transfer reaction networks in photosystem II complex: model studies for chlorophyll a fluorescence induction kinetics . Journal of Theoretical Biology 380 : 220–237. [ PubMed ] [ Google Scholar ]
• Matuszyńska A, Ebenhöh O. 2015. A reductionist approach to model photosynthetic self-regulation in eukaryotes in response to light . Biochemical Society Transactions 43 : 1133–1139. [ PubMed ] [ Google Scholar ]
• Matuszyńska A, Heidari S, Jahns P, Ebenhöh O. 2016. A mathematical model of non-photochemical quenching to study short-term light memory in plants . Biochimica et Biophysica Acta 1857 : 1860–1869. [ PubMed ] [ Google Scholar ]
• Matuszyńska A, Saadat NP, Ebenhöh O. 2019. Balancing energy supply during photosynthesis - a theoretical perspective . Physiologia Plantarum 166 : 392–402. [ PMC free article ] [ PubMed ] [ Google Scholar ]
• McAlister ED, Myers J. 1940. Time course of photosynthesis and fluorescence . Science 92 : 241–243. [ PubMed ] [ Google Scholar ]
• McDonald AE, Ivanov AG, Bode R, Maxwell DP, Rodermel SR, Hüner NP. 2011. Flexibility in photosynthetic electron transport: the physiological role of plastoquinol terminal oxidase (PTOX) . Biochimica et Biophysica Acta 1807 : 954–967. [ PubMed ] [ Google Scholar ]
• McGrath JM, Long SP. 2016. Can the cyanobacterial carbon-concentrating mechanism increase photosynthesis in crop species? A theoretical analysis . Plant Physiology 164 : 2247–2261. [ PMC free article ] [ PubMed ] [ Google Scholar ]
• Mehler AH. 1951. Studies on reactions of illuminated chloroplasts. I. Mechanisms of the reduction of oxygen and other Hill reagents . Archives of Biochemistry and Biophysics 33 : 65–77. [ PubMed ] [ Google Scholar ]
• Melis A, Homann PH. 1975. Kinetic analysis of the fluorescence induction in 3-(3′,4′-dichlorophenyl)-1,1-dimethylurea poisoned chloroplasts . Photochemistry and Photobiology 21 : 431–437. [ Google Scholar ]
• Mirkovic T, Ostroumov, Anna JM, van Grondelle R, Govindjee, Scholes GD. 2017. Light absorption and energy transfer in the antenna complexes of photosynthetic organisms . Chemical Reviews 117 : 249–293. [ PubMed ] [ Google Scholar ]
• Mishra KB, Mishra A, Kubásek J, Urban O, Heyer AG, Govindjee. 2019. Low temperature induced modulation of photosynthetic induction in non-acclimated and cold-acclimated Arabidopsis thaliana : chlorophyll a fluorescence and gas-exchange measurements . Photosynthesis Research 139 : 123–143. [ PubMed ] [ Google Scholar ]
• Mitchell P. 1961 a Coupling of phosphorylation to electron and hydrogen transfer by a chemiosmotic type of mechanism . Nature 191 : 144–148. [ PubMed ] [ Google Scholar ]
• Mitchell P. 1961 b Chemiosmotic coupling in oxidative and photosynthetic phosphorylation . Bodmin: Glynn Research. [ Google Scholar ]
• Mitchell P. 1975. Protonmotive Q-cycle-general formulation . FEBS Letters 59 : 137–139. [ PubMed ] [ Google Scholar ]
• Miyake C. 2010. Alternative electron flows (water–water cycle and cyclic electron flow around PSI) in photosynthesis: molecular mechanisms and physiological functions . Plant and Cell Physiology 51 : 1951–1963. [ PubMed ] [ Google Scholar ]
• Morales A, Kaiser E, Yin X, et al.. 2018. a Dynamic modelling of limitations on improving leaf CO 2 assimilation under fluctuating irradiance . Plant, Cell & Environment 41 : 589–604. [ PubMed ] [ Google Scholar ]
• Morales A, Yin X, Harbinson J, et al.. 2018. b In silico analysis of the regulation of the photosynthetic electron transport chain in C3 plants . Plant Physiology 176 : 1247–1261. [ PMC free article ] [ PubMed ] [ Google Scholar ]
• Müh F, Glöckner C, Hellmich J, Zouni A. 2012. Light-induced quinone reduction in photosystem II . Biochimica et Biophysica Acta 1817 : 44–65. [ PubMed ] [ Google Scholar ]
• Müller P, Li X, Niyogi KK. 2001. Non-photochemical quenching. A response to excess light energy . Plant Physiology 125 : 1558–1566. [ PMC free article ] [ PubMed ] [ Google Scholar ]
• Munday JC, Govindjee. 1969. Light-induced changes in the fluorescence yield of chlorophyll a in vivo. III. The dip and the peak in the fluorescence transient of Chlorella pyrenoidosa . Biophysical Journal 9 : 1–21. [ PMC free article ] [ PubMed ] [ Google Scholar ]
• Murata N. 1969 a Control of excitation transfer in photosynthesis. I. Light-induced change of chlorophyll a fluorescence in Porphyridium cruentum . Biochimica et Biophysica Acta 172 : 242. [ PubMed ] [ Google Scholar ]
• Murata N. 1969 b Control of excitation transfer in photosynthesis. II. Magnesium ion-dependent distribution of excitation energy between two pigment systems in spinach chloroplasts . Biochimica et Biophysica Acta 189 : 171–181. [ PubMed ] [ Google Scholar ]
• Murata N, Allakhverdiev SI, Nishiyama Y. 2012. The mechanism of photoinhibition in vivo: re-evaluation of the roles of catalase, α-tocopherol, non-photochemical quenching, and electron transport . Biochimica et Biophysica Acta 1817 : 1127–1133. [ PubMed ] [ Google Scholar ]
• Myers J. 1994. The 1932 experiments . Photosynthesis Research 40 : 303–310. [ PubMed ] [ Google Scholar ]
• Najafpour MM, Moghaddam NA, Allakhverdiev SI, Govindjee 2012. Biological water oxidation: Lessons from nature . Biochimica et Biophysica Acta 1817 : 1110–1121. [ PubMed ] [ Google Scholar ]
• Nawrocki WJ, Bailleul B, Picot D, et al.. 2019. The mechanism of cyclic electron flow . Biochimica et Biophysica Acta 1860 : 433–438. [ PubMed ] [ Google Scholar ]
• Nedbal L, Samson G, Whitmarsh J. 1992. Redox state of one-electron component controls the rate of photoinhibition of photosystem II . Proceedings of the National Academy of Sciences of the USA 89 : 7929–7933. [ PMC free article ] [ PubMed ] [ Google Scholar ]
• Nedbal L, Červený J, Schmidt H. 2009. Scaling and integration of kinetic models of photosynthesis: towards comprehensive e-photosynthesis. In: Laisk A, Nedbal AL, Govindjee, eds. Photosynthesis in silico: understanding complexity from molecules to ecosystems. Advances in photosynthesis and respiration , Vol. 29. Dordrecht: Springer, 17–29. [ Google Scholar ]
• Nelson N, Junge W. 2015. Structure and energy transfer in photosystems of oxygenic photosynthesis . Annual Review of Biochemistry 84 : 659–683. [ PubMed ] [ Google Scholar ]
• Nickelsen K. 2016. Explaining photosynthesis: models of biochemical mechanisms, 1840–1960 . Dordrecht: Springer. [ Google Scholar ]
• Nickelsen K, Govindjee. 2011. The maximum quantum yield controversy: Otto Warburg and the Midwest Gang . Bern Studies in the History and Philosophy of Science, Switzerland: Berne: University of Bern, Institute für Philosophie. [ Google Scholar ]
• Nikkanen L, Rintamäki E. 2019. Chloroplast thioredoxin systems dynamically regulate photosynthesis in plants . Biochemical Journal 476 : 1159–1172. [ PMC free article ] [ PubMed ] [ Google Scholar ]
• Nishiyama Y, Allakhverdiev SI, Murata N. 2006. A new paradigm for the action of reactive oxygen species in the photoinhibition of photosystem II . Biochimica et Biophysica Acta 1757 : 742–749. [ PubMed ] [ Google Scholar ]
• Nižnan J. 2014. Compact representation of photosynthesis biochemical processes . Diploma Thesis, Masaryk University. [ Google Scholar ]
• Noctor G, Foyer CH. 2000. Homeostasis of adenylate status during photosynthesis in a fluctuating environment . Journal of Experimental Botany 51 : 347–356. [ PubMed ] [ Google Scholar ]
• Oettmeier W, Masson K, Johanningmeier U. 1980. Photoaffinity labelling of the photosystem II herbicide binding protein . FEBS Letters 118 : 267–270. [ Google Scholar ]
• Okayama S, Butler WL. 1972. The influence of cytochrome b 559 on the fluorescence yield of chloroplasts at low temperature . Biochimica et Biophysica Acta 267 : 523–527. [ PubMed ] [ Google Scholar ]
• Ono T, Inoue Y. 1988. Discrete extraction of the Ca atom functional for O 2 evolution in higher plant Photosystem II by a simple low pH treatment . FEBS Letters 227 : 147–152. [ Google Scholar ]
• Ort DR, Merchant SS, Alric J, et al.. 2015. Redesigning photosynthesis to sustainably meet global food and bioenergy demand . Proceedings of the National Academy of Sciences of the USA 112 : 8529–8536. [ PMC free article ] [ PubMed ] [ Google Scholar ]
• Osmond B, Chow WS, Wyber R, et al.. 2017. Relative functional and optical absorption cross-sections of PSII and other photosynthetic parameters monitored in situ, at a distance with a time resolution of a few seconds, using a prototype light induced fluorescence transient (LIFT) device . Functional Plant Biology 44 : 985–1006. [ PubMed ] [ Google Scholar ]
• Page CC, Moser CC, Chen X, Dutton PL. 1999. Natural engineering principles of electron tunnelling in biological oxidation-reduction . Nature 402 : 47–52. [ PubMed ] [ Google Scholar ]
• Paillotin G. 1976. Movement of excitations in the photosynthetic domains of photosystem II . Journal of Theoretical Biology 58 : 237–252. [ PubMed ] [ Google Scholar ]
• Papageorgiou GC. 1975. Chlorophyll fluorescence: an intrinsic probe of photosynthesis. In: Govindjee, ed. Bioenergetics of photosynthesis . New York: Academic Press, 319–372. [ Google Scholar ]
• Papageorgiou GC, Govindjee. 1968 a Light-induced changes in the fluorescence yield of chlorophyll a in vivo. I. Anacystis nidulans . Biophysical Journal 8 : 1299–1315. [ PMC free article ] [ PubMed ] [ Google Scholar ]
• Papageorgiou GC, Govindjee. 1968 b Light induced changes in the fluorescence yield of chlorophyll a in vivo. II. Chlorella pyrenoidosa . Biophysical Journal 8 : 1316–1328. [ PMC free article ] [ PubMed ] [ Google Scholar ]
• Papageorgiou GC, Govindjee, eds. 2004. Chlorophyll a fluorescence: a signature of photosynthesis. Advances in photosynthesis and respiration , Vol. 19. Dordrecht: Springer. [ Google Scholar ]
• Papageorgiou GC, Govindjee. 2011. Photosystem II fluorescence: slow changes–scaling from the past . Journal of Photochemistry and Photobiology B: Biology 104 : 258–270. [ PubMed ] [ Google Scholar ]
• Papageorgiou GC, Govindjee. 2014. The non-photochemical quenching of the electronically excited state of chlorophyll a in plants: definitions, timelines, viewpoints, open questions. In: Demmig-Adams B, Garab G, Adams WW III, Govindjee, Sharkey TD, eds. Nonphotochemical quenching and energy dissipation in plants, algae and cyanobacteria. Advances in photosynthesis and respiration , vol. 40. Dordrecht: Springer, 1–44. [ Google Scholar ]
• Papageorgiou GC, Tsimilli-Michael M, Stamatakis K. 2007. The fast and slow kinetics of chlorophyll a fluorescence induction in plants, algae and cyanobacteria: a viewpoint . Photosynthesis Research 94 : 275–290. [ PubMed ] [ Google Scholar ]
• Pearcy RW. 1990. Sunflecks and photosynthesis in plant canopies . Annual Review of Plant Biology 41 : 421–453. [ Google Scholar ]
• Peers G, Truong TB, Ostendorf E, et al.. 2009. An ancient light-harvesting protein is critical for the regulation of algal photosynthesis . Nature 462 : 518–521. [ PubMed ] [ Google Scholar ]
• Pettersson G, Ryde-Pettersson U. 1988. A mathematical model of the Calvin photosynthesis cycle . European Journal of Biochemistry 175 : 661–672. [ PubMed ] [ Google Scholar ]
• Petrouleas V, Crofts AR. 2005. The quinone iron acceptor complex. In: Wydrzynski T, Satoh K eds. Photosystem II: the light-driven water: plastoquinone oxidoreductase. Advances in photosynthesis and respiration , Vol. 22. Dordrecht: Springer, 177–206. [ Google Scholar ]
• Pfündel E. 1998. Estimating the contribution of photosystem I to total leaf chlorophyll fluorescence . Photosynthesis Research 56 : 185–195. [ Google Scholar ]
• Poolman MG, Fell DA, Thomas S. 2000. Modelling photosynthesis and its control . Journal of Experimental Botany 51 : 319–328. [ PubMed ] [ Google Scholar ]
• Pribil M, Sandoval-Ibáñez O, Xu W. et al.. 2018. Fine-tuning of photosynthesis requires CURVATURE THYLAKOID1-mediated thylakoid plasticity . Plant Physiology 176 : 2351–2364. [ PMC free article ] [ PubMed ] [ Google Scholar ]
• Rabinowitch EI. 1945. Photosynthesis and related processes, vol 1. Chemistry of photosynthesis, chemosynthesis and related processes in vitro and in vivo . New York: Interscience Publishers. [ Google Scholar ]
• Rabinowitch EI, Govindjee. 1969. Photosynthesis . Chichester: Wiley & Sons. [ Google Scholar ]
• Rees D, Young A, Noctor G, Britton G, Horton P. 1989. Enhancement of the pH-dependent dissipation of excitation energy in spinach chloroplasts by light-activation: correlation with the synthesis of zeaxanthin . FEBS Letters 256 : 85–90. [ Google Scholar ]
• Rees D, Noctor G, Ruban AV, Crofts J, Young A, Horton P. 1992. pH dependent chlorophyll fluorescence quenching in spinach thylakoids from light treated or dark adapted leaves . Photosynthesis Research 31 : 11–19. [ PubMed ] [ Google Scholar ]
• Reinhold C, Niczyporuk S, Beran K, Jahns P. 2008. Short-term down-regulation of zeaxanthin epoxidation in Arabidopsis thaliana in response to photo-oxidative stress conditions . Biochimica et Biophysica Acta 1777 : 462–469. [ PubMed ] [ Google Scholar ]
• Renger G, Schulze A. 1985. Quantitative analysis of fluorescence induction curves in isolated spinach chloroplasts . Photobiochemistry and Photobiophysics 9 : 79–87. [ Google Scholar ]
• Renger G, Govindjee, eds. 1993. How plants and cyanobacteria make oxygen: 25 years of period four oscillations . Photosynthesis Research 38 : 211–469. [ Google Scholar ]
• Robinson HH, Crofts AR, 1983. Kinetics of the changes in oxidation-reduction reactions of the photosystem II quinone acceptor complex, and the pathway for deactivation . FEBS Letters 153 : 221–226. [ Google Scholar ]
• Rochaix J-D. 2014. Regulation and dynamics of the light-harvesting system . Annual Review of Plant Biology 65 : 287–309. [ PubMed ] [ Google Scholar ]
• Rochaix J-D. 2016. The dynamics of the photosynthetic apparatus in algae. In: Najafpour MM, ed. Applied photosynthesis - new progress . London: IntechOpen,23–52. [ Google Scholar ]
• Rochaix JD, Lemeille S, Shapiguzov A, et al.. 2012. Protein kinases and phosphatases involved in the acclimation of the photosynthetic apparatus to a changing light environment . Philosophical Transactions of the Royal Society B: Biological Sciences 367 : 3466–3474. [ PMC free article ] [ PubMed ] [ Google Scholar ]
• Roden JJJ, Bennett DIG, Whaley KB. 2016. Long-range energy transport in photosystem II . The Journal of Chemical Physics 144 : 245101. [ PubMed ] [ Google Scholar ]
• Roelofs TA, Lee C-H, Holzwarth AR. 1992. Global target analysis of picosecond fluorescence kinetics from pea chloroplasts. A new approach to the characterization of the primary processes in photosystem II α- and β-units . Biophysical Journal 61 : 1147–1163. [ PMC free article ] [ PubMed ] [ Google Scholar ]
• Rosenthal DM, Locke AM, Khozaei M, Raines CA, Long SP, Ort DR. 2011. Over-expressing the C3 photosynthesis cycle enzyme sedoheptulose-1–7 bisphosphatase improves photosynthetic carbon gain and yield under fully open air CO 2 fumigation (FACE) . BMC Plant Biology 11 : 123. [ PMC free article ] [ PubMed ] [ Google Scholar ]
• Ruban AV, Johnson MP, Duffy CD. 2012. The photoprotective molecular switch in the photosystem II antenna . Biochimica et Biophysica Acta 1817 : 167–181. [ PubMed ] [ Google Scholar ]
• Ruben S, Kamen MD. 1941. Long-lived radioactive carbon: C14 . Physics Reviews 59 : 349–354. [ Google Scholar ]
• Ruben S, Hassid WZ, Kamen MD. 1939. Radioactive carbon in the study of photosynthesis . Journal of the American Chemical Society 61 : 661–663. [ Google Scholar ]
• Ruben S, Randall M, Kamen M, Logan Hyde JL. 1941. Heavy oxygen ( 18 O) as a tracer in the study of photosynthesis . Journal of the American Chemical Society 63 : 877–879. [ Google Scholar ]
• Rubin A, Riznichenko G. 2009. Modeling of the primary processes in a photosynthetic membrane. In: Laisk A, Nedbal AL, Govindjee, eds. Photosynthesis in silico: understanding complexity from molecules to ecosystems. Advances in photosynthesis and respiration , Vol. 29. Dordrecht: Springer, 151–176. [ Google Scholar ]
• Šafránek D, Červený J, Klement M, Pospíšilová J, Brim L, Lazár D, Nedbal L. 2011. E-photosynthesis: Web-based platform for modeling of complex photosynthetic processes . BioSystems 103 : 115–124. [ PubMed ] [ Google Scholar ]
• Sapozhnikov DI, Krasnovskaya TA, Maevskaya AN. 1957. Change in the interrelationship of the basic carotenoids of the plastids of green leaves under the action of light . Doklady Akademii Nauk SSSR 113 : 465–467. [ Google Scholar ]
• Schansker G, Srivastava A, Govindjee, Strasser RJ. 2003. Characterization of the 820-nm transmission signal paralleling the chlorophyll a fluorescence rise (OJIP) in pea leaves . Functional Plant Biology 30 : 785–796 [ PubMed ] [ Google Scholar ]
• Schansker G, Tóth SZ, Strasser RJ. 2005. Methylviologen and dibromorhymoquinone treatments of pea leaves reveal the role of photosystem I in the Chl a fluorescence rise OJIP . Biochimica et Biophysica Acta 1706 : 250–261. [ PubMed ] [ Google Scholar ]
• Schansker G, Tóth SZ, Kovács L, Holzwarth AR, Garab G. 2011. Evidence for a fluorescence yield change driven by a light-induced conformational change within photosystem II during the fast chlorophyll a fluorescence rise . Biochimica et Biophysica Acta 1807 : 1032–1043. [ PubMed ] [ Google Scholar ]
• Schansker G, Tóth SZ, Holzwarth AR, Garab G. 2014. Chlorophyll a fluorescence: beyond the limits of the Q A model . Photosynthesis Research 120 : 43–58. [ PubMed ] [ Google Scholar ]
• Schatz GH, Brock H, Holzwarth AR. 1988. Kinetic and energetic model for the primary processes in photosystem II . Biophysical Journal 54 : 397–405. [ PMC free article ] [ PubMed ] [ Google Scholar ]
• Schlodder E, Meyer B. 1987. pH-dependence of oxygen evolution and reduction kinetics of photooxidized chlorophyll a II (P-680) in Photosystem II particles from Synechococcus sp . Biochimica et Biophysica Acta 890 : 23–31. [ Google Scholar ]
• Schreiber U. 1986. Detection of rapid induction kinetics with a new type of high-frequency modulated chlorophyll fluorometer . Photosynthesis Research 9 : 261–272. [ PubMed ] [ Google Scholar ]
• Schreiber U, Schliwa U, Bilger W. 1986. Continuous recording of photochemical and nonphotochemical chlorophyll fluorescence quenching with a new type of modulation fluorometer . Photosynthesis Research 10 : 51–62. [ PubMed ] [ Google Scholar ]
• Schreiber U, Neubauer C, Klughammer C. 1989. Devices and methods for room-temperature fluorescence analysis . Philosophical Transactions of the Royal Society B 323 : 241–251. [ Google Scholar ]
• Schreiber U, Klughammer C, Schansker G. 2019. Rapidly reversible chlorophyll fluorescence quenching induced by pulses of supersaturating light in vivo . Photosynthesis Research 142 : 35–50. [ PubMed ] [ Google Scholar ]
• Semer J, Štroch M, Špunda V, Navrátil M. 2018. Partitioning of absorbed light energy within photosystem II in barley can be affected by chloroplast movement . Journal of Photochemistry and Photobiology B: Biology 186 : 98–106. [ PubMed ] [ Google Scholar ]
• Semer J, Navrátil M, Špunda V, Štroch M. 2019. Chlorophyll fluorescence parameters to assess utilization of excitation energy in photosystem II independently of changes in leaf absorption . Journal of Photochemistry and Photobiology B: Biology 197 : 111535. [ PubMed ] [ Google Scholar ]
• Sétif P. 2015. Electron-transfer kinetics in cyanobacterial cells: Methyl viologen is a poor inhibitor of linear electron flow . Biochimica et Biophysica Acta 1847 : 212–222. [ PubMed ] [ Google Scholar ]
• Shen JR. 2015. The structure of photosystem II and the mechanism of water oxidation in photosynthesis . Annual Review of Plant Biology 66 : 23–48. [ PubMed ] [ Google Scholar ]
• Shevela D, Eaton-Rye JJ, Shen JR, Govindjee. 2012. Photosystem II and the unique role of bicarbonate: a historical perspective . Biochimica et Biophysica Acta 1817 : 1134–1151. [ PubMed ] [ Google Scholar ]
• Shevela D, Björn L, Govindjee. 2019. Photosynthesis: solar energy for life . Singapore: World Scientific. [ Google Scholar ]
• Shikanai TI, Yamamoto H. 2017. Contribution of cyclic and pseudo-cyclic electron transport to the formation of proton motive force in chloroplasts . Molecular Plant 10 : 20–29. [ PubMed ] [ Google Scholar ]
• Shinkarev VP, Govindjee. 1993. Insight into the relationship of chlorophyll a fluorescence yield to the concentration of its natural quenchers in oxygenic photosynthesis . Proceedings of the National Academy of Sciences of the USA 90 : 7466–7469. [ PMC free article ] [ PubMed ] [ Google Scholar ]
• Simkin AJ, McAusland L, Headland LR, Lawson T, Raines CA. 2015. Multigene manipulation of photosynthetic carbon assimilation increases CO 2 fixation and biomass yield in tobacco . Journal of Experimental Botany 66 : 4075–4090. [ PMC free article ] [ PubMed ] [ Google Scholar ]
• Simkin AJ, McAusland L, Lawson T, Raines CA. 2017. Overexpression of the RieskeFeS protein increases electron transport rates and biomass yield . Plant Physiology 175 : 134–145. [ PMC free article ] [ PubMed ] [ Google Scholar ]
• Simkin AJ, López-Calcagno PE, Raines CA. 2019. Feeding the world: improving photosynthetic efficiency for sustainable crop production . Journal of Experimental Botany 70 : 1119–1140. [ PMC free article ] [ PubMed ] [ Google Scholar ]
• Snellenburg J, Johnson MP, Ruban AV, van Grondelle R, van Stokkum IHM. 2017. A four state parametric model for the kinetics of the non-photochemical quenching in Photosystem II . Biochimica et Biophysica Acta 1858 : 854–864. [ PubMed ] [ Google Scholar ]
• South PF, Cavanagh AP, Lopez-Calcagno PE, Raines CA, Ort DR. 2018. Optimizing photorespiration for improved crop productivity . Journal of Integrative Plant Biology 60 : 1217–1230. [ PubMed ] [ Google Scholar ]
• Srivastava A, Guissé B, Greppin H, Strasser RJ. 1997. Regulation of antenna structure and electron transport in photosystem II of Pisum sativum under elevated temperature probed by the fast polyphasic chlorophyll a fluorescence transient: OKJIP . Biochimica et Biophysica Acta 1320 : 95–106. [ Google Scholar ]
• Steffen R, Christen G, Renger G. 2001. Time-resolved monitoring of flash-induced changes of fluorescence quantum yield and decay of delayed light emission in oxygen-evolving photosynthetic organisms . Biochemistry 40 :173–180. [ PubMed ] [ Google Scholar ]
• Steffen R, Eckert H-J, Kelly AA, Dörmann P, Renger G. 2005. Investigation on the reaction pattern of photosystem II in leaves from Arabidopsis thaliana by time resolved fluorometric analysis . Biochemistry 44 : 3123–3133. [ PubMed ] [ Google Scholar ]
• Stiehl HH, Witt HT. 1968. Die kurzzeitigen ultravioletten Differenzspektren bei der Photosynthese . Zeitschrift für Naturforschung 23b : 220–224. [ PubMed ] [ Google Scholar ]
• Stiehl HH, Witt HT. 1969. Quantitative treatment of the function of plastoquinone in photosynthesis . Zeitschrift für Naturforschung 24b : 1588–1598. [ PubMed ] [ Google Scholar ]
• Stirbet A. 2013. Excitonic connectivity between photosystem II units: what is it, and how to measure it? Photosynthesis Research 116 189–214. [ PubMed ] [ Google Scholar ]
• Stirbet A, Govindjee. 2011. On the relation between the Kautsky effect (chlorophyll a fluorescence induction) and photosystem II: basics and applications of the OJIP fluorescence transient . Journal of Photochemistry and Photobiology B: Biology 104 : 236–257. [ PubMed ] [ Google Scholar ]
• Stirbet A, Govindjee. 2012. Chlorophyll a fluorescence induction: a personal perspective of the thermal phase, the J–I–P rise . Photosynthesis Research 113 : 15–61. [ PubMed ] [ Google Scholar ]
• Stirbet A, Govindjee. 2016. The slow phase of chlorophyll a fluorescence induction in silico: origin of the S-M fluorescence rise . Photosynthesis Research 130 : 193–213. [ PubMed ] [ Google Scholar ]
• Stirbet A, Strasser RJ. 1995. Numerical simulation of the fluorescence induction in plants . Archives des Sciences – Université de Genève 48 : 41–60. [ Google Scholar ]
• Stirbet A, Strasser RJ. 1996. Numerical simulation of the in vivo fluorescence in plants . Mathematics and Computers in Simulation 42 : 245–253. [ Google Scholar ]
• Stirbet A, Govindjee, Strasser BJ, Strasser RJ. 1998. Chlorophyll a fluorescence induction in higher plants: modeling and numerical simulation . Journal of Theoretical Biology 193 : 131–151. [ Google Scholar ]
• Stirbet A, Rosenau P, Strőder AC, Strasser RJ. 2001. Parameter optimisation of fast chlorophyll fluorescence induction model . Mathematics and Computers in Simulation 56 : 443–450. [ Google Scholar ]
• Stirbet A, Riznichenko GY, Rubin AB, Govindjee. 2014. Modeling chlorophyll a fluorescence transient: relation to photosynthesis . Biochemistry (Mosc.) 79 : 291–323. [ PubMed ] [ Google Scholar ]
• Stirbet A, Lazár D, Kromdijk J, Govindjee. 2018. Chlorophyll a fluorescence induction: can just a one-second measurement be used to quantify abiotic stress responses? Photosynthetica 56 : 86–104. [ Google Scholar ]
• Stirbet A, Lazár D, Papageorgiou CG, Govindjee. 2019. Chlorophyll a fluorescence in cyanobacteria: relation to photosynthesis; In: Mishra AK, Tiwari DN, Rai AN eds. Cyanobacteria – from basic science to applications . London: Academic Press, 79–130. [ Google Scholar ]
• Strand DD, Kramer DM. 2014. Control of non-photochemical exciton quenching by the proton circuit of photosynthesis. In: Demmig-Adams B, Garab G, Adams WW III, Govindjee, Sharkey TD, eds. Nonphotochemical quenching and energy dissipation in plants, algae and cyanobacteria. Advances in photosynthesis and respiration , vol. 40. Dordrecht: Springer, 387–408. [ Google Scholar ]
• Strand DD, Fisher N, Davis GA, Kramer DM. 2016. Redox regulation of the antimycin A sensitive pathway of cyclic electron flow around photosystem I in higher plant thylakoids . Biochimica et Biophysica Acta 1857 : 1–6 [ PubMed ] [ Google Scholar ]
• Strand DD, Fisher N, Kramer DM. 2017. The higher plant plastid NAD(P)H dehydrogenase-like complex (NDH) is a high efficiency proton pump that increases ATP production by cyclic electron flow . The Journal of Biological Chemistry 292 : 11850–11860. [ PMC free article ] [ PubMed ] [ Google Scholar ]
• Strasser RJ. 1978. The grouping model of plant photosynthesis. In: Argyroudi-Akoyunoglou JH, Akoyunoglou G, eds. Chloroplast development . Amsterdam: Elsevier Biomedical, 513–515. [ Google Scholar ]
• Strasser RJ, Govindjee. 1991. The F 0 and the O-J-I-P fluorescence rise in higher plants and algae. In: Argyroudi-Akoyunoglou JH, ed. Regulation of chloroplast biogenesis . New York: Plenum Press, 423–426. [ Google Scholar ]
• Strasser RJ, Stirbet A, 1998. Heterogeneity of photosystem II probed by the numerically simulated chlorophyll a fluorescence rise (O-J-I-P) . Mathematics and Computers in Simulation 48 : 3–9. [ Google Scholar ]
• Strasser RJ, Stirbet A. 2001. Estimation of the energetic connectivity of PS II centres in plants using the fluorescence rise O-J-I-P. Fitting of experimental data to three different PS II models . Mathematics and Computers in Simulation 56 : 451–461. [ Google Scholar ]
• Strasser RJ, Srivastava A, Govindjee. 1995. Polyphasic chlorophyll a fluorescence transient in plants and cyanobacteria . Photochemistry and Photobiology 61 : 32–42. [ Google Scholar ]
• Strasser RJ, Tsimilli-Michael M, Srivastava A. 2004. Analysis of the chlorophyll fluorescence transient. In: Papageorgiou GC, Govindjee eds. Chlorophyll a fluorescence: a signature of photosynthesis. Advances in photosynthesis and respiration , vol. 19. Dordrecht: Springer, 321–362. [ Google Scholar ]
• Sušila P, Lazár D, Ilík P, Tomek P and Nauš J. 2004. The gradient of exciting radiation within a sample affects relative heights of steps in the fast chlorophyll a fluorescence rise . Photosynthetica 42 : 161–172. [ Google Scholar ]
• Sylak-Glassman EJ, Zaks J, Amarnath K, Leuenberger M, Fleming GR. 2016. Characterizing non-photochemical quenching in leaves through fluorescence lifetime snapshots . Photosynthesis Research 127 : 69–76. [ PubMed ] [ Google Scholar ]
• Tagawa K, Tsujimoto HY, Arnon DI. 1963. Role of chloroplast ferredoxin in the energy conversion process of photosynthesis . Proceedings of the National Academy of Sciences of the USA 49 : 567–572. [ PMC free article ] [ PubMed ] [ Google Scholar ]
• Thompson LK, Brudvig GW. 1988. Cytochrome b-559 may function to protect photosystem II from photoinhibitin . Biochemistry 27 : 6653–6658. [ PubMed ] [ Google Scholar ]
• Tian L, Xu P, Chukhutsina VU, Holzwarth AR, Croce R. 2017. Zeaxanthin-dependent nonphotochemical quenching does not occur in photosystem I in the higher plant Arabidopsis thaliana . Proceedings of the National Academy of Sciences of the USA 114 : 4828–4832. [ PMC free article ] [ PubMed ] [ Google Scholar ]
• Tikhonov AN. 2013. pH-Dependent regulation of electron transport and ATP synthesis in chloroplasts . Photosynthesis Research 116 : 511–534. [ PubMed ] [ Google Scholar ]
• Tikhonov AN, Vershubskii AV. 2014. Computer modeling of electron and proton transport in chloroplasts . Biosystems 121 : 1‒ 21. [ PubMed ] [ Google Scholar ]
• Tokarčík A. 2012. Rewriting complex biological models in stochastic process algebras. A case study . Bachelor Thesis, Masaryk University. [ Google Scholar ]
• Tomek P, Lazár D, Ilík P, Nauš J. 2001. On the intermediate steps between the O and P steps in chlorophyll a fluorescence rise measured at different intensities of exciting light . Australian Journal of Plant Physiology 28 : 1151–1160. [ Google Scholar ]
• Tomek P, Ilík P, Lazár D, Štroch M, Nauš J. 2003. On the determination of Q B -non-reducing photosystem II centers from chlorophyll a fluorescence induction . Plant Science 164 : 665–670. [ Google Scholar ]
• Trebst A, Reimer S. 1973. Energy conservation in photoreductions by Photosystem II. Reversal of dibromothymoquinone inhibition of Hill-reactions by phenylenediamines . Zeitschrift für Naturforschung 28c : 710. [ Google Scholar ]
• Trissl H-W, Lavergne J. 1995. Fluorescence induction from photosystem II: analytical equations for the yields of photochemistry and fluorescence derived from analysis of a model including exciton-radical pair equilibrium and restricted energy transfer between units . Australian Journal of Plant Physiology 22 : 183–193. [ PMC free article ] [ PubMed ] [ Google Scholar ]
• Trissl H-W, Gao Y, Wulf K. 1993. Theoretical fluorescence induction curves derived from coupled differential equations describing the primary photochemistry of photosystem II by an exciton-radical pair equilibrium . Biophysical Journal 64 : 974–988. [ PMC free article ] [ PubMed ] [ Google Scholar ]
• Tyystjärvi E. 2013. Photoinhibition of photosystem II . International Review of Cell and Molecular Biology 300 : 243–303. [ PubMed ] [ Google Scholar ]
• Tyystjärvi E, Hakala M, Sarvikas P. 2005. Mathematical modelling of the light response curve of photoinhibition of photosystem II . Photosynthesis Research 84 : 21–27. [ PubMed ] [ Google Scholar ]
• Valero E, Gonzalez-Sanchez MI, Macia H, Garcıa-Carmona F. 2009. Computer simulation of the dynamic behavior of the glutathione-ascorbate redox cycle in chloroplasts . Plant Physiology 149 : 1958–1969. [ PMC free article ] [ PubMed ] [ Google Scholar ]
• van Amerongen H, Croce R. 2013. Light-harvesting in photosystem II . Photosynthesis Research 116 : 251–263. [ PMC free article ] [ PubMed ] [ Google Scholar ]
• van Gorkom HJ. 1974. Identification of the reduced primary electron acceptor of Photosystem II as a bound semiquinone anion . Biochimica et Biophysica Acta 347 : 439–442. [ PubMed ] [ Google Scholar ]
• van Gorkom HJ, Pulles MPJ, Etienne A-L. 1978. Fluorescence and absorbance changes in Tris-washed chloroplasts. In: Metzner H, ed. Photosynthetic oxygen evolution . London: Academic Press, 135–145. [ Google Scholar ]
• van Kooten O, Snel JFH, Vredenberg VJ. 1986. Photosynthetic free energy transduction related to the electric potential changes across the thylakoid membrane . Photosynthesis Research 9 : 211–227. [ PubMed ] [ Google Scholar ]
• van Rensen JJS. 2002. Role of bicarbonate at the acceptor side of Photosystem II . Photosynthesis Research 73 : 185–192. [ PubMed ] [ Google Scholar ]
• Vavilin DV, Tyystjärvi E, Aro E-M. 1998. Model for the fluorescence induction curve of photoinhibited thylakoids . Biophysical Journal 75 : 503–512. [ PMC free article ] [ PubMed ] [ Google Scholar ]
• Velthuys BR, Amesz J. 1974. Charge accumulation at the reducing side of Photosystem 2 of photosynthesis . Biochimica et Biophysica Acta 333 : 85–94. [ PubMed ] [ Google Scholar ]
• Vermaas WFJ. 2007. Targeted genetic modification of cyanobacteria: new biotechnological applications. In: Richmond A, ed. Handbook of microalgal culture . Oxford: Blackwell Science, 457–470. [ Google Scholar ]
• Vermeglio A. 2002. The two-electron gate in photosynthetic bacteria . Photosynthesis Research 73 : 83–86. [ PubMed ] [ Google Scholar ]
• Vink M, Zer H, Alumot N, et al.. 2004. Light modulated exposure of the light-harvesting complex II (LHCII) to protein kinase(s) and state transition in Chlamydomonas reinhardtii xanthophyll mutants . Biochemistry 43 : 7824–7833. [ PubMed ] [ Google Scholar ]
• Visser D, Heijnen J. 2002. The mathematics of metabolic control analysis revisited . Metabolic Engineering 4 : 114–123. [ PubMed ] [ Google Scholar ]
• Vredenberg WJ. 2000. A three-state model for energy trapping and chlorophyll fluorescence in photosystem II incorporating radical pair recombination . Biophysical Journal 79 : 26–38. [ PMC free article ] [ PubMed ] [ Google Scholar ]
• Vredenberg WJ. 2008. Algorithm for analysis of OJDIP fluorescence induction curves in terms of photo- and electrochemical events in photosystems of plant cells. Derivation and application . Journal of Photochemistry and Photobiology B: Biology 91 : 58–65. [ PubMed ] [ Google Scholar ]
• Vredenberg WJ. 2011. Kinetic analyses and mathematical modeling of primary photochemical and photoelectrochemical processes in plant photosystems . BioSystems 103 : 138–151. [ PubMed ] [ Google Scholar ]
• Vredenberg WJ, Duysens LNM. 1963. Transfer of energy from bacteriochlorophyll to a reaction centre during bacterial photosynthesis . Nature 197 : 355–357. [ PubMed ] [ Google Scholar ]
• Wang X, Cao J, Maroti P, et al.. 1992. Is bicarbonate in photosystem II the equivalent of the glutamate ligand to the iron atom in bacterial reaction centers? Biochimica et Biophysica Acta 1100 : 1–8. [ PubMed ] [ Google Scholar ]
• Warburg O, Uyesugi T. 1924. Über die Blackmansche Reaktion . Biochemische Zeitschrift 146 : 486–492. [ Google Scholar ]
• Werdan K, Heldt HW, Milovancev M. 1975. The role of pH in the regulation of carbon fixation in the chloroplast stroma. Studies on CO 2 fixation in the light and dark . Biochimica et Biophysica Acta 396 : 276–292. [ PubMed ] [ Google Scholar ]
• Wientjes E, Croce R. 2012. PMS: photosystem I electron donor or fluorescence quencher . Photosynthesis Research 111 : 185–191. [ PMC free article ] [ PubMed ] [ Google Scholar ]
• Willstätter R, Stoll A. 1913. Untersuchungen über Chlorophyll . Berlin: Justus Springer. [ Google Scholar ]
• Witt HT. 2004. Steps on the way to building blocks, topologies, crystals and X-ray structural analysis of Photosystems I and II of water-oxidizing photosynthesis . Photosynthesis Research 80 : 85–107. [ PubMed ] [ Google Scholar ]
• Witt HT, Müller A, Rumberg B. 1961 a Experimental evidence for the mechanism of photosynthesis . Nature 191 : 194–195. [ PubMed ] [ Google Scholar ]
• Witt HT, Müller A, Rumberg B. 1961 b Oxidized cytochrome and chlorophyll in photosynthesis . Nature 192 : 967–969. [ PubMed ] [ Google Scholar ]
• Wood WH, Barnett SFH, Flannery S, Hunter CN, Johnson MP. 2019. Dynamic thylakoid stacking is regulated by LHCII phosphorylation but not its interaction with photosystem I . Plant Physiology 180 : 2152–2166. [ Google Scholar ]
• Wraight CA, Crofts AR. 1970. Energy-dependent quenching of chlorophyll a fluorescence in isolated chloroplasts . European Journal of Biochemistry 17 : 319–327. [ PubMed ] [ Google Scholar ]
• Wydrzynski T, Govindjee. 1975. A new site of bicarbonate effect in Photosystem II of photosynthesis; evidence from chlorophyll fluorescence transients in spinach chloroplasts . Biochimica et Biophysica Acta 387 : 403–408. [ PubMed ] [ Google Scholar ]
• Wydrzynski T, Satoh K, eds. 2005. Photosystem II: the light-driven water-plastoquinone oxidoreductase. Advances in photosynthesis and respiration , Vol. 22. Dordrecht: Springer. [ Google Scholar ]
• Xia Q, Tan J, Ji X, Jiang Y, Guo Y. 2018. Modelling and simulation of chlorophyll fluorescence from photosystem II as affected by temperature . IET Systems Biology 12 : 304–310. [ PMC free article ] [ PubMed ] [ Google Scholar ]
• Xin CP, Yang J, Zhu XG. 2013. A model of chlorophyll a fluorescence induction kinetics with explicit description of structural constraints of individual photosystem II units . Photosynthesis Research 117 : 339–354. [ PubMed ] [ Google Scholar ]
• Yamamoto HY, Higashi RM. 1978. Violaxanthin deepoxidase. Lipid composition and substrate specificity . Archives of Biochemistry and Biophysics 190 : 514–522. [ PubMed ] [ Google Scholar ]
• Yamamoto HY, Nakayama T, Chichester C. 1962. Studies on the light and dark interconversions of leaf xanthophylls . Archives of Biochemistry and Biophysics 97 : 168–173. [ PubMed ] [ Google Scholar ]
• Yamori W, Makino A, Toshiharu Shikanai T. 2016. A physiological role of cyclic electron transport around photosystem I in sustaining photosynthesis under fluctuating light in rice . Scientific Reports 6 : 20147. [ PMC free article ] [ PubMed ] [ Google Scholar ]
• Yin X, Harbinson J, Struik PC. 2009. A model of the generalized stoichiometry of electron transport limited C3 photosynthesis: development and applications. In: Laisk A, Nedbal AL, Govindjee, eds. Photosynthesis in silico: understanding complexity from molecules to ecosystems. Advances in photosynthesis and respiration , Vol. 29. Dordrecht: Springer, 247–273. [ Google Scholar ]
• Zaks J, Amarnath K, Kramer DM, Niyogi KK, Fleming GR. 2012. A kinetic model of rapidly reversible nonphotochemical quenching . Proceedings of the National Academy of Sciences of the USA 109 : 15757–15762. [ PMC free article ] [ PubMed ] [ Google Scholar ]
• Zaks J, Amarnath K, Sylak-Glassman EJ, Fleming GR. 2013. Models and measurements of energy-dependent quenching . Photosynthesis Research 116 : 389–409. [ PMC free article ] [ PubMed ] [ Google Scholar ]
• Zhou Y, Schideman LC, Park DS, et al.. 2015. Characterization of a Chlamydomonas reinhardtii mutant strain with improved biomass production under low light and mixotrophic conditions . Algal Research 11 : 134–147. [ Google Scholar ]
• Zhu XG, Govindjee, Baker NR, deSturler E, Ort DR, Long SP. 2005. Chlorophyll a fluorescence induction kinetics in leaves predicted from a model describing each discrete step of excitation energy and electron transfer associated with photosystem II . Planta 223 : 114–133. [ PubMed ] [ Google Scholar ]
• Zhu XG, de Sturler E, Long SP. 2007. Optimizing the distribution of resources between enzymes of carbon metabolism can dramatically increase photosynthetic rate: a numerical simulation using an evolutionary algorithm . Plant Physiology 145 : 513–526. [ PMC free article ] [ PubMed ] [ Google Scholar ]
• Zhu XG, Long SP, Ort DR. 2010. Improving photosynthetic efficiency for greater yield . Annual Review of Plant Biology 61 : 235–261. [ PubMed ] [ Google Scholar ]
• Zhu XG, Wang Y, Ort DR, Long SP. 2013. e-Photosynthesis: a comprehensive dynamic mechanistic model of C3 photosynthesis: from light capture to sucrose synthesis . Plant, Cell & Environment 36 : 1711–1727. [ PubMed ] [ Google Scholar ]
• Zhu XG, Lynch JP, LeBauer DS, Millar AJ, Stitt M, Long SP. 2016. Plants in silico: why, why now and what? – an integrative platform for plant systems biology research . Plant, Cell & Environment 39 : 1049–1057. [ PubMed ] [ Google Scholar ]
• Zito F, Finazzi G, Delosme R, Nitschke W, Picot D, Wollman FA. 1999. The Qo site of cytochrome b6f complexes controls the activation of the LHCII kinase . EMBO Journal 18 : 2961–2969. [ PMC free article ] [ PubMed ] [ Google Scholar ]
• Zouni A, Witt HT, Kern J, et al.. 2001. Crystal structure of photosystem II from Synechococcus elongatus at 3.8 Å resolution . Nature 409 , 739–743. [ PubMed ] [ Google Scholar ]

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Essay on Photosynthesis in Plants

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In this essay we will discuss about Photosynthesis in Plants. After reading this essay you will learn about: 1. Meaning of Photosynthesis 2. Significance of Photosynthesis to Mankind 3. History 4. Photosynthetic Apparatus 5. Pigments 6. Quantum Requirement and Quantum Yield 7. Mechanism 8. Evidences for Existence of Light and Dark Reactions 9. Source of Oxygen 10. Factors Affecting.

• Essay on the Factors Affecting Photosynthesis

Essay # 1. Meaning of Photosynthesis:

Although literary meaning of photosynthesis is ‘synthesis with the help of light’ but this term is usually applied to a very important vital process by which the green plants synthesize organic matter in presence of light. Photosynthesis is sometimes called as carbon assimila­tion and is represented by the following traditional equation.

Chlorophylls and other photosynthetic pigments are found in the form of protein pigment complexes mainly in thylakoid membranes of grana. The latter are sites of primary photochemi­cal reaction. Some of the protein-pigment complexes are also found in stroma lamellae.

Dark reaction of photosynthesis occurs in stroma. Besides necessary enzymes, some ribosomes and DNA have also been found in chloroplasts which give them (chloroplasts) a partial genetic autonomy.

Essay # 5. Photosynthesis Pigments:

Photosynthetic pigments are of three types:

(1) Chlorophylls,

(2) Carotenoids, and

(3) Phycobillins.

i. Chlorophylls and carotenoids are insoluble in water and can be extracted only with organic solvents.

ii. Phycobillins are soluble in water.

iii. Carotenoids include carotenes and xanthophylls. The latter are also called as carotenols.

iv. Different pigments absorb light of different wavelengths and characteristic absorption peak in vivo and in vitro.

v. They show property of fluoresces.

Distribution of Photosynthetic Pigments in Plant Kingdom :

The distribution of the different types of photosynthetic pigments in plant kingdom is shown in table 11.1.

A new form of chlorophyll has been discovered recently by Chen et al (2010) from stromatolites of Shark Bay in Western Australia which they have called as chlorophyll f. This pigment is believed to absorb light upto 706 nm in vitro, with a fluorescence of 722 nm. (stro­matolites are structures formed from layers of cyanobacteria (blue-green algae), and other mi­croorganisms, calcium carbonate and sediments).

Structure of Photosynthetic Pigments :

(1) Chlorophylls:

They are magnesium porphyrin compounds. The porphyrin ring consists of four pyrrol rings joined together by CH bridges. A long chain of C atoms called as phytol chain is attached to porphyrin ring at iv pyrrol ring.

I. Chemical structures of chlorophyll-a and chlorophyll-b are well established.

v. (In modern scientific literature, some plant physiologists equate PAR with visible part of spec­trum of radiant energy which is erroneous. This is because such scientists working on photobiology use commercially available instruments that are limited to that portion of spectrum between 400-700 nm only, thus excluding visible light in the 700-760 and 390-400 nm range.)

vi. Only about 1% of the total solar energy received by the earth is absorbed by the pigments and is utilised in photosynthesis.

vii. There is very weak absorption by pigments in green part of the spectrum and hence, the chloroplasts appear green in green plants.

Absorption Spectra of Chlorophylls:

They chiefly absorb in the violet-blue and red parts of the spectrum. The absorption band shown by the chlorophylls in violet-blue region is also called as soret band. Characteristic absorption peaks shown by different chlorophylls both in vivo (i.e., intact cell) and in vitro (i.e., in solvents) are given in Table 11.2.

Absorption Spectra of Carotenoids:

These pigments absorb light energy in blue, blue- green and green parts of the spectrum.

Absorption Spectra of Phycobillins:

This can be explained further by a schematic model for the photo-oxidation of water given by Bessel Kok et al (1970) which is widely accepted and is called as S state mecha­nism or sometimes as water oxidizing clock. It consists of a series of 5 states called as S 0 , S 1 , S 2 , S 3 and S 4 which represent successively more oxidised forms of the water oxidizing system or oxygen evolving complex (OEC) S 0 is uncharged state.

Each short flash of light (photon or hv) converts S 0 to S 1 , S 1 to S 2 , S 2 to S 3 and S 3 to S 4 . After the S 4 state has ac­quired four positive charges, it gets four electrons back in one step oxidation of two molecules of H 2 O and returns back to S 0 with four fewer charges than S 4 (fig. 11.14).

However, the chemical nature of S state in this ‘clock’ is yet unknown. Once it was believed that P680 becomes oxidised by loss of one electron after a brief flash of light to P680 + but P680 cannot be S because it can lose only one electron and can accumulate only one positive charge.

Later studies have shown that various S states probably represent oxi­dation states of manganese including Mn 2+ , Mn 3+ and Mn 4+ . This hypothesis has received strong support from a variety of experiments, especially X-ray absorption and ESR studies which detect the manganese directly (Yano at al, 2006).

It is now known that the immediate electron donor to PSII is a tyrosine (an amino acid) residue which is often designated as Z or Y z in subunit D 1 of PSII reaction centre. (Y is code letter for tyrosine; hence Z is now called as Y z ). It is believed that tyrosine radical regains its electron by oxidizing a cluster of 4 Mn ions in OEC.

With each single electron transfer, the Mn cluster becomes more oxidized. Four single electron transfers (each correspond­ing with one photon (hv) of light) produce four positive charges on Mn cluster. In this state, Mn complex can take four electrons (4e-) from a pair of water molecules. The exact mechanism of photo-oxidation of H 2 O 2 however, remains elusive.

(The OEC is a 33kD complex situated on lumenal side of thylakoid. The 4H + released by photoly­sis of 2H 2 O molecules are released into lumen of thylakoid where they add to the proton gradient nec­essary for photophosphorylation. Apart from Mn 2+ and Cr ions, Ca 2+ ions are also believed to be essen­tial for photolysis of water.)

(v) Electron Transport and the Production of Assimilatory Power (i.e., NADPH + H + + ATP):

It has already been said that when chlorophyll-a molecule receives a photon of light it becomes excited and expels the extra energy along with an electron in both the pigment systems. This electron after travelling through a number of electron carriers is either cycled back or is consumed in reducing NADP + (Nicotinamide Adenine Dinucleotide Phosphate) to NADPH + H + .

The extra light energy carried by the electron is utilised in the formation of ATP molecules at certain places during its transport. This process of the formation of ATP from ADP and inorganic phosphate (Pi) in photosynthesis is called as photosynthetic phosphorylation or photophosphorylation. Arnon has contributed a lot in our understanding of the electron transport and photo­phosphorylation in chloroplasts.

These are of two types:

(a) Non-cyclic Electron Transport and Non-cyclic Photophosphorylation (Z-Scheme):

This process of electron transport involves both PSI and PSII which act in tandem or series and is initiated by the absorption of a photon (quantum) of light by P700 form of chlorophyll- a molecule in pigment system I which gets excited. An electron is ejected from it so that an electron deficiency or a ‘hole’ is left in the P700 molecule (or in other words a positive charge comes on chlorophyll-a-molecule).

This ejected electron is trapped by FRS (Ferredoxin reduc­ing substance) which is an unknown oxidation-reduction system with a redox potential (E 0 ‘) of -0.6 volts and may be a pteridene. The electron is now transferred to a non-heme iron protein called ferredoxin (Fd) with E’ 0 of-0.432 V. From ferredoxin the electron is transferred to NADP (E 0 ‘ = -0.32 V) via intermediate protein electron carrier ferredoxin-NADP reductase (FNR) so that NADP is reduced to NADPH + H + .

Most recent researches have shown that FRS is in-fact a series of electron carriers which in their reduced form are very unstable and difficult to be identified and are designated as A 0 A 1 Fe-S 1 ,Fe-S A & Fe-S B . A 0 is probably a chlorophyll molecule that receives electron from P700.

A 1 is be­lieved to be phylloquinone (vit. K 1 ). Fe-S x , Fe-S A and Fe-S B are iron-sulphur centres situated on proteins in core complex I (CCI) and act as additional electron carriers. From Fe-S centres, the elec­tron is transferred to ferredoxin (Fd) which is a small, water soluble iron-sulphur protein situated on stroma side of thylakoid membrane (Fig. 11.16).

Now, when a photon (quantum) of light is absorbed by P680 form of chlorophyll-a mol­ecule in pigment system II, it gets excited and an electron is ejected from it so that an electron deficiency or a ‘hole’ is left behind in the P680 molecule. The ejected electron is trapped by a compound of unknown identity usually designated Y (Compound Y is some­times called as Q because it also causes quenching of the characteristic fluorescence of chlorophyll-a in pigment system II).

This unknown compound forms oxidation-reduction sys­tem with a redox-potential (E 0 ‘) value more negative than 0.0 V. From Q the electron passes downhill along a series of compounds or intermediate electron carriers and is ultimately received by pigment system I where it ‘fills the hole.’ Redox potential of P700 in pigment system is + 0.43 V.

The series of compounds consists of (i) cytochrome b-559 (E 0 ‘ = + 0. 055 V), (ii) plastoquinone (PQ) whose chemical structure shows similarity with vitamins of K Series. It has a redox potential (E 0 ‘) of + 0.113 V, (iii) cytochrome ƒ (E 0 ‘ = + 0.36 V) and (iv) plastocyanin (PC) which is copper containing protein (E 0 ‘ = + 0.39 V).

At one place during the electron transport i.e., between plastoquinone and cytochrome ƒ there is enough change in free energy which allows phosphorylation of one molecule of ADP to form one ATP molecule (photophosphorylation).

Most recent researches have shown that from p680, the electron is transferred to unknown compound ‘Q’ via pheophytin. The latter is special form of chlorophyll-a which lacks magnesium atom (Fig. 11.2B). The unknown compound Q exists in two forms Q A & Q B .

It is now known that Q A and Q B are infact specialized plastoquinones (PQ) which receive elec­tron from pheophytin and transfer it to Cyt. b 6 f complex. Q A is attached strongly to D 2 protein, while Q B is attached loosely to D 1 protein in core complex II (CC II). After the Q B has received two electrons from Q A (one by one in two turns), it also takes two protons (2H + ) from stroma and is fully reduced to uncharged plastoquinol or plastohydroquinone (PQH 2 or PQ B H 2 ).

The PQH 2 is now re­leased from the reaction centre and is replaced by another molecule of PQ which now occupies the Q B site (11.16). From PQH 2 , electrons are transferred to cytochrome b 6 f complex and its two protons (2H + ) are expelled into the lumen of thylakoid. Finally, the electrons from Cyt b 6 f complex reach to PSI via plastocyanin (PC).

(It is important to note that Q A is one electron acceptor, while Q B is two electrons acceptor).

i. Cytochrome ƒ is a typical c type of cytochrome, ‘ ƒ ’ is abbreviated from ‘frons’ which in Latin means leaf).

The ‘hole’ in pigment system I has been filled by the electron coming from pigment sys­tem II. But the ‘hole’ or an electron deficiency is still there in pigment system II. This is ful­filled by the electron coming from photolysis of water. Water here acts as electron donor. It has redox-potential (E’ 0 ) of +0.82 V. This transfer of electron from water probably involves a strong oxidant which is yet unknown and is designated as Z or Yz.

In the above scheme of electron transport the electron ejected from pigment system II did not return to its place of origin, instead it was taken by pigment system I. Similarly, the elec­tron ejected from pigment system I did not cycle back and was consumed in reducing NADP + . Therefore, this electron transport has been called as non-cycle electron transport and the accompanying photophosphorylation as non-cyclic photophosphorylation.

ii. Arrangement of PSI and PSII and various components of non-cyclic electron transport chain when depicted on paper according to their redox-potential values, takes a zig-zag shape like the letter ‘Z’ (Fig. 11.15) hence, non-cyclic electron transport is also called by the name Z-scheme.

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Photosynthesis, Fermentation, and Enzyme Activity Essay

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Photosynthesis and Respiration

Role of fermentation in energy generation, how enzyme catalyzes reaction, works cited.

Photosynthesis is a chemical process by which plants manufacture food as glucose using carbon dioxide, water and sunlight, releasing oxygen as an end product. This glucose is utilized as a direct source of energy in plants for reproduction, growth, as well as an energy reserve. This process occurs in chloroplasts of leaves which have a stroma containing thylakoids. The thylakoid membrane has a chlorophyll pigment that absorbs light energy which is converted and stored in a simple sugar molecule. Aerobic respiration is a process by which glucose is converted into energy for use by plants and other organisms. The chemical bonds of glucose are broken down (glycolysis) to pyruvic acid molecules, which are further broken down in the Krebs cycle. The end product is released as carbon dioxide which is a residue of the pyruvic acid. The electrons and hydrogen ions produced are carried to the electron transport system. Water is then released as well as high levels of energy in form of ATP (Adenosine Tri-Phosphate). The process takes place in mitochondria (Cell structure, par. 2-5). Whilst photosynthesis absorbs light energy releasing glucose and oxygen, aerobic respiration releases energy due to oxidation of glucose in the presence of oxygen.

Fermentation helps organisms to generate ATP energy in the absence of oxygen. Glucose formed during photosynthesis is broken down starting in the cytoplasm of the cell in two ways depending on oxygen. When oxygen is present, aerobic cellular respiration occurs with complete glucose oxidation generating the highest amount of ATP energy. In the absence of oxygen, anaerobic respiration sets in where glycolysis occurs with pyruvic acid and 2 ATP molecules of energy produced at the end which is utilized by the cell. Some organisms lack required enzymes in krebs cycle and electron transport system and only carry out Glycolysis. Even though aerobic respiration is the major process of ATP energy generation, Prokaryotic organisms and certain eukaryotic organisms still need a supply of energy and therefore use anaerobic respiration. They are able to use other molecules as final electron acceptors e.g. pyruvic acid other than oxygen. The oxidation is usually incomplete resulting in smaller hydrogen-containing organic molecules, ATP energy and heat. Anaerobic Organisms get energy from glucose via Glycolysis pathway. In the process, pyruvic acid is produced which then undergoes changes in different organisms influenced by various enzymes. This leads to formation of lactic acid, ethyl alcohol or acetone and carbon dioxide. These molecules are useful in regeneration of NAD (nicotinamide adenine dinucleotide) required in Glycolysis as opposed to aerobic respiration where it’s generated by the electron transport system (Audesirk et al., 2008).

Enzymes catalyse reactions by reducing the activation energy essential for that reaction to occur. They escalate rate of chemical reactions without being altered or shifting chemical equilibrium between reactants and products. They have an active site that binds to substrates forming an enzyme-substrate complex and other sites that bind to cofactors needed for catalysis. The bound substrate is transformed into a product that is generated from the enzyme. The interaction is very specific in nature. Some have sites for binding products /substrates of the reaction that is catalyzed which plays a role in feedback regulation of enzyme activity (Reactions and Enzymes, n.d). A Change in the cell environment affects enzyme production hence regulating their activity. Compartmentalization also helps in regulating activity whereby different metabolic pathways are organized to occur in different cellular compartments. Presence of inhibitors and activators helps regulate enzyme activity in a cell leading to a stable cell environment (Reactions and Enzymes, n.d).

Audesirk, T., Audesirk, G., and Byers, B. (2008). Biology: Life on earth with physiology (8th Ed.). San Francisco, CA: Benjamin Cummings.

Cell Structure. (n.d.). Web.

Reactions and Enzymes, (n.d.). Web.

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Photosynthesis

Affiliation.

• 1 Department of Molecular Biology and Biotechnology, University of Sheffield, Firth Court, Western Bank, Sheffield S10 2TN, U.K. [email protected].
• PMID: 27784776
• PMCID: PMC5264509
• DOI: 10.1042/EBC20160016
• Correction: Photosynthesis. Johnson MP. Johnson MP. Essays Biochem. 2017 Oct 31;61(4):429. doi: 10.1042/EBC20160016_COR. Print 2017 Oct 31. Essays Biochem. 2017. PMID: 29089380 Free PMC article. No abstract available.

Photosynthesis sustains virtually all life on planet Earth providing the oxygen we breathe and the food we eat; it forms the basis of global food chains and meets the majority of humankind's current energy needs through fossilized photosynthetic fuels. The process of photosynthesis in plants is based on two reactions that are carried out by separate parts of the chloroplast. The light reactions occur in the chloroplast thylakoid membrane and involve the splitting of water into oxygen, protons and electrons. The protons and electrons are then transferred through the thylakoid membrane to create the energy storage molecules adenosine triphosphate (ATP) and nicotinomide-adenine dinucleotide phosphate (NADPH). The ATP and NADPH are then utilized by the enzymes of the Calvin-Benson cycle (the dark reactions), which converts CO 2 into carbohydrate in the chloroplast stroma. The basic principles of solar energy capture, energy, electron and proton transfer and the biochemical basis of carbon fixation are explained and their significance is discussed.

Keywords: membrane; photosynthesis; thylakoid.

© 2016 The Author(s).

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Figure 1. The global carbon cycle

The relationship between respiration, photosynthesis and global CO 2…

Figure 2. Location of the photosynthetic machinery

( A ) The model plant Arabidopsis thaliana…

Figure 3. Division of labour within the…

Figure 3. Division of labour within the chloroplast

The light reactions of photosynthesis take place…

Figure 4. The photosynthetic electron and proton…

Figure 4. The photosynthetic electron and proton transfer chain

The linear electron transfer pathway from…

Figure 5. Z-scheme of photosynthetic electron transfer

The main components of the linear electron transfer…

Figure 6. Major photosynthetic pigments in plants

The chemical structures of the chlorophyll and carotenoid…

Figure 7. Basic absorption spectra of the…

Figure 7. Basic absorption spectra of the major chlorophyll and carotenoid pigments found in plants

Figure 8. Jablonski diagram of chlorophyll showing…

Figure 8. Jablonski diagram of chlorophyll showing the possible fates of the S 1 and…

Figure 9. Basic mechanism of excitation energy…

Figure 9. Basic mechanism of excitation energy transfer between chlorophyll molecules

Two chlorophyll molecules with…

Figure 10. Basic structure of a photosystem

Light energy is captured by the antenna pigments…

Figure 11. Basic structure of the PSII–LHCII…

Figure 11. Basic structure of the PSII–LHCII supercomplex from spinach

The organization of PSII and…

Figure 12. S-state cycle of water oxidation…

Figure 12. S-state cycle of water oxidation by the manganese cluster (shown as circles with…

Figure 13. Basic structure of the PSI–LHCI…

Figure 13. Basic structure of the PSI–LHCI supercomplex from pea

The organization of PSI and…

Figure 14. Cytochrome b 6 f complex

( A ) Structure drawn from PDB code 1Q90. (…

Figure 15. Lateral heterogeneity in thylakoid membrane…

Figure 15. Lateral heterogeneity in thylakoid membrane organization

( A ) Electron micrograph of the…

Figure 16. The Calvin–Benson cycle

Overview of…

Overview of the biochemical pathway for the fixation of CO…

Figure 17. Rubisco

( A ) Structure…

( A ) Structure of the Rubisco enzyme (the large subunits are…

Figure 18. Diagram of a C 4…

Figure 18. Diagram of a C 4 plant leaf showing Kranz anatomy

Figure 19. The C 4 pathway (NADP…

Figure 19. The C 4 pathway (NADP + –malic enzyme type) for fixation of CO…

• Editorial Note: Photosynthesis. [No authors listed] [No authors listed] Essays Biochem. 2021 Jul 26;65(2):405. doi: 10.1042/EBC-2016-0016C_EDN. Epub 2021 Jul 16. Essays Biochem. 2021. PMID: 34309653 Free PMC article. No abstract available.

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• Combined metabolomics and transcriptomics reveal the secondary metabolite networks in different growth stages of Bletilla striata (Thunb.) Reichb.f. Chen M, Wang X, Ye Y, Li X, Li S, Li M, Jiang F, Zhang C. Chen M, et al. PLoS One. 2024 Jul 24;19(7):e0307260. doi: 10.1371/journal.pone.0307260. eCollection 2024. PLoS One. 2024. PMID: 39046970 Free PMC article.
• Effect of harvest timing and plant parts on the nutritional and chemical profile of five potential fodder plants found in eastern coast of United Arab Emirates. Tsombou FM, Saeed Sulaiman Jemei Al Dhanhani A, Mirza SB, Youssouf B, Ridouane FL. Tsombou FM, et al. Sci Rep. 2024 May 18;14(1):11371. doi: 10.1038/s41598-024-62258-x. Sci Rep. 2024. PMID: 38762677 Free PMC article.
• Adjustments of the Phytochemical Profile of Broccoli to Low and High Growing Temperatures: Implications for the Bioactivity of Its Extracts. Šola I, Gmižić D, Pinterić M, Tot A, Ludwig-Müller J. Šola I, et al. Int J Mol Sci. 2024 Mar 26;25(7):3677. doi: 10.3390/ijms25073677. Int J Mol Sci. 2024. PMID: 38612494 Free PMC article.
• The best of both worlds: photosynthesis and Solanaceae biodiversity seeking a sustainable food and cosmetic industry. Aguirre-Bottger C, Zolla G. Aguirre-Bottger C, et al. Front Plant Sci. 2024 Feb 16;15:1362814. doi: 10.3389/fpls.2024.1362814. eCollection 2024. Front Plant Sci. 2024. PMID: 38434437 Free PMC article. No abstract available.
• Blankenship R.E. Early evolution of photosynthesis. Plant Physiol. 2010;154:434–438. doi: 10.1104/pp.110.161687. - DOI - PMC - PubMed
• Blankenship R.E. Molecular Mechanisms of Photosynthesis. Chichester: Wiley–Blackwell Publishing; 2014.
• Nelson N., Ben Shem A. The complex architecture of oxygenic photosynthesis. Nat. Rev. 2004;5:1–12. doi: 10.1038/nrm1525. - DOI - PubMed
• Raines C. The Calvin cycle revisited. Photosynth. Res. 2003;75:1–10. doi: 10.1023/A:1022421515027. - DOI - PubMed
• Ruban A.V. Evolution under the sun: optimizing light harvesting in photosynthesis. J. Exp. Bot. 2015;66:7–23. doi: 10.1093/jxb/eru400. - DOI - PubMed

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Home — Essay Samples — Science — Photosynthesis — Photosynthesis and Cellular Respiration

Photosynthesis and Cellular Respiration

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Published: Feb 12, 2019

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Prompt examples for the "photosynthesis" essays, photosynthesis essay example.

• The Process of Photosynthesis: Breaking It Down Explain the process of photosynthesis in detail, breaking down each step, the key resources involved (light energy, carbon dioxide, water), and the outcomes (glucose and oxygen). How does photosynthesis enable plants to create their own food?
• Photosynthesis vs. Cellular Respiration: Understanding the Differences Compare and contrast photosynthesis and cellular respiration. What are the key distinctions between these two processes? How do plants use these processes differently, and why is it essential for plants to perform photosynthesis during the day and cellular respiration at night?
• The Importance of Photosynthesis for Plant Survival Discuss the critical role of photosynthesis in a plant's survival. How does it provide plants with the necessary energy and nutrients? Explore the potential consequences if a plant were unable to perform photosynthesis.
• Common Misconceptions About Photosynthesis Address common misconceptions or incorrect claims about photosynthesis, such as those mentioned by Mika in the essay. Provide clear explanations to refute these misconceptions and offer accurate information about when photosynthesis and cellular respiration occur in plant cells.
• The Energy Acquisition Strategies of Plants and Animals Compare how plants and animals acquire and utilize energy. Explain the fundamental differences in their energy sources and processes. Why do plants rely on photosynthesis, while animals need to consume other organisms for energy?

Works Cited

• Alberts, B., Johnson, A., Lewis, J., Raff, M., Roberts, K., & Walter, P. (2014). Molecular Biology of the Cell. Garland Science.
• Campbell, N. A., & Reece, J. B. (2017). Biology. Pearson.
• Cox, M. M., & Doudna, J. A. (2017). Principles of Molecular Biology. W. H. Freeman.
• Freeman, S., Quillin, K., Allison, L., Black, M., Taylor, E., & Podgorski, G. (2017). Biological Science. Pearson.
• Lodish, H., Berk, A., Zipursky, S. L., Matsudaira, P., Baltimore, D., & Darnell, J. (2016). Molecular Cell Biology. W. H. Freeman.
• National Science Teachers Association. (2016). Photosynthesis and cellular respiration. NSTA.
• Raven, P. H., Evert, R. F., & Eichhorn, S. E. (2017). Biology of Plants. W. H. Freeman.
• Reece, J. B., Urry, L. A., Cain, M. L., Wasserman, S. A., Minorsky, P. V., & Jackson, R. B. (2014). Campbell Biology. Pearson.
• Sadava, D. E., Hillis, D. M., Heller, H. C., & Berenbaum, M. R. (2014). Life: The Science of Biology. W. H. Freeman.
• Taiz, L., & Zeiger, E. (2013). Plant Physiology. Sinauer Associates.

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Article Contents

Introduction, photosynthesis in plants, algae and cyanobacteria: some basics, modelling chl fluorescence induction in plants, algae and cyanobacteria, modelling the regulatory dependence between the light reactions and the carbon reactions, conclusions, acknowledgements, literature cited.

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Photosynthesis: basics, history and modelling

Since 2019 the legal name of Govindjee is ‘Govindjee Govindjee’.

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Alexandrina Stirbet, Dušan Lazár, Ya Guo, Govindjee Govindjee, Photosynthesis: basics, history and modelling, Annals of Botany , Volume 126, Issue 4, 14 September 2020, Pages 511–537, https://doi.org/10.1093/aob/mcz171

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With limited agricultural land and increasing human population, it is essential to enhance overall photosynthesis and thus productivity. Oxygenic photosynthesis begins with light absorption, followed by excitation energy transfer to the reaction centres, primary photochemistry, electron and proton transport, NADPH and ATP synthesis, and then CO 2 fixation (Calvin–Benson cycle, as well as Hatch–Slack cycle). Here we cover some of the discoveries related to this process, such as the existence of two light reactions and two photosystems connected by an electron transport ‘chain’ (the Z-scheme), chemiosmotic hypothesis for ATP synthesis, water oxidation clock for oxygen evolution, steps for carbon fixation, and finally the diverse mechanisms of regulatory processes, such as ‘state transitions’ and ‘non-photochemical quenching’ of the excited state of chlorophyll a.

In this review, we emphasize that mathematical modelling is a highly valuable tool in understanding and making predictions regarding photosynthesis. Different mathematical models have been used to examine current theories on diverse photosynthetic processes; these have been validated through simulation(s) of available experimental data, such as chlorophyll a fluorescence induction, measured with fluorometers using continuous (or modulated) exciting light, and absorbance changes at 820 nm (ΔA 820 ) related to redox changes in P700, the reaction centre of photosystem I.

We highlight here the important role of modelling in deciphering and untangling complex photosynthesis processes taking place simultaneously, as well as in predicting possible ways to obtain higher biomass and productivity in plants, algae and cyanobacteria.

‘ Complexity is the prodigy of the world. Simplicity is the sensation of the universe. Behind complexity, there is always simplicity to be revealed. Inside simplicity, there is always complexity to be discovered.’ Gang Yu

With limited agricultural land and increasing human population, it is essential to enhance photosynthetic activities. Oxygenic photosynthesis is a very important process, not only because it is the source of our food, fibre and many useful substances, but also because almost all life on the Earth depends on it, either directly or indirectly. Plants, algae and cyanobacteria are oxygenic photosynthetizers that use light energy to generate organic molecules [e.g. glucose (C 6 H 12 O 6 ), sugars, starch] from carbon dioxide (CO 2 ) and water (H 2 O), and release molecular oxygen (O 2 ) into the atmosphere (for a background on photosynthesis see, Eaton-Rye et al ., 2012 ; Blankenship, 2014 ; Shevela et al. , 2019 ):

Note that the above global equation of photosynthesis emphasizes that the oxygen molecules released into the atmosphere originate from water oxidation, not from carbon dioxide, as established using 18 O-labelled water ( Ruben et al. , 1941 ).

This process starts in the thylakoid membrane (TM) with two light reactions taking place simultaneously at photosystem (PS) II and PSI reaction centres (RCs; for PSII and PSI, see the review by Nelson and Junge, 2015 ). The light energy absorbed by pigment–protein antenna complexes of the PSs is converted, with very high efficiency, into redox chemical energy; a small part is, however, dissipated as heat (internal conversion), and as chlorophyll (Chl) fluorescence (2–10 %, Latimer et al. , 1956 ). Furthermore, water is oxidized to oxygen, and NADP + is reduced to NADPH, and, in addition, ATP is produced ( Rabinowitch and Govindjee, 1969 ; Blankenship, 2014 ; Shevela et al. , 2019 ). Both NADPH and ATP are then used for CO 2 assimilation in the stroma (for a historical background of the Calvin–Benson cycle, see, Bassham, 2005 ; Benson, 2005 ); here, Rubisco (ribulose 1,5-bisphosphate carboxylase/oxygenase) is a key enzyme, which catalyses the fixation of CO 2 on a five-carbon compound, RuBP (ribulose 1,5- bis phosphate). A diagram of the photosynthetic apparatus and the electron transport (ET) reactions is shown in Fig. 1 .

Diagram of the photosynthetic apparatus and electron transport (ET) pathways in plants and algae. Four major protein complexes in the thylakoid membrane (TM) participate in the production of ATP and nicotinamide adenine dinucleotide phosphate in reduced form (NADPH), needed for the Calvin–Benson cycle to fix CO 2 to produce sugars: two photosystems (PSII and PSI) connected in series via the cytochrome (Cyt) b 6 /f, and the ATP synthase. Light is absorbed simultaneously by pigments in the light harvesting complexes of PSI and PSII (LHCI and LHCII); excitation energy is transferred to reaction centre (RC) P700 (in PSI) and P680 (in PSII), where primary charge separation takes place, initiating a chain of redox reactions. PSII functions as a water/PQ (photo)-oxidoreductase, which has a manganese complex [Mn 4 O 5 Ca], and a tyrosine-161 (Y Z ), located on D1 protein on the electron donor side, as well as pheophytin (Pheo), plastoquinones Q A and Q B , and a non-haem (heme) iron binding a bicarbonate ion (HCO 3 ‒ ) on the electron acceptor side. By contrast, PSI is a plastocyanin (PC)/ferredoxin (Fd) (photo)-oxidoreductase; it uses reduced PC as an electron donor, and a particular Chl a molecule (A 0 ), vitamin K 1 (A 1 ), and three non-haem iron–sulfur centres (shown in the figure as Fe-S) are on the acceptor side of PSI. The Cyt b 6 /f complex includes a Cyt f, a Rieske iron–sulfur protein (Fe-S), two cytochromes b (Cyt b p and Cyt b n ) that participate in the oxidation and reduction of PQH 2 and PQ: PQH 2 is oxidized at the Q p -site by Cyt b p , while PQ is reduced at the Q n -site by Cyt b n . The Q p - and Q n -sides are also called Q o - and Q i -sides, respectively. Besides the linear ET flow from water to NADP + , there are several pathways leading to electron donation to alternative electron acceptors: cyclic electron flow (CEF) around PSI mediated by Fd (involving Fd-NADP + -reductase, FNR, and a proton gradient regulator, PGR5), or NADPH (via NADPH dehydrogenase, NDH); water–water cycle (WWC); chlororespiration (through the plastid terminal oxidase, PTOX); and the malate valve (through malate dehydrogenase, MDH). The proton motive force ( pmf ) [consisting of the proton concentration difference (ΔpH) and the electric potential (ΔΨ) across TM] is used by ATP synthase to produce ATP from ADP and phosphate (P i ); in the pmf formula, R is the gas constant, F is the Faraday constant, and T is the absolute temperature (in K). Modified from Alric (2010) .

The availability of high-performance computers and detailed knowledge of the various steps of photosynthesis have provided new opportunities to use mathematical modelling to better understand the dynamics of this process (see reviews by Lazár and Schansker, 2009 ; Jablonsky et al. , 2011 ; Stirbet et al. , 2014 ). In addition, several studies ( Zhu et al. , 2010 ; Long et al ., 2006 , 2015 ; Ort et al. , 2015 ; South et al. , 2018 ; Simkin et al. , 2019 ) strongly support the idea that the photosynthetic processes can be improved through genetic engineering to increase the yield potential of various crops (see also Rosenthal et al. , 2011 ; Simkin et al ., 2015 , 2017 ; Kromdijk et al. , 2016 ; McGrath and Long, 2016 ). Furthermore, mathematical modelling can be used to predict opportunities for specific genetic modifications and devise optimized engineering designs to improve photosynthesis ( Zhu et al. , 2007 ).

In this review, we first provide a background of oxygenic photosynthesis that forms the basis of its modelling. We then discuss a few selected studies on mathematical models describing photosynthetic processes. Partial reactions of photosynthesis have been often modelled separately, such as: (1) the primary photochemical reactions (e.g. Schatz et al. , 1988 ; Roelofs et al. , 1992 ); (2) water ‘splitting’ reactions (e.g. Kok et al. , 1970 ; Mar and Govindjee, 1972 ; Jablonsky and Lazár, 2008 ; Shen, 2015 ); (3) reduction of Q B , the secondary plastoquinone (PQ) acceptor of PSII (e.g. Velthuys and Amesz, 1974 ; Petrouleas and Crofts, 2005 ); and (4) the redox reactions of the PQ pool at the Cyt b 6 /f complex (which may include the Q-cycle; see e.g. Mitchell, 1975 ; Cramer et al. , 2011 ). However, in this review we mainly discuss larger models, which include several steps, providing information on complex photosynthetic processes.

Early discoveries

Not much was known about photosynthesis before the 20th century; for earlier discoveries in photosynthesis see chapter 2 in Rabinowitch (1945) and the timeline in Govindjee and Krogmann (2004) . The key discoveries were as follows (see chapter 1 in Rabinowitch and Govindjee, 1969 ): Jan van Helmont (1648) showed that plant growth was mainly from the water that plants had absorbed; it was only later that Nicolas Théodore de Saussure (1804) clearly showed that water was an essential reactant of photosynthesis. Joseph Priestley (1776) showed, in elegant experiments, that plants produced ‘oxygen’ (then called de-phlogisticated air) needed by a mouse to live, whereas Jan Ingen-Housz (1773) convincingly established that light was necessary for photosynthesis. The role of CO 2 in photosynthesis was shown by Jean Senebier (1782), whereas the synthesis of starch was shown by Julius von Sachs (1862, 1864). However, the involvement of chlorophyll (Chl) in this process has a long history. For some of the earliest concepts, we must remember to mention Pierre Joseph Pelletier and Joseph Bienaimé Caventou (1817, 1818), and René Joachim Henri Dutrochet (1837). However, Theodor Engelmann (1882) provided the first action spectrum of photosynthesis, showing that red and blue light, absorbed by Chl, produce oxygen (see figure 1.1 and its description in Shevela et al. , 2019 ).

Physiological and biochemical advances

An understanding of how photosynthesis functions began only after 1900, but by 1960 a basic model at the molecular level, including generation of NADPH and ATP as well as the steps leading to the assimilation of CO 2 to produce carbohydrates, was established (see Govindjee and Krogmann, 2004 ; Govindjee et al ., 2005; Nickelsen, 2016 ).

By measuring photosynthesis as a function of light intensity, Frederick Frost Blackman (1905) suggested that photosynthesis consists of two separate phases: a light-dependent phase (i.e. so-called ‘light’ reactions), and a temperature-dependent biochemical phase (so-called ‘dark’ reactions, or ‘Blackman reaction’; see Warburg and Uyesugi, 1924 ). However, because CO 2 fixation uses NADPH and ATP, formed in the light phase, these so-called ‘dark’ reactions are also light-dependent. Moreover, many enzymes, involved in CO 2 assimilation reactions, function only when they are ‘light-activated’, being controlled through the ferredoxin:thioredoxin reductase (FTR) system (see reviews by Buchanan et al. , 2002 ; Nikkanen and Rintamäki, 2019 ). Therefore, the term ‘dark phase’ is inappropriate; Buchanan (2016) has proposed the use of ‘carbon reactions’ for ‘dark reactions’. Furthermore, the true ‘light reactions’ end after the primary charge separation steps in the RCs; both the electron transfer and the proton transfer reactions, in principle, can occur in darkness.

Cornelis B. van Niel (1931, 1941) showed that certain photosynthetic bacteria use H 2 S instead of H 2 O as an electron donor, producing sulfur instead of oxygen, and the global reaction of photosynthesis is:

where A is sulfur in sulfur bacteria and oxygen in plants, algae and cyanobacteria. By analogy with photosynthetic bacteria, van Niel suggested that O 2 released by plants is derived from H 2 O rather than CO 2 . This was confirmed by Sam Ruben, Merle Randall, Martin Kamen and James Logan Hyde (see Ruben et al. , 1941 ), based on results using 18 O-labelled water.

Chlorophyll a fluorescence

As mentioned earlier, in addition to primary photochemistry, photosynthetic organisms lose some energy as heat (internal conversion) and as light (fluorescence). Fluorescence is radiative deactivation of (usually) the first singlet excited state of a molecule to the ground state. Kautsky and Hirsch (1931) discovered what others later called the ‘Kautsky effect’, which is Chl a fluorescence induction (ChlFI; see Govindjee, 1995 ). Kautsky and Hirsch observed (visually) transitory variations in Chl a fluorescence (ChlF) emitted by samples that were illuminated after a period of darkness; this ChlF has an increasing phase (peak, ~1 s) followed by a slower (5–10 min) decreasing phase. McAlister and Myers (1940) made an important observation by showing an inverse relationship between ChlF emission and CO 2 uptake. These ChlF transients were then studied, among other places, in the Photosynthesis Laboratory at the University of Illinois, Urbana-Champaign (beginning in the 1950s; see Govindjee and Papageorgiou, 1971 ; Papageorgiou, 1975 ; Govindjee and Satoh, 1986 ; Papageorgiou et al. , 2007 ). Because ChlF has been shown to be directly or indirectly affected by complex physical and biochemical processes taking place during photosynthesis, analysis of ChlFI curves is of importance in photosynthesis research (see reviews by Krause and Weis, 1991 ; Lazár, 1999 , 2015 ; Strasser et al. , 2004 ; Stirbet and Govindjee, 2011 ; Stirbet et al. , 2018 ).

Photosynthetic unit (antenna and reaction centres): excitation energy transfer

An essential concept related to the light phase of photosynthesis is ‘photosynthetic unit’. It was developed based on the crucial discovery by Emerson and Arnold (1932 a , b ) that ~2400 Chl molecules cooperate to evolve one molecule of O 2 , while the minimum quantum requirement for the evolution of one O 2 molecule was 8–10 ( Emerson, 1958 ; for the history of this discovery, see Nickelsen and Govindjee, 2011 ; Nickelsen, 2016 ). Gaffron and Wohl (1936) suggested the existence of ‘photosynthetic units’, where light energy absorbed by any antenna molecule is transferred as excitation energy among the pigment molecules, until finally it is trapped with high efficiency by a limiting enzyme (a ‘photoenzyme’, as implied by Emerson and Arnold, 1932 b ), which is equivalent to what we now call reaction centre (RC), a term introduced by Duysens (1952) . Here, the primary charge separation (i.e. photochemistry) takes place (see e.g. Myers, 1994 ; Govindjee and Krogmann, 2004 ). Experimental evidence for excitation energy transfer (EET) between photosynthetic pigments was initially obtained by comparing action spectra of photosynthesis and of sensitized ChlF in green, brown and red algae (see chapters 10–12 in Rabinowitch and Govindjee, 1969 ). We now have much more detailed knowledge on the molecular mechanisms of electronic EET in antenna, as well as on exciton trapping by the RCs (e.g. Croce and van Amerongen, 2013 ; van Amerongen and Croce, 2013 ; Roden et al. , 2016 ; Mirkovic et al. , 2017 ; Chan et al. , 2018 ).

Taking things apart

Robert Hill (1937) found that the ‘light phase’ of photosynthesis can operate independently from the ‘dark phase’ (the carbon reaction phase), since isolated chloroplasts can evolve O 2 in the presence of artificial electron acceptors [this reaction is called the ‘Hill-reaction’ in honor of Robert (Robin) Hill], even in the absence of CO 2 . This concept led to a ‘modularization’ in the study of photosynthesis ( Nickelsen, 2016 ), since even if these two partial processes are interrelated, the tendency after 1940 was to investigate them separately. Note that Mehler (1951) had found that molecular oxygen is also a Hill electron acceptor, and this reaction, called the ‘Mehler reaction’, has been shown to play an important role in photoprotection of photosynthetic organisms ( Miyake, 2010 ).

The carbon reactions

The long-lived form of radioactive carbon, 14 C, was discovered by Samuel Ruben and Martin Kamen (1941) . This radioactive isotope was used to decipher the major pathway of CO 2 reduction by photosynthetic organisms, by Andrew Benson (who did most of the early pioneering work, using 14 C), Melvin Calvin, James A. Bassham and co-workers (see Calvin et al. , 1950 ; Calvin, 1989 ; Bassham, 2005 ; Benson, 2005 ). For example, they found that ribulose 1,5-bisphosphate (RuBP; a 5-C sugar) was the acceptor of CO 2 ; the first stable product of CO 2 reduction was 3-phosphoglyceraldehyde (G3P; a triose phosphate); and that there was a cycle to regenerate the RuBP. Melvin Calvin received the Nobel Prize in Chemistry in 1961 for these discoveries; we are of the opinion that Andrew Benson should have been a co-recepient.

Photophosphorylation

Daniel Arnon et al . (1954 a , b ) showed that isolated chloroplasts can produce ATP in light; in addition, they showed that intact isolated chloroplasts can even perform complete photosynthesis (i.e. CO 2 fixation). Furthermore, Allen et al. (1958) found that photophosphorylation can be ‘cyclical’ (i.e. ATP is produced when there is a cyclic ET, which was shown to involve cyclic electron flow around PSI via Cyt b 6 /f, CEF-PSI), or when there is ‘non-cyclic’ [i.e. during linear electron flow (LEF) from PSII to PSI) (see also Arnon, 1984 ; Tagawa et al. , 1963 ). A third pathway, labelled as ‘pseudo-cyclic photophosphorylation’, was also established, in which molecular oxygen plays the role of a terminal electron acceptor (i.e. the Mehler reaction; Mehler, 1951 ; Heber, 2002 ). Furthermore, a coupling mechanism between ATP synthesis and the ET, also in chloroplasts, was demonstrated by Dave Krogmann, Mordhay Avron and André Jagendorf (see Krogmann et al. , 1959 ). Note that the chloroplast coupling factor (CF1) for photophosphorylation, today known as ATP synthase, was discovered by Avron (1963) .

The two-light reaction and the two-pigment system concept

The idea of two light reactions and two types of PSs had its beginning in the 1943 experiments of Robert Emerson and Charleton Lewis on the ‘red drop’ in the action spectrum of the quantum yield of photosynthesis ( Emerson and Lewis, 1943 ) and in the 1957 ‘Emerson enhancement’ effect, that is when the rate of photosynthesis in two lights given together was higher than the sum of the rates of photosynthesis measured when the two lights were given separately ( Emerson et al. , 1957 ; also see: Govindjee and Rabinowitch, 1960 ); this discovery led to the well-known ‘Z’-scheme of photosynthesis ( Hill and Bendall, 1960 ; for the evolution of the Z-scheme, see Govindjee et al. , 2017 ). The very first Chl electron donors in the two PSs are P700 for PSI (identified also by an absorbance change around 705 nm; see Kok, 1956 ; Govindjee and Renger, 1993 ), and P680 in PSII, first suggested by Krey and Govindjee (1964) and shown to exist by Döring et al. (1969) . Key experiments proving the Z-scheme were provided by Duysens et al. (1961) on the red alga Porphyridium cruentum , who showed the antagonistic effect of light 1 and light 2 on the redox state of cytochrome (Cyt). (Here, light absorbed by PSI was ~680 nm, and that absorbed by PSII was ~562 nm.) Furthermore, based on flashing light experiments, Witt et al . (1961 a , b ) provided evidence for the kinetics and on the existence of other intermediate steps in the Z-scheme; details of the ET components involved in the photosynthetic electron transport chain (PETC) are given in Fig. 1 . However, of course, the physical confirmation for the existence and organization of the two PSs was the isolation and characterization via X-ray crystallography of the high-resolution spatial structure of PSII (e.g. Zouni et al. , 2001 ) and PSI (e.g. Jordan et al. , 2001 ).

Evidence from Chl a fluorescence measurements

Additional evidence for the two-pigment-system/two-light-reaction scheme in oxygenic photosynthesis was obtained by Govindjee et al. (1960) on Chlorella cells, using ChlF measurements. They showed an antagonistic effect of light 1 (i.e. predominantly absorbed by PSI) and light 2 (i.e. predominantly absorbed by PSII) on ChlF: addition of far-red light (light 1) to a shorter wavelength light (light 2) caused a decline (rather than an enhancement) of ChlF yield, compared to that produced by the two beams separately. As an explanation of this effect, Duysens and Sweers (1963) proposed that light 2 reduces a quencher Q, while light 1 oxidizes Q ‒ back to Q. The quencher theory of Duysens and Sweers was based not only on ChlF data published by Govindjee et al. (1960) , but also by Butler (1962) , who showed that variable fluorescence is mostly from PSII, and far-red light, absorbed by PSI, gives a smaller amount of PSI fluorescence. The quencher Q (named X-320, but now labelled Q A ) was identified using single turnover flashes, and has an absorption spectrum with maximal spectral changes in the UV, at 270 and 320 nm ( Stiehl and Witt, 1968 ). In several experimental studies ( Stiehl and Witt, 1969 ; van Gorkom, 1974 ; see also Witt, 2004 ), plastoquinone difference spectra in the near UV (300–350 nm) were similar to light-minus-dark spectra of the first plastoquinone acceptor of PSII (i.e. Q A −• − Q A ). According to Duysens and Sweers (1963) , ChlF is proportional to the fraction of the reduced quencher ([Q A − ]/[Q A ] total ; see a discussion in Stirbet and Govindjee, 2012 ; for other views see, Schansker et al ., 2011 , 2014 ; Magyar et al. , 2018 ). Later, it was shown that several non-photochemical quenching (NPQ) processes take place in parallel with the photochemical quenching (i.e. by Q A ) during the so-called slow (~10 min) phase of the ChlF transient, and the proportionality of the fluorescence yield with [Q A − ]/[Q A ] total , observed during the initial (<1 s) Chl fluorescence rise, is lost (see below the section On NPQ of the excited state of Chl). Real advances in the study of these NPQ processes became possible only after Ulrich Schreiber developed a pulse-amplitude modulated (PAM) fluorescence instrument (Walz, Effeltrich, Germany) that could be used on leaves in the presence or the absence of actinic light ( Schreiber, 1986 ; Schreiber et al. , 1986 ).

Vredenberg and Duysens (1963) observed that closure of RCs is accompanied by an increase in fluorescence yield of bacteriochlorophyll in Rhodospirillum rubrum , a purple anoxygenic photosynthetic bacterium, and concluded that several RCs share the same antenna. In an oxygenic photosynthesizer, the green alga Chlorella , Anne and Pierre Joliot ( Joliot and Joliot, 1964 ) measured the rate of steady-state oxygen evolution, and correlated it with the fraction of active PSIIs (see also Joliot and Joliot, 2003 ). Joliot and Joliot (1964) observed that both the oxygen yield and the fluorescence yield are related, in a hyperbolic manner, to the fraction of closed PSII centres; this suggested that there is an energetic connectivity within PSIIs, that is an excitation visiting a closed PSII (i.e. with Q A reduced) is redirected to another PSII. In this manner, the trapping cross-section of the open PSIIs increases as their neighbouring PSIIs become closed (see a review on PSII excitonic connectivity by Stirbet, 2013 ). Joliot and Joliot (1964) also derived theoretical equations describing the dependence of the ChlF yield (Φ  F ) and the photochemical yield (Φ  P ) on the fraction of open PSIIs, which included a connectivity parameter ( p ) for the probability of excitation energy transfer from a closed PSII to a neighbouring PSII (either closed or open). This was followed by publication of detailed papers on PSII excitonic connectivity by Paillotin (1976) , Strasser (1978) and Butler (1980) , the last two describing the process, using bipartite and tripartite PSII models of Butler and co-workers ( Butler and Kitajima, 1975 ; Butler and Strasser, 1977 ). Later, Lavergne and Trissl (1995) and Trissl and Lavergne (1995) extended the concept of PSII excitonic connectivity, using an exciton–radical pair equilibrium model. The latter is equivalent to the reversible radical pair (RRP) model of Schatz et al. (1988) ; it assumes rapid exciton equilibration between all PSII pigments, including P680, and describes primary photochemistry (charge separation, recombination and stabilization) leading to closed PSII RCs. The major feature of the RRP model is equilibrium , i.e. reversibility of charge separation, meaning fast charge separation followed by fast charge recombination, in both the open and the closed PSII centres (see Fig. 2 ).

Scheme showing the RRP (reversible radical pair) model and related reactions. The original RRP model is represented by the reactions on lines I and II, which are reactions occurring in an open PSII RC (when Q A is initially oxidized) and a closed PSII RC (when Q A is initially reduced), respectively. (L–P680)* denotes Chls in the light harvesting antenna of PSII (L) plus P680, which are in ultrafast excitation kinetic equilibrium, the asterisk (*) indicating the excited state. The rates constants are: k L , overall rate constant of antenna excitation; k 3 , overall rate constant of the excited state deactivation through heat dissipation and ChlF emission; k 1 o and k 1 c , rate constants of the primary charge separation in open and closed PSIIs, respectively; k -1 o and k -1 c , rate constants of the radiative (i.e. to the excited state) charge recombination between P680 + and Pheo − in open and closed PSIIs, respectively; k 2 o , rate constant of charge stabilization in an open PSII, i.e. the ET from Pheo ‒ to Q A ; k 2 c , rate constant of non-radiative (i.e. to the ground state) charge recombination between P680 + and Pheo ‒ in a closed PSII. The scheme presented here also includes excitation energy transfer (the energetic connectivity) between open and closed PSIIs (rate constant k UU ) and reversible reduction of P680 + by Y Z (rate constants k Pred and k Pox ), as well as the reduction of Y Z + by the manganese cluster of the oxygen-evolving complex (OEC; rate constant k Yred ), which produces an S-state transition from S i to S i+1 , where S i and S i+1 represent particular S-states. Modified from Lazár and Schansker (2009) .

ATP synthesis

Peter Mitchell (1961 a , b ) proposed a chemiosmotic theory for phosphorylation, which suggests that a ‘proton motive force’ ( pmf ), i.e. the electrochemical potential of protons, couples the ET reactions with ATP synthesis (from ADP and inorganic phosphate, P i ). Mitchell received the Nobel Prize in Chemistry in 1978 for this hypothesis. Later, Paul Boyer and John E. Walker received the Nobel Prize in Chemistry in 1997 for their work on the structure of F1 mitochondrial ATPase and the mechanism of ATP synthesis (see e.g. Boyer, 2002 ). Hind and Jagendorf (1963) (see also Jagendorf and Uribe, 1966 ) showed how photosynthetic cells convert light energy into free energy stored in the ATP molecule on the basis of the chemiosmotic theory, particularly the ΔpH component. The pmf has two components, one due to the trans-thylakoid electric potential difference (i.e. the membrane potential, ΔΨ), and the other due to the trans-thylakoid difference in proton concentration (ΔpH), which builds up during water splitting reactions on the lumen side of PSII, and the translocation of stroma protons to the lumen during PQ pool reduction by PSII, and by Cyt b 6 /f (including the Q-cycle; Mitchell, 1975 ) in relation to both the linear and the cyclic photosynthetic ET (see Fig. 1 , and a historical review by Jagendorf, 2002 ). We remind the readers that just as André Jagendorf’s work proved the importance of the ΔpH component (of pmf ) for ATP synthesis, Wolfgang Junge’s work proved the importance of ΔΨ in making ATP (see mini-review by Junge, 2004 ). However, a high ∆Ψ component of the pmf was also shown to affect the equilibrium of redox reactions within PSII, and has been linked to higher rates of PSII charge recombination in vivo , and subsequent photodamage due to increased production of singlet oxygen ( Davis et al. , 2016 ). On the other hand, low pH has been shown to inactivate oxygen evolution ( Schlodder and Meyer, 1987 ); furthermore, release of Ca 2+ from the oxygen evolving complex (OEC) has also been suggested to be the cause of this inactivation ( Ono and Inoue, 1988 ; Krieger and Weis, 1993 ). For recent research (and reviews) on ΔΨ and ΔpH across the TM see, Strand and Kramer (2014) , Kaňa and Govindjee (2016) , and Lyu and Lazár (2017 a , b ).

Oxygen evolution

The key experiments that preceded the discovery of the water splitting mechanism, leading to O 2 evolution and P680 + reduction in PSII, were done by Pierre Joliot and co-workers ( Joliot, 1965 ; Joliot et al. , 1969 ). Joliot et al. (1969) discovered period 4 oscillations in oxygen evolution in algal suspensions when they were exposed to a sequence of single turnover (ST) saturating light flashes. These results were explained by Bessel Kok et al. (1970) , who proposed a model (now known as Kok’s oxygen clock model, or the Kok–Joliot model to many), in which the formation of oxygen requires sequential accumulation of four positive charges on the OEC, which cycles through five redox states, labelled as S 0 , S 1 , S 2 , S 3 and S 4 (see Fig. 3 ). For the history of this discovery, see Renger and Govindjee (1993) and Joliot (2003) . The first evidence for the participation of Mn in the S-states was obtained by Chuck Dismukes and Yona Siderer (1980) , who obtained electron paramagnetic resonance (EPR) signals for the same. For a review on the functioning of the OEC, see Najafpour et al . (2012) . For a recent review on oxygen evolution, see Lubitz et al. (2019) .

Highly simplified scheme of Kok’s oxygen clock model; misses and double hits are not shown. S i (i = 0, 1, 2, 3, 4) represent the particular S-states of the manganese cluster of OEC. The S 4 -state is assumed to be kinetically indistinguishable from the S 0 -state. During an S-state transition, Y Z + (formed through PSII reactions) is reduced (with rate constants k 01 , k 12 , k 23 and k 30 ). Modified from Lazár and Schansker (2009) . For a review, including the involvement of manganese, see Najafpour et al. (2012) .

Mechanistic models for early events in photosynthesis

Bay and Pearlstein (1963) provided one of the first mathematical models of the exciton kinetics and trapping in a photosynthetic system; it was based on electronic excitation transfer, FRET (Förster resonance energy transfer; see Förster 1946 , 1948 ; also see a historical review by Clegg, 2006 ). According to this model, the electronic excitation energy moves in a so-called ‘random walk’, hopping from one Chl to another Chl in the antenna, until it is trapped by an RC, or is dissipated as heat or fluorescence (also see: Govindjee, 2004 ). Starting from FRET, other more complex and elegant theories have now been developed to characterize the exciton dynamics in antenna (e.g. Engel et al ., 2007 ; Ishizaki and Fleming, 2009 ; Clegg et al. , 2010 ; Fassioli et al. , 2014 ).

On ‘state transition’ for regulation of balanced excitation in the two photosystems

State transition, a light-adaptive phenomenon that optimizes photosynthesis by synchronizing the turnover rates of PSII RCs and of PSI RCs, when there is an excitation imbalance between their antenna, was discovered by Cecilia Bonaventura and Jack Myers (1969) in Chlorella and, independently, by Norio Murata (1969 a , b ) in the red alga Porphyridium cruentum and spinach chloroplasts. The equilibration of PSII and PSI activities takes place through adjustment of the relative size of their antenna: During a transition from ‘state 1’ to ‘state 2’, the absorption cross-section (CS) of PSII antenna (which provides information on the PSII-specific rates of light absorption and represents an ‘apparent’ measure of PSII antenna size in situ , in units of Å  2 per PSII centre; see Osmond et al. , 2017 ) decreases and that of PSI antenna increases, while the opposite occurs during transition from ‘state 2’ to ‘state 1’. The result is: the overall ChlF yield decreases in ‘state 2’ and increases in ‘state 1’, because, at room temperature, PSI has a much lower ChlF yield than PSII ( Butler, 1962 ). State transitions have been shown by John Allen and collaborators to be regulated by the redox state of the PQ pool ( Allen et al. , 1981 ; see Allen, 2002 ): the transition from ‘state 1’ to ‘state 2’ is triggered by the reduction of the PQ pool, and the transition from ‘state 2’ to ‘state 1’ is triggered by the oxidation of the PQ pool. In plants and algae, the controlling events take place at the Qp site of Cyt b 6 /f (i.e. the binding site of PQH 2 ; see Zito et al. , 1999 ), where the PQ redox-state is sensed, which triggers the activation or inactivation of a protein kinase ( Allen et al. , 1981 ): PQ pool reduction activates the protein kinase, and thus induces phosphorylation of mobile light harvesting complex (LHC) II, followed by its attachment to PSI antenna, while PQ pool oxidation inhibits the protein kinase, followed by dephosphorylation of the mobile LHCIIs by a phosphatase, and their re-attachment to PSII antenna (see Fig. 4 and reviews by Papageorgiou and Govindjee, 2011 ; Rochaix, 2014 ). For background on PSII, see Wydrzynski and Satoh (2005) , on PSI, see Golbeck (2006) , and on the Cyt b6f complex, see Cramer and Kallas (2016) . Note that extensive dynamic changes in the organization and structure of the TMs are associated with state transitions, which include PSII antenna dissociation after LHCII phosphorylation by Stt7/STN7 kinases, or association with PSII after dephosphorylation by PPHI/TAP38 phosphatases (see above, and Iwai et al. , 2010 ). However, new research suggests that these protein kinases and phosphatases can also affect the likelihood of cyclic ET around PSI (see Wood et al. , 2019 ). On the other hand, Pribil et al. (2018) have shown that the changes in the shape of grana stacks are mediated by the CURVATURE THYLAKOID1 (CURT1) protein complexes, which were shown to facilitate adjustments in membrane curvature at the grana margins in a dose-dependent manner.

Diagram of the mechanism of state transitions in plants and algae. In the diagram, the system is shown to be initially in ‘state 1’, with the absorption cross section (CS) of photosystem (PS) II being larger than that of PSI (it will have high Chl fluorescence yield because Chl in PSII is much more fluorescent than in PSI). During illumination, the plastoquinone (PQ) pool will be reduced by PSII because of higher absorption there. This is sensed by the Cyt b 6 /f (via its PQH 2 -oxidizing site, Q p ), and leads to activation of a kinase ( Stt7/STN7 ) and phosphorylation of the mobile light harvesting complexes of PSII (LHCII), which then associate with the PSI antenna. The reverse occurs when the system is in ‘state 2’ initially, with the absorption CS of PSI being larger than that of PSII. Here, oxidation of the PQ pool by PSI during illumination will be sensed by the Cyt b 6 /f, which leads to the inactivation of kinases, followed by de-phosphorylation of the mobile LHCIIs (by the phosphatases Pph1/TAB38 ) and their relocation to PSII. Abbreviations: A 0 and A 1 , a particular Chl a molecule and a vitamin K1 molecule, respectively; Fe-S, three non-haem (heme) iron–sulfur centres; Fd, ferredoxin; Q A and Q B , plastoquinone electron acceptors of PSII; NADP + and NADPH, nicotinamide adenine dinucleotide phosphate in oxidized and reduced state; P680 and P700, reaction centre chlorophylls/primary electron donors of PSII and PSI; PC, plastocyanin. Figure modified from Allen (2003) and Rochaix (2014) .

Two-electron gate on the electron acceptor side of PSII, and the requirement of bicarbonate

Bernadette Bouges-Bocquet (1973) and Bruno Velthuys and Jan Amesz (1974) independently discovered the two-electron gate (TEG) mechanism on the electron acceptor side of PSII in plants; it describes ET from Q A to Q B (see also Robinson and Crofts, 1983 ). As mentioned above, both Q A and Q B are PQs, but Q A is a one-electron acceptor, and is permanently bound to the D2 protein of PSII. By contrast, Q B is a two-electron acceptor that is bound to the D1 protein of PSII; it is strongly bound only when it is in Q B − -state, but is weakly bound in its fully oxidized state (Q B ), and very weakly bound when in the fully reduced state (Q B H 2 ). Following the primary charge separation: (1) Q A is reduced to Q A − (via pheophytin, Pheo; discovered by Vyacheslav Klimov et al. , 1977 ); (2) Q A − then reduces Q B to Q B − , and the latter remains tightly bound to D1; (3) after another light reaction, Q B − is then further reduced by Q A − , becoming fully reduced to Q B H 2 (PQH 2 ), after the addition of two protons; and finally (4) because Q B H 2 is loosely bound to D1, it is released in the membrane and replaced by another PQ molecule from the PQ pool (see Fig. 5 , and reviews discussing light-induced PQ pool reduction by PSII by Cardona et al. , 2012 ; Müh et al. , 2012 ). A bicarbonate ion has been shown to have a very important role in the functioning of the TEG and Q B H 2 formation ( Wydrzynski and Govindjee, 1975 ; see reviews by Govindjee and van Rensen, 1978 ; van Rensen, 2002 ; Shevela et al. , 2012 ). A similar TEG was also discovered in bacteria, independently by Colin Wraight and André Vermeglio (see Vermeglio, 2002 ), but there is no bicarbonate effect there (see Wang et al. , 1992 , and references therein). Note that the TEG model, the Kok model and the RRP model are important partial models that are used in more complex (or complete) models describing the photosynthetic ET (e.g. Nedbal et al. , 2009 ).

Scheme of the two-electron gate (TEG) model and related reactions. The two-electron gate mechanism, by which electrons are transferred from Q A to Q B , is represented by the reactions on line II. The rate constants are: k L , overall rate constant of Q A reduction; k AB1 and k AB2 , rate constants of ET from the reduced Q A to Q B and Q B ‒ , respectively; k BA1 and k BA2 , rate constants of backward ET from Q B ‒ and Q B 2‒ to Q A , respectively. The reactions above and below line II describe the reversible exchange of doubly reduced Q B (after its double protonation, which is implicitly assumed) with a PQ molecule from the PQ pool (rate constants k (B/PQ)exch and k (PQ/B)exch ); the reversible oxidation of the plastoquinol (rate constants k ox and k red ) is implicitly assumed to be the result of chlororespiration and cyclical electron flow around PSI. Modified from Lazár and Schansker (2009) .

On NPQ of the excited state of Chl

In general, NPQ processes can be defined as processes that decrease ChlF through mechanisms other than photochemical quenching (i.e. Q A quenching; e.g. Müller et al. , 2001 ; for a time line, see Papageorgiou and Govindjee, 2014 ). In this sense, the avoidance movement of chloroplasts in the leaf under high light conditions (i.e. qM; Dall’Osto et al. , 2014 ; Baránková et al. , 2016 ; Semer et al ., 2018 , 2019 ), the state 1 to state 2 transition (qT 12 ; see above), as well as the photoinhibition (qI), initiated by the photodamage of PSII ( Tyystjärvi et al. , 2005 ; Murata et al. , 2012 ; Tyystjärvi, 2013 ), would all be considered to be NPQ processes. However, according to Papageorgiou and Govindjee (2014) , it is preferable to consider as NPQ processes only those in which the excess energy accumulated as singlet excited Chl a ( 1 Chl a *) in PSII antenna is dissipated as heat (see Kitajima and Butler, 1975 ), such as the quickly reversible ‘high-energy non-photochemical quenching’ (qE), which develops in a few seconds and relaxes in 1–2 min (see Jahns and Holzwarth, 2012 ; and chapters in Demmig-Adams et al ., 2014 ), or other less clearly elucidated sustained forms of ChlF quenching processes (such as qH; Malnoë, 2018 ). This type of NPQ is induced by low lumen pH, being fully activated only after the pmf is established across the TM, when the TM is in a ‘high-energy’ state; it regulates the utilization of the light energy in PSII antenna in order to reduce photo-oxidative events that can damage the RCs. The exact relationship between lumen pH and NPQ is not fully understood; however, see discussions by Johnson (2011) and Zaks et al. (2013) . There are three main requirements for qE activation: (1) a trans-thylakoid ΔpH formed in light ( Wraight and Crofts, 1970 ; Briantais et al. , 1979 ); (2) the xanthophyll (VAZ) cycle, particularly the conversion of the carotenoid violaxanthin (V) to antheraxanthin (A) and zeaxanthin (Z) ( Yamamoto et al. , 1962 ; Yamamoto and Higashi, 1978 ); and (3) the PSII protein subunit S (PsbS) ( Li et al. , 2000 ; Brooks et al. , 2014 ). Barbara Demmig-Adams et al. (1989) (see also a historical review by Demmig-Adams, 2003 ) were the first to demonstrate that the extent of qE is proportional to the Z content of leaves; Demmig et al. (1987) further showed a correlation between Z and a form of qI manifested as a dark-sustained NPQ. Thus, they proposed that Z, which is derived from V in the xanthophyll cycle, is the link between the high energy state of the membrane and the heat dissipation of excess excitation energy of Chl a (see also Rees et al. , 1989 , 1992 ). In the xanthophyll cycle, the content of V decreases during illumination and is restored in darkness: Light ↝V⇄A⇄Z⇐ Dark . Violaxanthin deepoxidase (VDE) has a higher affinity for A than for V ( Yamamoto and Higashi 1978 ), and binds on the lumen side of the membrane, at pH ≈ 5.0 ( Hager and Holocher, 1994 ), which induces qE. Also, the NPQ kinetics was shown to depend on [Z], its induction being faster and its relaxation being slower when Z is present (see Johnson et al. , 2008 ). Adam Gilmore made an important contribution to the field, which included a successful collaboration with one of us (G) on the effects of intrathylakoid pH and VAZ cycle pigments on Chl a lifetime distributions and intensity in thylakoids ( Gilmore et al ., 1995 , 1998 ; Gilmore, 1997 ). On the other hand, the role of PsbS protein in qE is that of a pH sensor and quenching amplifier, as its amount in plant modulates the maximal qE level, but the underlying event is not yet fully understood ( Horton et al. , 2008 ; Holzwarth et al. , 2009 ; Brooks et al. , 2014 ). However, there is also evidence that qE can be induced in the absence of PsbS ( Johnson et al. , 2011 ), or even xanthophylls ( Johnson et al. , 2012 ), if the lumenal pH is sufficiently low (i.e. lower than the value assumed by the ‘moderate lumen pH paradigm’; see Kramer et al. , 1999 ). Finally, qE in algae is much more species-dependent than in plants. In unicellular green algae, or other algal groups (e.g. diatoms), the qE extent depends on the Light-Harvesting Complex Stress-Related (LHCSR) proteins ( Peers et al. , 2009 ). In most organisms, the LHCSR level is strongly light-dependent, and in some species, such as Chlamydomonas reinhardtii , acclimation to low light leads to very low NPQ levels ( Peers et al. , 2009 ).

Recently, Schreiber et al. (2019) have described a rapidly induced NPQ process during a pulse of high-light intensity in a dilute suspension of Chlorella vulgaris ; they called this process HIQ [high (light) intensity quenching]. The amplitude of the HIQ increases linearly with the effective rate of quantum absorption by PSII, reaching ~8 % of F M (i.e. the maximum Chl fluorescence measured in dark-adapted samples). This quenching rapidly relaxed after the pulse, and was shown to be caused by annihilation of 1 Chl* a by 3 Car* (excited state of a carotenoid in triplet state).

ChlF emitted by plants and algae has little involvement in the process of photosynthesis, being one of the pathways in which excess excitation energy is dissipated by photosynthetic organisms. However, ChlFI kinetics is well recognized to have an intricate connection with many processes taking place during the conversion of light energy into a stable chemical form. Because it is a non-destructive measurement, although indirect, the ChlFI has numerous applications in the study of photosynthesis (see chapters in Papageorgiou and Govindjee, 2004 ), while its modelling is a straightforward way to verify various theories regarding different photosynthetic processes. Note that ChlFI in cyanobacteria is in part affected in different ways by the activity of the photosynthetic apparatus than in plants and algae, and this is due to their structural differences (see Stirbet et al. , 2019 ), but its modelling is not described in this review.

The ChlFI curve has been labeled O-J-I-P-S-(M)-T, where O-J-I-P represents the first fast (<1 s) phase, also known as the fast ChlF rise, and P-S-(M)-T the slower (5–10 min) phase (see Fig. 6 , and a review by Govindjee, 1995 ). Level O (origin) is the first measured minimum fluorescence level; J and I are intermediate inflections; P is the peak; S is the semi-steady state; M is a maximum, which, in plants, at room temperature is often seen only at low light intensities, but has been observed in Arabidopsis thaliana under low (freezing) temperature conditions ( Mishra et al. , 2019 ); and T is a terminal steady state level.

Chlorophyll a fluorescence induction curves measured in leaves of 10-d-old barley ( Hordeum vulgare L.) plants kept in darkness for 20 min before the measurement, shown on a logarithmic time scale (A), and on a linear time scale (B); a.u., arbitrary units. The O, J, I, P, S, M and T steps marked in the figure represent: O, the origin (minimum fluorescence F O ); J and I, intermediary fluorescence levels at 2 and 30 ms (F J and F I ); P, the peak (F P ); S, a semi-steady state level; M, a maximum; and T, the terminal steady state. Measurements were made under continuous red (650 nm) light of 2500 μmol photons m –2 s –1 with a Plant Efficiency Analyser (Hansatech, UK). Modified from Stirbet et al. (2018) .

The fast phase was labelled OIDP ( Munday and Govindjee, 1969 ), as OI 1 I 2 P ( Schreiber, 1986 ) and then OJIP ( Strasser and Govindjee, 1991 ); the O-J-I-P curves are measured only under a high intensity of excitation light. At low light the J step is missing, so that only an O-I-P curve is observed ( Strasser et al. , 1995 ; Tomek et al. , 2001 ). Below, we briefly discuss several models for the O-J-I-P fluorescence rise, as well as for the entire O-J-I-P-S-(M)-T transient or just the slow P-S-(M)-T phase (see also reviews by Lazár, 1999 ; Lazár and Schansker, 2009 ; Stirbet et al. , 2014 ).

Modelling strategy, definition of the Chl fluorescence signal, and some selected partial models of PSII

Mathematical modelling is an essential part of modern biology and can have several purposes. In any experimental study, the measured data provide information about how the explored system works, and based on these, we formulate hypotheses about how the explored system is functioning. By converting the hypotheses into a mathematical model, running the model and comparing the calculated results with experimental data, we can judge if the model describes the data well or not. In this case, the structure of the model (i.e. the hypotheses as such) and also the values of model parameters can cause agreement/disagreement between the results obtained with the model and the measured data. Regarding the values of the model parameters, we can run the model with fixed parameter values, taken from the literature, or we can fit the values to get the best agreement between the model results and experimental data. However, in the latter case, we may find a perfect agreement, but only by using unrealistic values of the model parameters (based on the literature), which usually rules out the correctness of the model. On the other hand, when values of system variables are not known from the litrrature and/or are not directly accessible from experiments, the fitting can provide this information, assuming the model structure is correct.

Furthermore, a so-called metabolic control analysis (MCA) can be performed, which quantifies the extent to which a given process (hypothesis) affects a given result (for a review see Visser and Heijnen, 2002 ). Sometimes, this quantification can be made easy only by using modelling rather than by doing experiments, because it is not always possible to infer the desired (initial) state of the experimental system, or to experimentally modify the parameters of the system, as needed to perform MCA.

Finally, if we have a robust model that describes well the various measured data, we can modify the model parameters and track the results, or in other words, we can perform ‘experiments’ without measuring anything – i.e. biological experiments in silico . These in silico experiments are very useful in making predictions that allow us to determine the role of model parameters, or to design experiments to prove or refute certain predictions. Concerning the modelling of ChlFI discussed below, it is important to keep in mind that a qualitative agreement between experiment and theory is a useful goal. The ChlFI is a manifestation of a very complex biological system, and therefore describing it correctly and comprehensively is difficult – this is quite different from modelling technical systems, which can be described correctly, and where a quantitative agreement between experiments and theory is strictly required.

Several approaches have been used for the formulation of a fast ChlF rise model, or for the entire ChlFI. The variable ChlF is emitted mostly from PSII (reviewed by Krause and Weis, 1991 ; Dau, 1994 ; Govindjee, 1995 ; Lazár, 1999 , 2006 ; Stirbet and Govindjee, 2011 , 2012 ). The basic strategy for modelling the fast ChlF rise has been to first use a model of the ET reactions occurring only in PSII, but then later add ET reactions beyond PSII, especially for the modelling of the entire ChlFI. The formulation of a ChlFI model also depends on the specific ET components considered, and then, on the way, the variable ChlF emitted during the transient is defined. The basic approach in the definition of the variable ChlF is based on the early work of Duysens and Sweers (1963) and the quencher theory defined there, later identified to be due to Q A (see above the subsection Evidence from Chl a fluorescence measurements). According to this theory, if Q A is oxidized, ChlF is low and if Q A is reduced, ChlF is high, and the variable ChlF is proportional to the fraction of Q A − . Moreover, the energetic PSII connectivity (mentioned earlier) can be also considered in modelling the variable ChlF.

Taken together, the most basic approach used to model the fast ChlF rise has been to define a PSII model that describes the redox changes of Q A during reduction of the PQ pool. These redox changes are modulated by Q B , the second PQ electron acceptor of PSII, which unlike Q A is a two-electron PQ acceptor of the PSII RC; originally, it came from the PQ pool, transiently binding to the Q B -site. The reduction of Q B to plastoquinol is described by the TEG model ( Bouges-Bocquet, 1973 ; Velthuys and Amesz, 1974 ), which is the fundamental partial model used in ChlFI modelling (see discussion earlier, and Fig. 5 ). Thus, one group of models describing the fast ChlF rise, including the first ever models (see below the subsection Modelling the fast Chl fluorescence rise by using only models of PSII reactions), are based on the TEG model. The charge stabilization on Q A (i.e. the reduction of Q A by Pheo − ) means that the PSII RC is closed and thus the ChlF is high. However, this charge stabilization is preceded by the formation of P680 + Pheo − (see Fig. 2 ). Thus, when either P680 + and/or Pheo − are present, the PSII RC is closed, but the ChlF decreases in their presence, as both P680 + and Pheo − are quenchers of ChlF (for P680 + , see Okayama and Butler, 1972 ; Shinkarev and Govindjee, 1993 ; Steffen et al ., 2001 , 2005 ; for Pheo − , see Klimov et al. , 1977 ). Quenching of Chl fluorescence by P680 + accumulation has been considered in several models of the fast ChlF rise (e.g. Lazár, 2003 ; Laisk and Oja, 2018 ). Accumulation of reduced Pheo was shown to take place only under illumination at 200–220 K ( Klimov et al. , 1980 ; Breton, 1982 ). Nonetheless, Vredenberg (2000 , 2008 , 2011 ) has assumed, in his O-J-I-P model, not only that Pheo ‒ accumulates at room temperature, but also that ChlF is higher when both Q A and Pheo are reduced than when only Q A is reduced. Strasser and Stirbet (2001) have also simulated and fitted a fast ChlF rise with a simple TEG-based model, but considering three different PSII redox states that contribute to the fluorescence signal: (1) with Q A ‒ ; (2) with Pheo ‒ ; and (3) with PheoQ A ‒ and Pheo ‒ Q A ‒ ; ChlF in the presence of Pheo ‒ Q A ‒ was considered to be two-fold larger than that when PheoQ A ‒ was present. The experimental O-J-I-P curve was fitted quite well by all three models, but the parameters of the models and the kinetics of the PSII redox states were different in each case. Thus, overparametrized models cannot be validated by fitting one experimental curve, and other approaches must be also used to reach firm conclusions. These can be, for example, measurements of the kinetics of the redox states of PSII during the ChlF transient, as well as through in silico experiments, in which the basic parameters of the model are kept constant.

On the other hand, ChlF yield during ChlFI has also been defined by using ratios of the rate constants related to fluorescence emission, heat dissipation and photochemistry ( Goltsev and Yordanov, 1997 ; Laisk et al. , 2006 ; Ebenhöh et al. , 2014 ; Stirbet and Govindjee, 2016 ). A better estimation of the ChlF signal, in models used to simulate the ChlFI, is obtained by considering fluorescence as a radiative deactivation of the singlet excited state of Chl (i.e. 1 Chl*); this was used in the modelling of the fast ChlF rise by Baake and Schlöder (1992) (see also Lebedeva et al. , 2002 ; Lazár, 2003 ; Belyaeva, 2004 ). If the ChlF signal is defined by the redox states of Q A or by the concentration of 1 Chl*, the model must include these entities. The reactions among the excited states of Chl a in PSII antenna that include P680 and Pheo, besides Q A , have been described by the RRP model of Schatz et al. (1988) ; it was based on measurements of ChlF decay in the picosecond range after excitation by a short laser pulse. In the RRP model, charge separation between P680 and Pheo is reversible and is followed by charge stabilization (ET from Pheo − to Q A ) in the open PSII RCs, and by non-radiative charge recombination (to the ground state) in closed PSII RCs (see Fig. 2 ). Thus, the RRP model is the second fundamental partial model, in addition to the TEG model, which must be considered in modelling the ChlFI.

If the formation of P680 + is considered in a model, then the reduction of P680 + must be also included, i.e. reactions on the donor side of PSII, as well as the recombination reactions between P680 + and Pheo ‒ or Q A ‒ . The P680 + is reduced by tyrosine 161 (i.e. Y Z ; Debus et al. , 1988 ), which is, in turn, reduced by OEC. Electrons are donated to Y Z + , by OEC, as it undergoes the S-state cycle ( Kok et al. , 1970 ; Fig. 3 ). Kok’s model of OEC is the third fundamental partial model for the description of PSII function. This model also includes parameters called ‘misses’ (when the light flash used does not lead to an S-state advancement) and ‘double hits’ (when the flash leads to an advancement by two S-states). Kok’s model has been modified by Jablonsky and Lazar (2008) by including the so-called intermediate S-states, which enable omission of the misses and double hits in the model.

Modelling of the fast Chl fluorescence rise measured after treatment with a herbicide

Because many photosynthetic processes affect ChlFI, herbicides that interrupt the ET from Q A to Q B have been used to simplify the observed curves. Note that many different herbicides are employed to kill weeds, and this can be achieved by using different substances that operate through various other mechanisms, but here we discuss only those that block the Q B -pocket of PSII. DCMU (3-(3′,4′-dichlorophenyl)-1,1-dimethylurea) is a herbicide that has been frequently used in such studies; it binds to the Q B -pocket, blocking ET beyond PSII (e.g. Oettmeier et al. , 1980 ), which leads to a faster closure of PSII RCs during illumination and to a faster accumulation of Q A ‒ . Binding of DCMU at the Q B -pocket results in a faster sigmoidal ChlF rise to its maximal value (F M ), which is reached approximately at the J step (~2 ms) of the ChlF rise, measured (under saturating light) with an untreated sample. The gradual binding of DCMU to the Q B -pocket of PSII, and thus the gradual closure of PSII, as reflected in changes in the O-J-I-P transient, was modelled by Lazár et al. (1998) . Here, the diffusion of DCMU was described using Fick’s laws, and the reaction of DCMU at the Q B -binding site of PSII, by second-order kinetics. From this work, Lazár et al. (1998) provided values of the diffusion coefficient of DCMU, and the second-order rate constant of DCMU binding to the Q B -pocket of PSII.

The sigmoidal shape of the fast ChlF rise measured with DCMU has been suggested to reflect energetic connectivity ( p ) between the PSII units ( Joliot and Joliot, 1964 ; also see above for discussion). This concept is tightly connected with a type of PSII heterogeneity, namely PSII α/β antenna heterogeneity ( Melis and Homann, 1975 ). The PSIIα units, the main PSIIs, have a large and energetically connected light-harvesting antenna. The size of the antenna is reflected in the rate constant of the fast ChlF rise, measured with DCMU, and PSII connectivity is reflected in the value of the parameter p ; the PSIIβ units have smaller antenna and a lower energetic connectivity. Several different procedures have been used to obtain quantitative information on this PSII heterogeneity (see Hsu et al. , 1989 ). To increase the reliability and accuracy in the determination of PSII antenna heterogeneity, Lazár et al. (2001) have fitted the values of rate constants, the parameter p and the fractions of particular PSII types to several curves of fast ChlF rise in the presence of DCMU, measured at different light intensities, by using just one fitting procedure; results from this work were in good agreement with those in the literature.

The fast ChlF rise measured with DCMU has also been explored using the RRP model by Trissl et al. (1993) , Lavergne and Trissl (1995) , and Trissl and Lavergne (1995) , with PSII energetic connectivity included. The RRP model has been further improved by Lazár and Pospíšil (1999) by the addition of P680 + reduction step(s) on the (electron) donor side of PSII; for this, they had used the fast ChlF rise in the presence of DCMU measured at high temperatures. Decreases in PSII energetic connectivity and in the rate of P680 + reduction by Y Z were suggested to occur in the photosynthetic samples kept at high temperatures (e.g. 47 °C for 5 min; Guissé et al. , 1995 ; Srivastava et al. , 1997 ), but these conclusions were based on results on samples, without DCMU. By contrast, Lazár and Pospíšil (1999) have simulated the fast ChlF rise, in the presence of DCMU, at high temperatures by omitting PSII energetic connectivity, and by decreasing the rate constants related to the electron donation to P680 + .

To study photoinhibition in DCMU-treated samples, Vavilin et al. (1998) and Lazár et al. (2005) have simulated fast ChlF rise curves by using the RRP model. Lazár et al. (2005) further extended the RRP model by considering a possible protective function of Cyt b 559 against photoinhibition, as proposed by Thompson and Brudvig (1988) and by Nedbal et al. (1992) . Cyt b 559 is indeed reduced by Pheo − , which then donates electrons to P680 + , involving a CEF around PSII. However, an argument against such an ET may be in the crystal structure of PSII (e.g. Zouni et al. , 2001 ; Kamiya and Shen, 2003 ), which shows that the distance from the Pheo in the active D1 branch of PSII and the Cyt b 559 is too long (~45 Å) to allow an ET between them. However, the distance between Pheo in the inactive D2 branch of PSII and the Cyt b 559 is shorter (22 Å), and ET by tunnelling has been reported for such distances ( Page et al. , 1999 ). Thus, the Pheo in the model of Lazár et al. (2005) could be Pheo in the D2 branch of PSII.

Modelling the fast Chl fluorescence rise by using only models of PSII reactions

Mathematical analyses of the fast ChlF rise were published in the 1960s ( Malkin and Kok, 1966 ; Malkin, 1966 ; Munday and Govindjee 1969 ). Munday and Govindjee (1969) measured the O-I-D-P (where D is for a dip) ChlF rise curve in Chlorella pyrenoidosa and related it successfully to variations in the fraction of reduced Q A . In their paper, the dip was analysed by studying the transient oxidation of Q A − by PSI.

In all likelihood, the first ‘real’ model of the fast ChlF rise [i.e. a scheme of ET reactions and a related set of coupled ordinary differential equations (ODEs)] was that of Holzapfel and Bauer (1975) . This model was rather complex: it described the complete ET chain in the TM, including the formation of NADPH and ATP. On the other hand, some details of the photosynthetic ET were not included in the model, due to limited knowledge of the photosynthesis process at that time. In this model, the ChlF was assumed to be proportional to the amount of Q A − . Holzapfel and Bauer (1975) were able to qualitatively simulate the rate of oxygen evolution at different light intensities, the fast ChlF rise of control samples, and of those treated with DCMU and/or 2,5-dibromo-3-methyl-6-isopropyl-p-benzoquinone (DBMIB, which blocks the electron flow between PQ and Cyt b 6 /f; cf. Trebst and Reimer, 1973 ), as well as of samples that were dark-adapted under anaerobic conditions. This model was further used by Holzapfel (1978) , where the effect of ΔΨ across the TM was included. It is unclear why these models were missed by others. However, several models on the fast O-I-P ChlF rise, measured using light intensities lower than 1200 µmol photons m −2 s −1 , are available ( Renger and Schulze, 1985 ; Hsu, 1992 a , b ; Goltsev and Yordanov, 1997 ; Tomek et al. , 2003 ); these models were based on the TEG model, where ChlF signal was assumed to be proportional to the amount of reduced Q A (for an exception, see Goltsev and Yotdanov, 1997). Tomek et al. (2003) have further used the amplitude of the I step to estimate the fraction of ‘Q B -non-reducing centres’ (i.e. PSIIs which cannot reduce Q B ).

Different TEG models, and PSII redox states with reduced Q A to calculate the ChlF signal, were also used in modelling the O-J-I-P ChlF rise measured under saturating light (~3000 µmol photons m −2 s −1 ; Stirbet and Strasser, 1995 , 1996 ; Lazár et al. , 1997 ; Stirbet et al. , 1998 , 2001 ; Strasser and Stirbet, 2001 ; Tomek et al. , 2001 ; Sušila et al. , 2004 ). In these studies, the authors mainly showed how selected parameters of the models (e.g. initial concentrations and values of the rate constants) affect the shape of the O-J-I-P curves. However, Stirbet and Strasser (1996) showed that consideration of second-order kinetics for the reactions between Q A and Q B in the TEG model gives different simulated O-J-I-P curves compared to those obtained in the simulation where first-order kinetics is used. Strasser and Stirbet (1998) have also simulated O-J-I-P ChlF transients with a TEG model, by taking into account the heterogeneity of the PSII population in relation to PSII antenna, PSII energetic connectivity, and the ability of PSII to reduce Q B (‘Q B -reducing’ vs. ‘Q B -non-reducing’ RCs).

Sušila et al. (2004) considered a hypothetical sample divided into ten layers of the same thickness, and calculated the light intensity in each layer, based on the Lambert–Beer attenuation law, in order to determine the light gradient inside the sample. They then simulated the fast ChlF rise curve for each layer, by using the same model as in Lazár et al. (1997) and Tomek et al. (2001) , and summed the ChlF signal from all the layers to obtain the total ChlF signal. Their results showed that the light gradient inside a sample can significantly affect the shape of the fast ChlF transient. We note that in all the above models for the O-J-I-P ChlF rise, with the exception of those used by Stirbet et al . (1998 , 2001 ) and Strasser and Stirbet (1998, 2001 ), the presence of an unknown component X that accepts electrons from the Q B ‒ was assumed to exist.

Guo and Tan (2011) have extended the TEG model by taking in account the existence of a light-harvesting antenna system. Later, Feng et al. (2018) extended the above model by including the pH-dependent NPQ process, which allows the fitting of the decrease of the ChlF signal from the peak ‘P’ to ‘S’ and/or the ‘T’ level. To fit the O-J-I-P ChlF curves measured at different temperatures (20, 25, 30 °C), the rate constants in the model of Guo and Tan (2011) were assumed to be dependent on the temperature according to the Arrhenius law ( Xia et al. , 2018 ). Because the formation of 1 Chl* during illumination was included in the models used in all three studies above, the ChlF signal was defined as radiative deactivation of 1 Chl* in the PSII antenna.

In some of the models just mentioned, the function of the PSII donor side was implicitly included. By contrast, in the models of Stirbet et al . (1998 , 2001 ), Chernev et al. (2006) , Lazár and Jablonský (2009) , and Laisk and Oja (2018) , the function of the PSII donor side was included explicitly, and that too in combination with the TEG model. Stirbet et al . (1998 , 2001 ) not only included the S-states of OEC, but also the PSII energetic connectivity, and the quenching of the ChlF signal by P680 + and by the oxidized PQ molecules. Stirbet et al . (1998 , 2001 ) then simulated (or fitted) the O-J-I-P ChlF transient by defining the ChlF signal to be proportional to the amount of reduced Q A , and by considering different initial fractions of Q B and Q B ‒ , or of the S 1 and S 0 states of OEC. In the model of Lazár and Jablonský (2009) , all the S-state transitions of OEC were taken into account, as well as the redox states of P680 + that were explicitly considered in combination with the TEG model, which was then used for simulation of the O-J-I-P ChlF transient. In their study, the effect on the simulated fast ChlF curve was described by using (1) first- or second-order reaction kinetics for electron donation from the OEC to P680 + ; (2) one second-order reaction or two subsequent reactions for the Q B 2‒ /PQ exchange; and (3) all possible reactions between the ET components, or of fewer ‘logical’ reactions.

Other models used for simulation of the fast ChlF rise are those that include, in addition to the TEG model, the description of the fast events in the PSII RC (i.e. charge separation, recombination and stabilization) described by the RRP model. Models by Baake and Schlőder (1992) and Belyaeva et al. (2011) belong to this group, where reduction of P680 + by Y Z (via OEC) was implicitly included. Other authors ( Lazár, 2003 ; Zhu et al. , 2005 ; Matsuoka et al. , 2015 ) have explicitly included Y Z and the S-state transitions of OEC.

Lazár (2003) provided a detailed analysis of how values of particular rate constants and initial conditions affect the simulated fast O-J-I-P ChlF curves. An important aspect of the ChlFI curves analysed by simulations in this work is the origin of the minimal ChlF level (F O ) which is the initial ChlF, when all PSII RCs have all Q A in the oxidized state; F O originates from the radiative deactivation of the excited PSII state [(antenna-P680)*PheoQ A Q B ; see Fig. 7 ]. Interestingly, although the model of Lazár (2003) is one of the most detailed models of PSII reactions (consisting of a set of 44 coupled ODEs), yet it was not able to simulate typical O-J-I-P ChlF transients, as the ChlF signal increased from the J step to a maximum, which was reached at the I step position in the experimental curves ( Fig. 7 ).

Simulations of the O-J-I(=P) ChlF rise (see text) and of the model forms of photosystem (PS) II in the excited state, which mainly contribute to the (chlorophyll a ) fluorescence transient, are shown on a logarithmic time scale. Abbreviations: (L-P)*, the excited state of the PSII antenna, which is equilibrated among all light harvesting Chls, including P680; Ph, pheophytin; A and B, the first and second plastoquinone acceptors of PSII (Q A and Q B ). The time course of the PSII model form (L-P)*PhAB at the beginning of the transient, which represents excited open PSII RCs (i.e. with oxidized Q A ), is at the origin of the minimal ChlF, F O . Modified from Lazár (2003) .

The inability to simulate the proper time-dependence of the ChlF signal by the detailed model based only on PSII redox states is one of the arguments that a proper model for the O-J-I-P ChlF rise should also describe ET reactions occurring beyond the PQ pool, as already inferred by Munday and Govindjee (1969) and later confirmed in other studies (i.e. Schreiber et al. , 1989 ; Schansker et al ., 2003 , 2005 ).

Modelling the fast Chl a fluorescence rise with models that consider electron transport in and around the TM

The last group of models used in simulation of the O-J-I-P ChlF transients are those that include ET reactions occurring in and around the TM ( Lebedeva et al. , 2002 ; Kroon and Thoms, 2006 ; Lazár, 2009 ; Makarov et al. , 2012 ; Belyaeva et al ., 2016 , 2019 ), or even the metabolic reactions in the stroma (e.g. the Calvin–Benson cycle; see Laisk et al ., 2006 , 2009 ; Zhu et al. , 2013 ). Given the all-inclusive nature of these models, some of them were also used for modelling of the the entire ChlFI (see below). A diagram of the reactions considered in the model proposed by Lazár (2009) is shown in Fig. 8 . This model consists of a set of 42 coupled ODEs, and the ChlF emission is defined as being proportional to the amount of reduced Q A . In addition, the ΔA 820 signal, describing redox changes of P700 and plastocyanin (PC), was also modelled. To show that the ET reactions beyond the PQ pool affect the shape of the simulated fast ChlF transients, Lazár (2009) also analysed in silico the effects of DBMIB and MV [methylviologen, which accepts electrons from both the iron–sulfur cluster of PSI and ferredoxin (Fd); Sétif, 2015 ]. The shapes of the simulated fast ChlF transients and of ΔA 820 signal were qualitatively in agreement with the experimental curves (see Fig. 8 ). This model is also a part of e-photosynthesis.org ( Šafránek et al. , 2011 ), which is a web-based platform for modelling complex photosynthetic processes.

Diagram of the ET reactions used in the model of Lazár (2009) (A), the O-J-I-P ChlF transients measured on control (= untreated) leaves, as well as on leaves treated with 2,5-dibromo-3-methyl-6-isopropyl-p-benzoquinone (DBMIB, which inhibits ET in the cytochrome b 6 /f, see A) or with methyl-viologen (MV, which accepts electrons from the iron–sulfur cluster of PSI and ferredoxin, Fd, see A) (B), and the respective curves simulated with the model (C), the Δ A 820 curves measured under the same conditions (D), and the respective curves simulated by the model (E). The curves are shown on a logarithmic time scale. Abbreviations: S i , the S-states of the oxygen-evolving complex (OEC); f, b L , b H … c, cytochrome f, low/potential cytochrome b 6 , and high-potential cytochrome b 6 in kinetic equilibrium with the haem c of cytochrome b 6 /f complex; PC, plastocyanin. Modified from Lazár (2009) .

In all the models mentioned above, the variable ChlF signal was assumed to originate from the PSII antenna. The problem with direct measurement of the variable ChlF from PSI in vivo (not from isolated PSI complexes) is that it overlaps spectrally with the PSII ChlF. However, some experimental results, presented in the literature (see Lazár, 2013 ), show the existence of a variable ChlF originating in PSI, at least under certain conditions. Lazár (2013) presented a very detailed model of the ET reactions in PSI (i.e. a set of 106 coupled ODEs), and simulated fast ChlF transients originating only from PSI. The ChlF signal was defined as the radiative deactivation of 1 Chl*. PSI was further shown to emit variable ChlF, and its contribution to the total maximal variable ChlF signal from the two PSI and PSII was ~8–17 % ( Lazár, 2013 ). Future studies are needed to quantitatively assess these findings.

Rule-based modelling of the fast Chl fluorescence rise

All the models of the fast ChlF rise discussed thus far have described the photosynthetic processes by using sets of coupled ODEs. Each ODE was used to describe the time-change of a particular PSII redox form (i.e. state variable) of the model. This approach is deterministic, because in any run of the model, the same solution is obtained.

If too many state variables (coupled ODEs) are considered in a model, it becomes difficult to obtain model results, due to high requirements of computational time and hardware; this is because all ODEs must be solved simultaneously at each time of system evolution. While there are ways (specific for each model) to decrease the number of equations, this problem can be better overcome by employing a rule-based modelling approach, where rules are defined that are equivalent to the particular ET reactions. Furthermore, random numbers are generated, and these determine (using internal decision process) which rules should be considered in each particular step of the model run, i.e. in each ‘evolvement’ of the system in time. Thus, a time course of the system behaviour would be described by a sequence of particular rules, which are slightly different in different model runs, i.e. small differences between solutions are obtained after different runs of the model. Thus, this approach would be stochastic (i.e. random). The rule-based stochastic approach by means of kinetic Monte Carlo simulations has been applied for modelling of the O-J-I-P ChlF transient by Xin et al. (2013) , Guo and Tan (2014) , Maslakov et al. (2016) and Antal et al. (2018) . However, in all these cases, the shapes of simulated ChlFI curves were the same (except for the noise) as when using the deterministic approach. Similarly, the O-J-I-P curve was also simulated using stochastic π-calculus ( Tokarčík, 2012 ) and rule-based language-simplified Kappa ( Nižnan, 2014 ). Much further work is needed to obtain conclusive results from this approach.

Modelling the slow PS(M)T phase of the Chl a fluorescence induction curve

The nomenclature of P-S-(M)-T for the slow phase of the ChlFI was first used by Papageorgiou and Govindjee (1968 a , b ). Compared with the fast ChlF rise, this phase is much more complex and less well understood, as the fluorescence yield is modulated by an increasing number of processes triggered during this phase, besides the photochemical quenching by Q A (see above), such as: (1) the NPQ of excited singlet 1 Chl* a in PSII antenna, induced by low pH in the lumen (i.e. the high-energy NPQ qE; Horton et al. , 1996 ; Rochaix, 2014 ); (2) state transitions (i.e. qT 12 or qT 21 ) that regulate the absorption CS of PSI and PSII (with ‘state 1’ being more fluorescent than ‘state 2’; see Papageorgiou and Govindjee, 2011 , 2014 ); (3) photoinactivation processes (qI) due to the photodamage of PSII (e.g. Tyystjärvi, 2013 ); (4) cyclic electron flow around PSI (e.g. Miyake, 2010 ; Buchert et al. , 2018 ), chlororespiration ( Bennoun, 1982 ) and electron flow to molecular oxygen ( Mehler, 1951 ; Asada, 1999 ); as well as (5) activation of the Calvin–Benson cycle. Therefore, besides the partial models necessary for modelling the fast ChlF rise discussed in the previous section (e.g. RRP, Kok’s oxygen clock, TEG, the Q-cycle at the Cyt b 6 /f complex), the processes listed above are fundamental for modelling the whole ChlFI; however, qT and qI, with a few exceptions, have been usually neglected by most authors.

Laisk et al. (1997) were the first to model the qE process, which they used later to simulate successfully the slow PS(M)T phase of ChlFI ( Laisk et al. , 2006 ). This qE model was later adapted by Zhu et al. (2013) for C 3 photosynthesis, but the descending M-T phase is missing in their simulated ChlFI curve. Note that these two papers were centred on the detailed description of metabolic reactions.

The transmembrane pmf , i.e. both ΔpH and ΔΨ, was modelled by Lebedeva et al. (2002) , which predicts that a sufficiently large transmembrane electric potential (positive inside) would slow the rate of PQH 2 oxidation by the Cyt b 6 /f (the so-called backpressure effect; see van Kooten et al. , 1986 ), and consequently the ET rate from PSII to PSI (see also comments in Stirbet et al. , 2014 ). This pmf model was further used by, for example, Rubin et al. (2009) and Belyaeva et al . (2016 , 2019 ) to model the complete ChlFI curve, with a TM model that describes the electron/proton transfer reactions between membrane protein complexes: PSII, PSI, Cyt b 6 /f, mobile PQ pool in the TM, PC in lumen and Fd in stroma, CEF-PSI, and reduction of NADP + via Fd-NADP + -oxidoreductase (FNR) (see Fig. 1 ). Belyaeva et al. (2016) used the TM model to fit both ChlFI data and P700 redox changes (Δ A 810 ), measured in pea leaves, from 20 μs to 20 s. Belyaeva et al. (2019) added to their earlier TM model partial models for the light-induced activation of FNR and qE, with the goal to simulate the ChlFI and Δ A 810 kinetics on the time scale from 40 μs to 30 s. Their results showed that the time-dependent rate constants changed substantially upon the release of ET on the (electron) acceptor side of PSI and during qE induction. Belyaeva et al. (2019) also discussed differences between the parameters related to FNR activation and qE induction evaluated for dark-adapted and pre-illuminated pea leaves, and also analysed the transition between CEF-PSI and LEF modes.

Because the photosynthetic organisms are exposed continuously to fluctuations in the environmental conditions, the activity of their photosynthetic apparatus is dynamic, being feedback-regulated by several processes that reduce imbalances between the rate of energy trapping by the PSs and CO 2 assimilation. These serve to optimize the photosynthetic ET to, for example, light-induced pH changes in the lumen and in the stroma (see Tikhonov, 2013 ; Rochaix, 2014 ; Strand and Kramer, 2014 ), or changes in the PQ pool redox state, as modulated by variations in light irradiance, ATP/ADP ratio and the ambient CO 2 level ( Rochaix, 2014 , 2016 ). Light-induced acidification of the lumen slows down PQH 2 oxidation by the Cyt b 6 /f (the backpressure effect), and also decreases PSII activity by inducing excitonic energy dissipation as heat in PSII antenna through qE ( Jahns and Holzwarth, 2012 ; Rochaix, 2014 , 2016 ). This reduces the excess of input energy in the system, and thus oxidative damage ( Nishiyama et al. , 2006 ), which occurs when singlet excited 1 Chl* forms triplet-state Chl ( 3 Chl) ( Durrant et al. , 1990 ) that interacts with ground state oxygen, generating ‘noxious’ reactive oxygen species (ROS), such as singlet oxygen ( 1 O 2 ). Furthermore, the alkalization of stroma activates the Calvin–Benson cycle, which stimulates the consumption of NADPH and ATP ( Werdan et al. , 1975 ; Noctor and Foyer, 2000 ). As shown earlier, state transitions re-equilibrate PSI and PSII activities through changes in their absorption CS, which are triggered by PQ pool redox state changes (for plants and algae, see reviews by Rochaix, 2014 , 2016 ; Goldschmidt-Clermont and Bassi, 2015 ), and involve phosphorylation/dephosphorylation of the PSII mobile antenna by kinases and phosphatases (i.e. STN7/TAP38 in Arabidopsis thaliana , or Stt7/Pph1 in Chlamydomonas reinhardtii ; Rochaix et al. , 2012 ). Furthermore, during induction of the Calvin–Benson cycle, changes in illumination, or anaerobiosis, photosynthetic electron fluxes are optimally redistributed between the linear electron transport (LET) from water to NADP + , and alternative electron pathways, i.e. cyclic electron flows, pseudocyclic O 2 -dependent electron flows and the malate valve ( Backhausen et al. , 2000 ; Miyake, 2010 ; Hemschemeier and Happe, 2011 ).

Modelling the state transition process

Ebenhöh et al. (2014) were the first to model state transitions in plants and algae based on a mechanism, described by Allen et al. (1981) ; they investigated the dynamics and regulation of state transitions by simulating experimental PAM-SP curves from Chlamydomonas reinhardtii cells, grown under dim light, and thus with little capacity for qE, having a low LHCSR3 content ( Peers et al. , 2009 ). Here, a simplified mathematical model (based on eight coupled ODEs) was used, where the most relevant ET routes, necessary for modelling state transitions in this green alga, were used: LEF, CEF-PSI, and chlororespiration through the plastid terminal oxidase PTOX (see Fig. 1 ; and Bennoun, 1982 ; McDonald et al. , 2011 ). Individual reactions of the Calvin–Benson cycle were treated implicitly, using steady-state consumption of NADPH and ATP, and a quasi-steady state approximation for the dynamics of oxygen evolution and charge separation in PSII. For simplicity, in the partial model of state transitions, it was assumed that the PSII mobile antennas phosphorylated by the kinase Stt7 (activated by the PQ pool reduction) are relocated directly to PSI (i.e. state 1 to state 2 transition, qT 12 ); also, after the Stt7 inhibition (triggered by the PQ pool oxidation), the PSII mobile antennas are dephosphorylated by the phosphatase Pph1, and directly re-associate with PSII (i.e. state 2 to state 1 transition, qT 21 ) (see Fig. 4 ). Finally, the ChlF signal is defined by the ratios of rate constants related to fluorescence emission, heat dissipation and photochemistry, which include changes in the absorption CS of PSI and PSII (due to state transition). Ebenhöh et al. (2014) successfully simulated with their model the main features of the experimental fluorescence signal measured with a PAM instrument from dark-adapted wild-type Chlamydomonas cells illuminated for 10 min with low light (100 μmol photons m −2 s −1 ). The saturating F M ′ peaks during illumination reflect changes in the antenna CS of PSII (i.e. a partial state transition to ‘state 2’), which take place in parallel with the establishment of a stationary redox poise of the PQ pool.

State transitions were also modelled by Stirbet and Govindjee (2016) , with the goal to simulate the slow PS(M)T phase of the ChlFI, in order to determine the origin of the S–M rise of Chlamydomonas reinhardtii cells (see Kodru et al. , 2015 ; Zhou et al. , 2015 ). Here, the photosynthesis model of Ebenhöh et al. (2014) was adapted for the simulation of ChlF data obtained by using a Plant Efficiency Analyser (PEA; Hansatech, UK). Stirbet and Govindjee (2016) confirmed that, under anaerobic conditions, in darkness, the PQ pool reduction through chlororespiration triggers a state 1 to state 2 transition (see Fig. 9A ), when the relative CS of PSII (CSII) is lower than that of PSI (see Bulté et al. , 1990 ). Next, it was shown that, during the subsequent illumination, the hypothetical sample undergoes a transition from this ‘state 2’ to a ‘state 1’, which is the origin of the slow S-M fluorescence rise (see Fig. 9B ). However, if the dark-adaptation period is too short, and the transition to ‘state 2’ in darkness is not complete, the subsequent illumination triggers a state 1 to state 2 transition (see Fig. 9C ). We note, however, that the M-T fluorescence decline observed experimentally ( Kodru et al. , 2015 ; see also Fig. 6B ) is missing in the simulated curves, and, thus, further research is needed to determine its origin.

Simulated kinetics of the fraction of the oxidized plastoquinone (PQ) pool (i.e. PQ/PQ tot ) and the relative absorption cross-section of photosystem (PS) II (i.e. CSII) during dark adaptation under anoxic conditions of a hypothetical sample of Chlamydomonas reinhardtii cells (see A), as well as simulated time courses of PQ/PQ tot , CSII and Chl fluorescence induction (F) during illumination in the presence of oxygen of the hypothetical sample after 600 s (see B) and 200 s (see C) anoxic dark adaptation. Note that a decrease in CSII reflects a state 1 to state 2 transition, while an increase reflects a state 2 to state 1 transition. Modified from Stirbet and Govindjee (2016) .

Stirbet and Govindjee (2016) also examined in silico the influence of different factors on the amplitude of the S-M fluorescence rise under low light conditions (~100 to 300 μmol photons m −2 s −1 ). For example, they found that, under conditions that trigger a qT 21 during a dark-to-light transition (i.e. reduced PQ pool, and CSII < 0.5 at the beginning of illumination), an increase in the CEF-PSI rate leads to a lower CSII increase at the end of the state transition, and a smaller amplitude of the S-M fluorescence rise (see Fig. 10A ). This simulation also confirmed that, when the CEF-PSI is much more rapid, the ATP level increases, while the NADPH level decreases. When the light intensity is higher, the simulations also showed a decrease in the S-M fluorescence rise. This result is in agreement with the experimental ChlFI data on Chlorella published by Papageorgiou and Govindjee (1968 a ), who showed that the slow S-M fluorescence rise is larger at lower exciting light intensities. By contrast, under other conditions taken into account by Stirbet and Govindjee (2016) , such as the increase in NADPH and ATP consumption by the Calvin–Benson cycle, or an increase in the rate of the Mehler reaction, the S-M amplitude increased, due to a larger increase in the PSII CS during the qT 21 (see Fig. 10B ). However, the increase in the S-M rise becomes saturated by further increasing these rate constants. The conclusion is that the factors reducing the PQ pool (e.g. higher light intensity, or more rapid CEF-PSI) decrease the S-M amplitude, and those that oxidize further the PQ pool (e.g. more rapid NADPH consumption or Mehler reaction) increase the S-M amplitude.

Simulated kinetics of the fraction of the oxidized plastoquinone (PQ) pool (i.e. PQ/PQ tot ), the relative absorption cross-section of photosystem (PS) II (i.e. CSII), and of chlorophyll (Chl) fluorescence induction (F) during illumination in the presence of oxygen of a hypothetical sample of Chlamydomonas reinharditii cells dark-adapted for 600 s under anoxic conditions, by considering that: (1) the illumination is equivalent to 100 μmol photons m −2 s −1 , and the rate constant of the cyclic electron flow (CEF) around PSI is k Cyc = 1 or 5 s −1 (see A); and (2) the illumination is equivalent to 300 μmol photons m −2 s −1 , the rate constant of CEF-PSI is 1 s −1 , and that of the Mehler reaction (i.e. ET from ferredoxin to O 2 ) k O2 = 0 or 11 s −1 (see B). Note that an increase in CSII reflects a state 2 to state 1 transition. These simulations show that the S-M fluorescence rise decreases when light intensity increases or when CEF-PSI is faster, but increases when the Mehler reaction is also functioning. Modified from Stirbet and Govindjee (2016) .

Modelling the qE component of NPQ

Because NPQ in plants and algae is associated with LHCs of PSII (see Horton et al. , 1996 ; Tian et al. , 2017 ), models simulating qE usually include reactions around PSII, and focus on describing the ChlFI (see reviews by Zaks et al. , 2013 ; Matuszyńska and Ebenhöh, 2015 ). Different photosynthesis models have been used to simulate either ChlFI curves measured with instruments using direct light (e.g. PEA), or with PAM-SP fluorometers (for a review see Stirbet et al. , (2014) . But, of course, the main phenomenon under analysis with either of these instruments is the same. Besides measurements of ChlF lifetime (e.g. Gilmore et al ., 1995 , 1998 ; Sylak-Glassman et al. , 2016 ), measurements of Chl fluorescence yield with PAM-SP fluorometers are especially suitable for the study of NPQ processes ( Müller et al. , 2001 ). It is clear that models that simulate experimental PAM data are valuable tools to analyse the qE component of NPQ.

Several original qE models have been proposed by, for example, Ebenhöh et al. (2011) and Zaks et al. (2012) ; these have been used for the simulation of the dynamics of ChlF quenching, as measured by PAM-SP instruments (see review by Stirbet et al. , 2014 ). Now, photosynthesis models that include qE are available ( Ebenhöh et al. , 2014 ; Matuszyńska et al ., 2016 , 2019 ; Snellenburg et al. , 2017 ; Morales et al ., 2018 a , b ).

The qE model of Ebenhöh et al. (2014) takes into account the induction of qE by low pH in the lumen (see above), but it is based on the simplifying assumption that the xanthophyll cycle is the only component involved in qE-dependent quenching. Thus, it was assumed that the decrease in lumenal pH leads directly to the formation of ‘Z’ through the xanthophyll cycle (i.e. the de-epoxidation of V via A), which then acts as a fluorescence quencher in the PSII antenna; the quencher acts by increasing the rate constant of the non-radiative deactivation of the 1 Chl*. Furthermore, the qE is reversed in darkness as Z is epoxidized to V by an active epoxidase. The results of the simulations, obtained with this qE model, showed that high light illumination leads to a plateau of the PQ pool redox state, which is relatively constant for a range of CSII values. Based on these theoretical results, Ebenhöh et al. (2014) concluded that, due to qE induction, the requirement to adjust the antenna CS through state transition under high light is much lower than under low light conditions. Indeed. Allorent et al. (2013) showed that the phosphorylation of LHCII antenna, mainly mediated by the STN7/Stt7 kinase in low light, is inhibited by high light, due either to a negative regulation of the kinase through the thioredoxin pathway under high light (see e.g. Lemeille and Rochaix, 2010 ), or to a conformational change in the PSII antenna ( Vink et al. , 2004 ).

To avoid the harmful effects of over-excitation, plants optimize their photosynthetic performance based on their illumination history through a process in which Z seems to play a key role (e.g. Ruban et al. , 2012 ). Matuszyńska et al. (2016) used a combined experimental and theoretical approach in the study of qE, particularly designed to determine if plants have a ‘memory’ of their recent (minutes to hours) light exposure, similar to what occurs after really long (days, months) periods of stress ( Demmig et al. , 1987 ; Adams and Demmig-Adams, 2004 ). In these studies, fluorescence measurements were made on Epipremnum aureum (a shadow (shade)-tolerant, ornamental plant) by PAM-SP. Here, F M ′ was used instead of NPQ, as suggested by Holzwarth et al. (2013) , to avoid mathematical distortion of the ChlF quenching kinetics. Additionally, the pigment composition was measured at the end of each phase of the experiment, in order to determine the contribution of Z to the ‘memory’ effect. These data confirmed the presence of a short-term ‘memory’ effect, which is influenced by both light intensity and the period of dark-relaxation between two light exposures. Matuszyńska et al. (2016) concluded that the ‘memory’ of recent light exposure related to qE can be assigned to dynamic changes in pigment composition, being due to a slower conversion of Z to V, as observed by, for example, Demmig et al. (1987) and Reinhold et al. (2008) . By implementing a qE model based on the ‘4 state-2-site quenching’ system ( Holzwarth and Jahns, 2014 ) in the photosynthesis model of Ebenhöh et al. (2014) (but without state transitions), Matuszyńska et al. (2016) were able to simulate successfully changes in the quantum yield of ChlF during the PAM-SP experiments, discussed above. In these simulations, the ChlF signal was also calculated using ratios of rate constants related to fluorescence emission, heat dissipation and photochemistry, where the rate constant of the heat dissipation was assumed to be modulated by the concentration of a quencher (Q), which was, in turn, calculated by taking into account the concentrations at any time of both Z and the protonated PsbS protein. [Note that Snellenburg et al. (2017) and Morales et al . (2018 a , b ) have used similar qE models, depending on the relative concentrations of Z and protonated PsbS.]

Modelling alternative electron flows

Besides LEF, which provides the Calvin–Benson cycle with NADPH and ATP, other ET routes function during oxygenic photosynthesis (see Fig. 1 ; Alric and Johnson, 2017 ; Shikanai and Yamamoto, 2017 ): (1) CEF-PSI via ferredoxin-plastoquinone reductase, or NADPH dehydrogenase (NDH); and (2) ‘alternative’ non-cyclic pathways that involve reduction of electron acceptors such as O 2 [the water–water cycle (WWC); see a model by Valero et al. (2009) ], or oxaloacetate [by malate dehydrogenase (MDH); see a model by Fridlyand et al. (1998) ]. The main role of CEF-PSI is to increase the ATP/NADPH ratio, as ‘required’ by the metabolic reactions in stroma or other energy-dependent processes in the chloroplast; furthermore, the pH difference, which induces qE, protects PSI and PSII against photoinhibition ( Strand et al , 2016 , 2017 ). The electron pathway to molecular oxygen (Mehler reaction, WWC), besides contributing to the acidification of the lumen and to the reduction of the excitation pressure on PSs, is also important in chloroplast redox signalling during abiotic stress, and in the regulation of CEF-PSI ( Miyake, 2010 ). The respective contributions of alternative electron pathways to the total ET is strictly regulated, depending on environmental conditions, but further research is needed to understand how these diverse pathways and their regulatory mechanisms function (see Yamori et al. , 2016 ; Nawrocki et al. , 2019 ).

Comprehensive dynamic C 3 photosynthesis models, such as those by Laisk et al . (2006 , 2009 ) and Zhu et al. (2013) , include light reactions, proton and electron transport, detailed carbon metabolism reactions, exchange of intermediates between cytosol and stroma, photorespiration, amino acid synthesis, and regulatory mechanisms. However, because these models involve a large number of model parameters, simplified photosynthesis models are much more suitable, and practical, for the study of dynamic responses of the photosynthetic apparatus to diverse changes of environmental factors. Indeed, a number of simplified photosynthesis models have been used in several studies to analyse PETC regulation in silico , through simulation of experimental data measured with a variety of methods ( Ebenhöh et al. , 2011 ; Zaks et al. , 2013 ; Tikhonov and Vershubskii, 2014 ; Stirbet and Govindjee, 2016 ; Snellenburg et al. , 2017 ; Morales et al ., 2018 a , b ; Matuszyńska et al ., 2016 , 2019 ). According to Morales et al. (2018 b ), the term ‘regulation’ means: reaching simultaneously, during environmental fluctuations, a suitable redox state of PETC, dissipation of excess excitation energy and ATP/NADPH ratio through adjustments of NPQ processes, CEF-PSI and reduction of alternative electron acceptors (also including the reduction of NO 2 ‒ during NH 4 + assimilation, NiR), as well as pmf optimization through changes in ATP synthase activity.

We have reviewed above results obtained in studies of photosynthesis regulation through state transitions and qE, based on simulations of ChlFI data. By contrast, Morales et al. (2018 b ) used, for simulations, several types of experimental data on Arabidopsis thaliana , such as PAM-SP ChlF data (for effective quantum yield of PSII and NPQ), Δ A 820 (for the P700 redox state, which is related to LET and alternative ET pathways), the electrochromic shift in A 520 (for pmf and its components), and net CO 2 assimilation ( A n , for the Calvin–Benson cycle and CO 2 diffusion). The results of these simulations have shown that CEF-PSI and alternative ET pathways are strongly interacting, and, thus, changes in FQR- or NDH-dependent CEF-PSI kinetics indirectly influence WWC, NiR and MDH activities, due to changes in the redox state of Fd. It is also known that the steady-state pH in the lumen cannot be controlled only by CEF-PSI and alternative ET, because it is also greatly affected by the pH sensitivity of qE, Cyt b 6 /f and ATP synthase. Additionally, Morales et al. (2018 b ) have examined the influence of the ADP/ATP ratio in stroma on the metabolic regulation of ATP synthesis, and their simulations showed that there is a coordination between the regulation of Rubisco, NPQ and PETC over a large range of light intensities and CO 2 concentrations. These are important observations for programming plants for better productivity.

The slow part of the ChlFI induction also reflects changes due to the induction of the Calvin–Benson cycle during a dark to light transition. The activation and gradual increase in CO 2 assimilation during this phase leads to a parallel activation of ATP synthesis and an increase in the rate of LEF, which decreases the initial excitation pressure. As a result: (1) the level of Q A reduction decreases and photochemical quenching increases; and (2) qE decreases, because, due to a faster synthesis of ATP, the ΔpH decreases. Therefore, only models that include the induction of the Calvin–Benson cycle are suitable for correctly modelling the slow part of the ChlFI induction (see Laisk et al ., 2006 , 2009 ; Zhu et al. , 2013 ).

The Calvin–Benson cycle is one of the best-studied plant metabolic processes. Besides photosynthesis models, which include both the light and carbon reactions (e.g. Laisk et al ., 2006 , 2009 ; Zhu et al. , 2013 ; Belassio, 2019 ; Matuszyńska et al. , 2019 ), the carbon assimilation was often modelled separately, by considering a simplified relationship for NADPH and ATP supply (see review by Jablonsky et al. , 2011 ). In these models, carbon metabolism was analysed either by taking into account the kinetic properties of the enzymes involved, i.e. dynamic modelling ( Pettersson and Ryde-Pettersson, 1988 ; Zhu et al. , 2007 ), or without the need to use these, i.e. stoichiometric modelling ( Boyle and Morgan, 2009 ). In addition, a combination of both the above approaches has also been used ( Fleming et al. , 2010 ). In many models for the Calvin–Benson cycle, the steady-state behaviour of the photosynthetic apparatus has been analysed based on the equations of Farquhar et al . (1980) . Here we briefly mention some recent results on (short-term) regulation of photosynthesis obtained with the photosynthesis models of Morales et al. (2018 a ), Belassio (2019) and Matuszyńska et al. (2019) .

Fluctuating irradiances, which were shown to limit the performance of photosynthesis ( Pearcy, 1990 ), can be due to transient sun exposure, penumbra effects, shading by clouds, gaps in the canopy that produce ‘light (sun) flecks’, or movements of the leaves in the wind. Morales et al. (2018 a ) used a simplified dynamic model of CO 2 assimilation in a leaf to analyse the effects of fluctuating irradiances. In this study, they extended the canonical steady-state model by adding original empirical (phenomenological) partial models for the effects of chloroplast movement (qM; Dall’Osto et al. , 2014 ; Baránková et al. , 2016 ; Semer et al ., 2018 , 2019 ), qE, qI, regulation of enzyme activity in the Calvin–Benson cycle, metabolite concentrations, and the dynamic CO 2 diffusion through different leaf compartments. Changes in qE were assumed to follow PsbS protonation and Z generation, as was the case with the approach used by Matuszyńska et al. (2016) . With their model, Morales et al. (2018 a ) analysed potential improvements in CO 2 assimilation that may result after removing the kinetic limitation of different regulatory processes. Their simulations predicted that the most limiting steps in the carbon reactions are the activation rates of the Calvin–Benson cycle enzymes and stomatal opening (up to 17 % improvement), followed by the rate of qE relaxation and chloroplast movement (up to 10 % improvement), depending on the frequency of light fluctuations. However, up to 32 % improvement in CO 2 assimilation has been predicted, when all the kinetic limitations were simultaneously removed. Belassio (2019) has presented a dynamic photosynthesis model which also includes both light and carbon reactions, coupled to a mechanistic hydro-mechanical partial model for stomatal behaviour. This model successfully simulates responses to rapid changes in light intensity (light flecks), as well as in atmospheric CO 2 and O 2 concentrations. This model is freely available (as a supplement to the paper), and runs as a stand-alone workbook in Microsoft Excel.

Finally, Matuszyńska et al. (2019) have proposed a dynamic photosynthetic model describing the light reactions and the Calvin–Benson cycle in C 3 plants, for which they have used their earlier models [for light reactions: Ebenhöh et al. (2014) and Matuszyńska et al. (2016) ; for carbon reactions: Pettersson and Ryde-Pettersson (1988) and Poolman et al. (2000) ]. This newly merged model is based on nine coupled ODEs for the PETC, and 15 coupled ODEs for the carbon reactions. Analysis of this model shows the need for a ‘stand-by’ mode of the Calvin–Benson cycle in darkness, so that it can be restarted after prolonged dark periods; in this sense, the oxidative pentose phosphate pathway can play this function. Matuszyńska et al. (2019) have also used MCA (e.g. Visser and Heijnen, 2002 ) and metabolic supply–demand analysis ( Hofmeyr and Cornish-Bowden, 2000 ) to investigate the regulatory dependence between the PETC and the Calvin–Benson cycle, and to quantify the ‘control distribution’ of supply and demand under different light conditions and CO 2 assimilation rates. Th results obtained with MCA have indicated that, when CO 2 is saturating, the demand reactions control the flux under light-saturating conditions (with seduheptulose-1,7- bis phosphatase maintaining the highest overall flux control; see Poolman et al. , 2000 ), while the supply reactions display higher overall flux control under light-limited conditions, with PSII and PSI activities sustaining the highest overall flux control.

In this review, we have shown the important role played by models in deciphering and untangling different less well-understood and complex processes of photosynthesis, emphasizing the necessity and importance of modelling in the analysis of hypotheses developed from experimental studies. One major example, used in this review, is the ChlFI, which is simultaneously influenced by various photosynthetic processes affecting different segments of the fluorescence transient. As shown here, this process has been simulated by many modellers, who were focused either on understanding the dynamics of the redox states of different PETC components (see also reviews by Lazár, 1999 ; Lazár and Schansker, 2009 ; Stirbet et al. , 2014 ), or that of more complex, regulatory mechanisms involved in processes such as state transitions and qE, or of the relative contributions of alternative ET pathways, as well as their relationship with the CO 2 assimilation (the Calvin–Benson cycle) (see also Stirbet et al ., 2014 ). From the examples discussed in this review, it is evident that correctly simplified but complete dynamic models of photosynthesis are well suited to obtaining information about how the photosynthetic organisms cope with variable environmental conditions (see also Matuszyńska and Ebenhöh, 2015 ). Indeed, modelling is a very efficient method to identify important morphological and physiological parameters of a biological system and to find their optimal values. In addition, by using a larger variety of experimental data to verify such models, the simulations can lead to much more meaningful information about the organizational principles of the photosynthetic apparatus, which can also reveal original ways and means to improve the photosynthetic efficiency of plant crops ( Zhu et al. , 2007 ; Rosenthal et al. , 2011 ; Kromdijk et al. , 2016 ), besides being of theoretical interest. Moreover, multi-scale plant models (also known as plant system models), which quantitatively integrate physical, biochemical and physiological processes at different organizational levels (e.g. molecular, cell, organ, plant, population, or ecosystem), are able to predict physiological and growth properties of plants beyond photosynthetic metabolism, and they represent the future challenge in plant modelling (see Zhu et al. , 2016 ; Marshall-Colón et al. , 2017 ; Chang et al. , 2019 ; Marshall-Colón and Kliebenstein, 2019 ).

D.L. was supported by European Regional Development Fund project ‘Plants as a tool for sustainable global development’ [No. CZ.02.1.01/0.0/0.0/16_019/0000827].

Govindjee is grateful for IT support provided by the UIUC Life Sciences Office of Information Technology (Andrew Debevec, Karl Schlipf, Thomas Uebele, Jeffrey Haas), and the staff of the Department of Plant Biology and of the Department of Biochemistry, University of Illinois at Urbana-Champaign; he encourages all readers to visit his web site ( http://www.life.illinois.edu/govindjee/ ) to download available educational material on photosynthesis for personal use.

Adams WW III , Demmig-Adams B . 2004 . Chlorophyll fluorescence as a tool to monitor plant response to the environment. In: George C , Papageorgiou GC , Govindjee . eds: Chlorophyll a fluorescence: a signature of photosynthesis. Advances in photosynthesis and respiration . Vol. 19 . Dordrecht : Springer , 583 – 604 .

Google Scholar

Google Preview

Allen JF . 2002 . Plastoquinone redox control of chloroplast thylakoid protein phosphorylation and distribution of excitation energy between photosystems: discovery, background, implications . Photosynthesis Research 73 : 139 – 148 .

Allen JF . 2003 . State transitions – a question of balance . Science 299 : 1530 – 1532 .

Allen JF , Bennett J , Steinback KE , Arntzen CJ . 1981 . Chloroplast protein phosphorylation couples plastoquinone redox state to distribution of excitation-energy between photosystems . Nature 291 : 25 – 29 .

Allen MB , Whatley FR , Arnon DI . 1958 . Photosynthesis with isolated chloroplasts. VI. Rates of conversion of light into chemical energy in photosynthetic phosphorylation . Biochimica et Biophysica Acta 27 : 16 – 23 .

Allorent G , Tokutsu R , Roach T , et al.  2013 . A dual strategy to cope with high light in Chlamydomonas reinhardtii . Plant Cell 25 : 545 – 557 .

Alric J . 2010 . Cyclic electron flow around photosystem I in unicellular green algae , Photosynthesis Research 106 : 47 – 56 .

Alric J , Johnson X . 2017 . Alternative electron transport pathways in photosynthesis: a confluence of regulation . Current Opinion in Plant Biology 37 : 78 – 86 .

Antal TK , Maslakov A , Yakovleva OV , Krendeleva TE , Riznichenko GY , Rubin AB . 2018 . Simulation of chlorophyll fluorescence rise and decay kinetics, and P 700 -related absorbance changes by using a rule-based kinetic Monte-Carlo method . Photosynthesis Research 138 : 191 – 206 .

Arnon DI . 1984 . The discovery of photosynthetic phosphorylation . Trends in Biochemical Sciences 9 : 258 – 262 .

Arnon DI , Allen MB , Whatley FR . 1954 a . Photosynthesis by isolated chloroplasts . Nature 174 : 394 – 396 .

Arnon DI , Whatley FR , Allen MB . 1954 b . Photosynthesis by isolated chloroplasts. II. Photosynthetic phosphorylation, the conversion of light energy into phosphate bond energy . Journal of the American Chemical Society 76 : 6324 – 6329 .

Asada K . 1999 . The water–water cycle in chloroplasts: scavenging of active oxygens and dissipation of excess photons . Annual Review of Plant Physiology and Plant Molecular Biology 50 : 601 – 639 .

Avron M . 1963 . A coupling factor in photophosphorylation . Biochimica et Biophysica Acta 77 : 699 – 702 .

Baake E , Schlöder JP . 1992 . Modelling the fast fluorescence rise of photosynthesis . Bulletin of Mathematical Biology 54 : 999 – 1021 .

Backhausen JE , Kitzmann C , Horton P , Scheibe R . 2000 . Electron acceptors in isolated intact spinach chloroplasts act hierarchically to prevent over-reduction and competition for electrons . Photosynthesis Research 64 : 1 – 13 .

Baránková B , Lazár D , Nauš J . 2016 . Analysis of the effect of chloroplast arrangement on optical properties of green tobacco leaves . Remote Sensing of Environment 174 : 181 – 196 .

Bassham JA . 2005 . Mapping the carbon reduction cycle: a personal perspective. In: Govindjee , Beatty JT , Gest H , Allen JF , eds. Discoveries in photosynthesis. Advances in photosynthesis and respiration . Dordrecht : Springer , 815 – 832 .

Bay Z , Pearlstein RM . 1963 . A theory of energy transfer in the photosynthetic unit . Proceedings of the National Academy of Sciences of the USA 50 : 1071 – 1078 .

Belassio C . 2019 . A generalised dynamic model of leaf-level C3 photosynthesis combining light and dark reactions with stomatal behavior . Photosynthesis Research 141 : 99 – 118 .

Belyaeva NE . 2004 . Generalized model of primary photosynthetic processes in chloroplasts . PhD thesis, Lomonosov Moscow State University .

Belyaeva NE , Bulychev AA , Riznichenko GYu , Rubin AB . 2011 . A model of photosystem II for the analysis of fast fluorescence rise in plant leaves . Biophysics 56 : 464 – 477 .

Belyaeva NE , Bulychev AA , Riznichenko GYu , Rubin AB . 2016 . Thylakoid membrane model of the Chl a fluorescence transient and P700 induction kinetics in plant leaves . Photosynthesis Research 130 : 491 – 515 .

Belyaeva NE , Bulychev AA , Riznichenko GYu , Rubin AB . 2019 . Analyzing both the fast and the slow phases of chlorophyll a fluorescence and P700 absorbance changes in dark-adapted and preilluminated pea leaves using a thylakoid membrane model . Photosynthesis Research 140 : 1 – 19 .

Benson AA . 2005 . Following the path of carbon in photosynthesis: a personal story. In: Govindjee , Beatty JT , Gest H , Allen JF , eds. Discoveries in photosynthesis. Advances in photosynthesis and respiration . Dordrecht : Springer , 793 – 813 .

Bennoun P . 1982 . Evidence for a respiratory chain in the chloroplast . Proceedings of the National Academy of Sciences of the USA 79 : 4352 – 4356 .

Blackman FF . 1905 . Optima and limiting factors . Annals of Botany 19 : 281 – 295 .

Blankenship RE . 2014 . Molecular Mechanisms of Photosynthesis , 2nd edn. Oxford : Wiley-Blackwell .

Bonaventura C , Myers J . 1969 . Fluorescence and oxygen evolution from Chlorella pyrenoidosa . Biochimica et Biophysica Acta 189 : 366 – 383 .

Bouges-Bocquet B . 1973 . Electron transfer between two photosystems in spinach chloroplasts . Biochimica et Biophysica Acta 31 : 250 – 256 .

Boyer PD . 2002 . A research journey with ATP synthase . The Journal of Biological Chemistry 277 : 39045 – 39061 .

Boyle NR , Morgan JA . 2009 . Flux balance analysis of primary metabolism in Chlamydomonas reinhardtii . BMC Systems Biology 3 : 4 .

Breton J . 1982 . The 692 nm fluorescence (F695) of chloroplasts at low temperature is emitted from the primary acceptor of photosystem II . FEBS Letters 147 : 16 – 20 .

Briantais J-M , Vernotte C , Picaud M , Krause GH . 1979 . A quantitative study of the slow decline of chlorophyll a fluorescence in isolated chloroplasts . Biochimica et Biophysica Acta 548 : 128 – 138 .

Brooks MD , Jansson S , Niyogi KK . 2014 . PsbS-dependent non-photochemical quenching. In: Demmig-Adams B , Garab G , Adams WW III , Govindjee , Sharkey TD , eds. Nonphotochemical quenching and energy dissipation in plants, algae and cyanobacteria. Advances in photosynthesis and respiration , vol. 40. Dordrecht : Springer , 297 – 314 .

Buchanan BB , 2016 . The carbon (formerly dark) reactions of photosynthesis . Photosynthesis Research 128 : 215 – 217 .

Buchanan BB , Schürmann P , Wolosiuk RA , Jacquot JP . 2002 . The ferredoxin/thioredoxin system: from discovery to molecular structures and beyond . Photosynthesis Research 73 : 215 – 222 .

Buchert F , Hamon M , Gäbelein P , Scholz M , Hippler M , Wollman F . 2018 . The labile interactions of cyclic electron flow effector proteins . Journal of biological chemistry 293 : 17559 – 17573 .

Bulté L , Gans P , Rebeillé F , Wollman FA . 1990 . ATP control on state transitions in vivo in Chlamydomonas reinhardtii . Biochimica et Biophysica Acta 1020 : 72 – 80 .

Butler WL . 1962 . Effects of red and far-red light on the fluorescence yield of chlorophyll in vivo . Biochimica et Biophysica Acta 64 : 309 – 317 .

Butler WL . 1980 . Energy transfer between photosystem II units in a connected package model of the photochemical apparatus of photosynthesis (photochemical model) . Proceedings of the National Academy of Sciences of the USA 77 : 4697 – 4701 .

Butler WL , Kitajima M . 1975 . Fluorescence quenching in photosystem II of chloroplasts . Biochimica et Biophysica Acta 376 : 116 – 125 .

Butler WL , Strasser RJ . 1977 . Tripartite model for the photochemical apparatus of green plant photosynthesis . Proceedings of the National Academy of Sciences of the USA 74 : 3382 – 3385 .

Calvin M . 1989 . Forty years of photosynthesis and related activities . Photosynthesis Research 23 : 3 – 16 .

Calvin M , Bassham JA , Benson AA . 1950 . Chemical transformations in photosynthesis . Federation Proceedings 9 : 524 – 534 .

Cardona T , Sedoud A , Cox N , Rutherford AW . 2012 . Charge separation in Photosystem II: a comparative and evolutionary overview . Biochimica et Biophysica Acta 1817 : 26 – 43 .

Chan HCH , Gamel OE , Fleming GR , Whaley KB . 2018 . Single-photon absorption by single photosynthetic light-harvesting complexes . Journal of Physics B: Atomic, Molecular and Optical Physics 51 : 054002 .

Chang TG , Chang S , Song QF , Perveen S , Zhu XG . 2019 . Systems models, phenomics and genomics: three pillars for developing high-yielding photosynthetically efficient crops . In silico Plants 1 : diy003 .

Chernev P , Goltsev V , Zaharieva I , Strasser RJ . 2006 . A highly restricted model approach quantifying structural and fuctional parameters of photosystem II probed by the chlorophyll a fluorescence rise . Ecological Engineering and Environment Protection 2 : 19 – 29 .

Clegg RM . 2006 . The history of FRET. In: Geddes CD , Lakowicz JR , eds. Reviews in fluorescence . New York : Springer , 1 – 45 .

Clegg RM , Sener M , Govindjee . 2010 . From Forster resonance energy transfer (FRET) to coherent resonance energy transfer (CRET) and back – A wheen o’mickles mak’s a muckle. In: Alfano RR , eds. Optical biopsy VII , vol. 7561. Proceedings of SPIE, 7561 – 7572 .

Cramer WA , Kallas T , eds. 2016 . Cytochrome complexes: evolution, structures, energy transduction, and signaling. Advances in photosynthesis and respiration , Vol. 41. Dordrecht : Springer .

Cramer WA , Hasan SS , Yamashita E . 2011 . The Q cycle of cytochrome bc complexes: a structure perspective . Biochimica et Biophysica Acta 1807 : 788 – 802 .

Croce R , van Amerongen H . 2013 . Light-harvesting in photosystem I . Photosynthesis Research 116 : 153 – 166 .

Dall’Osto L , Cazzaniga S , Wada M , Bassi R . 2014 . On the origin of a slowly reversible fluorescence decay component in the Arabidopsis npq4 mutant . Philosophical Transactions of the Royal Society B: Biological Sciences 369 , 20130221 .

Dau H . 1994 . Molecular mechanism and quantitative models of variable photosystem II fluorescence . Photochemistry and Photobiology 60 : 1 – 23 .

Davis GA , Kanazawa A , Schöttler MA , et al.  2016 . Limitations to photosynthesis by proton motive force-induced photosystem II photodamage . eLife 5 , e16921 .

Debus RJ , Barry BA , Sithole I , Babcock GT , McIntosh L . 1988 . Direct mutagenesis indicates that the donor to P680+ in photosystem II is tyrosine-161 of the D1 polypeptide . Biochemistry 27 : 9071 – 9074 .

Demmig-Adams B . 2003 . Linking the xanthophyll cycle with thermal energy dissipation . Photosynthesis Research 76 : 73 – 80 .

Demmig B , Winter K , Krüger A , Czygan F-C . 1987 . Photoinhibition and zeaxanthin formation in intact leaves: a possible role of the xanthophyll cycle in the dissipation of excess light energy . Plant Physiology 84 : 218 – 224

Demmig-Adams B , Winter K , Krüger A , Czygan F-C . 1989 . Zeaxathin and the induction and relaxation kinetics of the dissipation of excess excitation energy in leaves in 2% O 2 , 0% CO 2 . Plant Physiology 90 : 887 – 893 .

Demmig-Adams B , Garab G , Adams WW III , Govindjee , Sharkey TD , eds. 2014 . Nonphotochemical quenching and energy dissipation in plants, algae and cyanobacteria. Advances in photosynthesis and respiration , vol. 40. Dordrecht : Springer .

Dismukes GC , Siderer Y . 1980 . EPR spectroscopic observations of a manganese center associated with water oxidation in spinach chloroplasts . FEBS Letters 121 : 78 – 80 .

Döring G , Renger G , Vater J. Witt HT . 1969 . Properties of the photoactive chlorophyll-aII in photosynthesis . Zeitschrift für Naturforschung 24 : 1139 – 1143 .

Durrant J , Giorgi L , Barber J , Klug D , Porter G . 1990 . Characterisation of triplet states in isolated photosystem II reaction centres: oxygen quenching as a mechanism for photodamage . Biochimica et Biophysica Acta 1017 : 167 – 175 .

Duysens LNM . 1952 . Transfer of excitation energy in photosynthesis . PhD Thesis, Leiden University .

Duysens LMN , Amesz J , Kamp BM . 1961 . Two photochemical systems in photosynthesis . Nature 190 : 510 – 511 .

Duysens LMN , Sweers HT . 1963 . Mechanism of the two photochemical reactions in algae as studied by means of fluorescence. In: Japanese Society of Plant Physiologists , ed. Studies on microalgae and photosynthetic bacteria . Tokyo : University of Tokyo Press , 353 – 372 .

Eaton-Rye JJ , Tripathy BC , Sharkey TD , eds. 2012 . Photosynthesis: plastid biology, energy conversion and carbon assimilation . Dordrecht : Springer .

Ebenhöh O , Houwaart T , Lokstein H , Schlede S , Tirok K . 2011 . A minimal mathematical model of nonphotochemical quenching of chlorophyll fluorescence . Biosystems 103 : 196 – 204 .

Ebenhöh O , Fucile G , Finazzi GG , Rochaix J-D , Goldschmidt-Clermont M . 2014 . Short-term acclimation of the photosynthetic electron transfer chain to changing light: a mathematical model . Philosophical Transactions of the Royal Society B: Biological Sciences 369 : 20130223 .

Edwards GE , Black CC Jr . 1971 . Isolation of mesophyll cells and bundle sheath cells from Digitaria sanguinalis (L.) Scop. leaves and a scanning microscopy study of the internal leaf cell morphology . Plant Physiology 47 : 149 – 156 .

Emerson R . 1958 . The quantum yield of photosynthesis . Annual Review of Plant Physiology 9 : 124 .

Emerson R , Arnold W . 1932 a . A separation of the reactions in photosynthesis by means of intermittent light . Journal of General Physiology 15 : 391 – 420 .

Emerson R , Arnold W . 1932 b . The photochemical reaction in photosynthesis . The Journal of General Physiology 16 : 191 – 205 .

Emerson R , Lewis CM . 1943 . The dependence of the quantum yield of Chlorella photosynthesis on wavelength of light . American Journal of Botany 30 : 165 – 178 .

Emerson R , Chalmers RV , Cederstrand CN . 1957 . Some factors influencing the long wave limit of photosynthesis . Proceedings of the National Academy of Sciences of the USA 43 : 133 – 143 .

Engel GS , Calhoun TR , Read EL. et al.  2007 . Evidence for wavelike energy transfer through quantum coherence in photosynthetic systems . Nature 446 : 782 – 786

Farquhar GD , von Caemmerer S , Berry JA . 1980 . A biochemical model of photosynthetic CO 2 assimilation in leaves of C3 species . Planta 149 : 78 – 90 .

Fassioli F , Dinshaw R , Arpin PC , Scholes GD . 2014 . Photosynthetic light harvesting: excitons and coherence . Journal of the Royal Society Interface 11 : 20130901 .

Feng S , Fu L , Xia Q , Tan J , Jiang Y , Guo Y . 2018 . Modelling and simulation of photosystem II chlorophyll fluorescence transition from dark-adapted state to light-adapted state . IET Systems Biology 12 : 289 – 293 .

Fleming RMT , Thiele I , Provan G , Nasheuer HP . 2010 . Integrated stoichiometric, thermodynamic and kinetic modelling of steady state metabolism . Journal of Theoretical Biology 264 : 683 – 692 .

Förster T . 1946 . Energiewanderung und fluoreszenz . Naturwissenschaften 6 : 166 – 175 .

Förster T . 1948 . Zwischenmolekulare energiewanderung und fluoreszenz . Annalen der Physik 2 : 55 – 75 .

Fridlyand LE , Backhausen JE , Scheibe R . 1998 . Flux control of the malate valve in leaf cells . Archives of Biochemistry and Biophysics 349 : 290 – 298 .

Gaffron H , Wohl K . 1936 . Zür theorie der assimilation . Naturwissenschaften 24 : 103 – 107 .

Gilmore AM . 1997 . Mechanistic aspects of xanthophyll cycle dependent energy dissipation in higher plant chloroplasts and leaves . Physiologia Plantarum 99 : 197 – 209 .

Gilmore AM , Hazlett TL , Govindjee . 1995 . Xanthophyll cycle dependent quenching of Photosystem II chlorophyll a fluorescence: formation of a quenching complex with a short fluorescence lifetime . Proceedings of the National Academy of Sciences of the USA 92 : 2273 – 2277 .

Gilmore AM , Shinkarev VP , Hazlett TL , Govindjee . 1998 . Quantitative analysis of the effects of intra-thylakoid pH and xanthophylls cycle pigments on chlorophyll a lifetime distributions and intensity in thylakoids . Biochemistry 37 : 13582 – 13593 .

Golbeck JH , ed. 2006 . Photosystem I. The light-driven plastocyanin:ferredoxin oxidoreductase. Advances in photosynthesis and respiration , Vol. 24. Dordrecht : Springer .

Goldschmidt-Clermont M , Bassi R . 2015 . Sharing light between two photosystems: mechanism of state transitions . Current Opinion in Plant Biology 25 : 71 – 78 .

Goltsev V , Yordanov I . 1997 . Mathematical model of prompt and delayed chlorophyll fluorescence induction kinetics . Photosynthetica 33 : 571 – 586 .

Govindjee . 1995 . Sixty-three years since Kautsky: chlorophyll a fluorescence . Australian Journal of Plant Physiology 22 : 131 – 160 .

Govindjee . 2004 . Chlorophyll a fluorescence: a bit of basics and history. In: Papageorgiou GC , Govindjee , eds. Chlorophyll a fluorescence: a signature of photosynthesis . Advances in photosynthesis and respiration , Vol 19. Dordrecht : Springer , 1 – 41 .

Govindjee , Krogmann DW . 2004 . Discoveries in oxygenic photosynthesis (1727–2003): a perspective: dedicated to the memories of Martin Kamen (1920–2002) and William A. Arnold (1904–2001) . Photosynthesis Research 80 : 15 – 57 .

Govindjee , Papageorgiou GC . 1971 . Chlorophyll fluorescence and photosynthesis: fluorescence transients. In: Giese AC, ed. Photophysiology . New York : Academic Press , 1 – 46 .

Govindjee , Rabinowitch EI . 1960 . Two forms of chlorophyll a in vivo with distinct photochemical function . Science 132 : 355 – 356 .

Govindjee , Renger G . 1993 . In appreciation of Bessel Kok . Photosynthesis Research 38 : 211 – 213 .

Govindjee , Satoh K . 1986 . Fluorescence properties of chlorophyll b- and chlorophyll c-containing algae. In: Govindjee , Amesz J , Fork DC . eds. Light emission by plants and bacteria . Orlando : Academic Press , 497 – 537 .

Govindjee , van Rensen JJS . 1978 . Bicarbonate effects on the electron flow in isolated broken chloroplasts . Biochimica et Biophysica Acta 505 : 183 – 213 .

Govindjee , Ichimura S , Cederstrand C , Rabinowitch EI . 1960 . Effect of combining far-red light with shorter wave light on the excitation of fluorescence in Chlorella . Archives of Biochemistry and Biophysics 89 : 322 – 323 .

Govindjee , Barber J , Cramer WA , et al. . , eds. 1986 . Excitation and electron transfer in photosynthesis – special issue dedicated to Warren L Butler . Photosynthesis Research 10 : 147 – 518 .

Govindjee , Beatty JT , Gest H , Allen JF , eds. 2005 . Discoveries in photosynthesis. Advances in photosynthesis and respiration . Dordrecht : Springer .

Govindjee , Kern JF , Messinger J , Whitmarsh J . 2010 . Photosystem II. In: Encyclopedia of Life Sciences (ELS) . Chichester : John Wiley & Sons, Ltd , 1 – 15 .

Govindjee , Shevela D , Björn L . 2017 . Evolution of the Z-scheme of photosynthesis: a perspective . Photosynthesis Research 133 : 5 – 15 .

Guissé B , Srivastava A , Strasser RJ . 1995 . The polyphasic rise of the chlorophyll a fluorescence (O-K-J-I-P) in heat stressed leaves . Archives des Sciences - Université de Genève 48 : 147 – 160 .

Guo Y , Tan J . 2011 . Modeling and simulation of the initial phases of chlorophyll fluorescence from photosystem II . BioSystems 103 : 152 – 157 .

Guo Y , Tan J . 2014 . Kinetic Monte Carlo simulation of the initial phases of chlorophyll fluorescence from photosystem II . BioSystems 115 : 1 – 4 .

Hager A , Holocher K . 1994 . Localization of the xanthophyll-cycle enzyme violaxanthin de-epoxidase within the thylakoid lumen and abolition of its mobility by a (light-dependent) pH decrease . Planta 192 : 581 – 589 .

Harbinson J , Woodward FI . 1987 . The use of light-induced absorbance changes at 820 nm to monitor the oxidation state of P-700 in leaves . Plant, Cell & Environment 10 : 131 – 140 .

Heber U . 2002 . Irrungen, Wirrungen? The Mehler reaction in relation to cyclic electron transport in C3 plants . Photosynthesis Research 73 : 223 – 231 .

Hemschemeier A , Happe T . 2011 . Alternative photosynthetic electron transport pathways during anaerobiosis in the green alga Chlamydomonas reinhardtii . Biochimica et Biophysica Acta 1807 : 919 – 926 .

Hill R . 1937 . Oxygen evolution by isolated chloroplasts . Nature 139 : 881 – 882 .

Hill R , Bendall F . 1960 . Function of the two cytochrome components in chloroplasts: a working hypothesis . Nature 186 : 136 – 140 .

Hind G , Jagendorf AT . 1963 . Separation of light and dark stages in photophosphorylation . Proceedings of the National Academy of Sciences of the USA 49 : 715 – 722 .

Hofmeyr JHS , Cornish-Bowden A . 2000 . Regulating the cellular economy of supply and demand . FEBS Letters 476 : 47 – 51 .

Holzapfel C . 1978 . Analysis of the prompt fluorescence induction by means of computer simulation of the primary photosynthetic reactions . Zeitschrift für Naturforschung 33c : 402 – 407 .

Holzapfel C , Bauer R . 1975 . Computer simulation of primary photosynthetic reactions – Compared with experimental results on O 2 -exchange and chlorophyll fluorescence of green plants . Zeitschrift für Naturforschung 30c : 489 – 498 .

Holzwarth A , Jahns P . 2014 . Non-photochemical quenching mechanisms in intact organisms as derived from ultrafast-fluorescence kinetic studies. In: Demmig-Adams B , Garab G , Adams WW III , Govindjee , Sharkey TD , eds. Nonphotochemical quenching and energy dissipation in plants, algae and cyanobacteria. Advances in photosynthesis and respiration , vol. 40. Dordrecht : Springer , 129 – 156 .

Holzwarth AR , Miloslavina Y , Nilkens M , Jahns P . 2009 . Identification of two quenching sites active in the regulation of photosynthetic light-harvesting studied by time-resolved fluorescence . Chemical Physics Letters 483 : 262 – 267 .

Holzwarth AR , Lenk D , Jahns P . 2013 . On the analysis of non-photochemical chlorophyll fluorescence quenching curves: I. Theoretical considerations . Biochimica et Biophysica Acta 1827 : 786 – 792 .

Horton P , Ruban A , Rees D , Pascal A , Noctor G , Young A . 1991 . Control of the light-harvesting function of chloroplast membranes by aggregation of the LHCII chlorophyll protein complex . FEBS Letters 292 : 1 – 4 .

Horton P , Ruban V , Walters RG . 1996 . Regulation of light harvesting in green plants . Annual Review of Plant Physiology and Plant Molecular Biology 47 : 655 – 684 .

Horton P , Johnson MP , Perez-Bueno ML , Kiss AZ , Ruban AV . 2008 . Photosynthetic acclimation: does the dynamic structure and macro-organisation of photosystem II in higher plant grana membranes regulate light harvesting states? The FEBS Journal 275 : 1069 – 1079 .

Hsu B-D . 1992 a . A theoretical study on the fluorescence induction curve of spinach thylakoids in the absence of DCMU . Biochimica et Biophysica Acta 1140 : 30 – 36 .

Hsu B-D . 1992 b . The active photosystem II centers can make a significant contibution to the initial fluorescence rise from F 0 to F i . Plant Science 81 : 169 – 174 .

Hsu B-D , Lee Y-S , Jang Y-R . 1989 . A method for analysis of fluorescence induction curve from DCMU-poisoned chloroplasts . Biochimica et Biophysica Acta 975 : 44 – 49 .

Ishizaki A , Fleming GR . 2009 . United treatment of quantum coherent and incoherent hopping dynamics in electronic energy transfer: reduced hierarchy equation approach . The Journal of Chemical Physics 130 : 234111 .

Iwai M , Yokono M , Inada N , Minagawa J . 2010 . Live-cell imaging of photosystem II antenna dissociation during state transitions . Proceedings of the National Academy of Sciences of the USA 107 : 2337 – 2342 .

Jablonsky J , Lazar D . 2008 . Evidence for intermediate S-states as initial phase in the process of oxygen-evolving complex oxidation . Biophysical Journal 94 : 2725 – 2736 .

Jablonsky J , Bauwe H , Wolkenhauer O . 2011 . Modeling the Calvin–Benson cycle . BMC Systems Biology 5 : 185 .

Jagendorf AT . 2002 . Photophosphorylation and the chemiosmotic perspective . Photosynthesis Research 73 : 233 – 241 .

Jagendorf AT , Uribe E . 1966 . ATP formation caused by acid-base transition of spinach chloroplasts . Proceedings of the National Academy of Sciences of the USA 55 : 170 – 177 .

Jahns P , Holzwarth AR . 2012 . The role of the xanthophyll cycle and of lutein in photoprotection of photosystem II . Biochimica et Biophysica Acta 1817 : 182 – 193 .

Johnson MP , Ruban AV . 2011 . Restoration of rapidly reversible photoprotective energy dissipation in the absence of PsbS protein by enhanced ΔpH . Journal of Biological Chemistry 286 : 19973 – 19981 .

Johnson MP , Davison P , Ruban A , Horton P . 2008 . The xanthophyll cycle pool size controls the kinetics of non-photochemical quenching in Arabidopsis thaliana . FEBS Letters 582 : 259 – 263 .

Johnson MP , Zia A , Ruban AV . 2012 . Elevated ΔpH restores rapidly reversible photoprotective energy dissipation in Arabidopsis chloroplasts deficient in lutein and xanthophyll cycle activity . Planta 235 : 193 – 204 .

Joliot A , Joliot P . 1964 . Étude cinétique de la réaction photochimique libérant l’oxygène au cours de la photosynthèse . Comptes Rendus de l’Académie des Sciences (Paris) 258 : 4622 – 4625 .

Joliot P . 1965 . Cinétiques de réactions liées à l’émission d’oxygène photosynthétique . Biochimica et Biophysica Acta 102 : 116 – 134 .

Joliot P . 2003 . Period-four oscillations of the flash-induced oxygen formation in photosynthesis . Photosynthesis Research 76 : 65 – 72 .

Joliot P , Joliot A . 2003 . Excitation transfer between photosynthetic units: the 1964 experiment . Photosynthesis Research 76 : 241 – 245 .

Joliot P , Barbieri G , Chabaud R . 1969 . Un nouveau modèle des centres photochimiques du système II . Photochemistry and Photobiology 10 : 309 – 329 .

Jordan P , Fromme P , Witt HT , Klukas O , Saenger W , Krauss N . 2001 . Three dimensional structure of cyanobacterial photosystem I at 2.5 Å resolution . Nature 411 : 909 – 917 .

Junge W . 2004 . Protons, proteins and ATP . Photosynthesis Research 80 : 197 – 221 .

Kaiser E , Morales A , Harbinson J , Kromdijk J , Heuvelink E , Marcelis LFM . 2015 . Dynamic photosynthesis in different environmental conditions . Journal of Experimental Botany 66 : 2415 – 2426 .

Kaiser E , Kromdijk J , Harbinson J , Heuvelink E , Marcelis LFM . 2017 . Photosynthetic induction and its diffusional, carboxylation and electron transport processes as affected by CO 2 partial pressure, temperature, air humidity and blue irradiance . Annals of Botany 119 : 191 – 205 .

Kamen MD . 1947 . Radioactive tracers in biology . New York : Academic Press .

Kamiya N , Shen R-J . 2003 . Crystal structure of oxygen-evolving photosystem II from Thermosynechococcus vulcanus at 3.7-Å resolution . Proceedings of the National Academy of Sciences of the USA 100 : 98 – 103 .

Kaňa R , Govindjee . 2016 . Role of ions in the regulation of light harvesting . Frontiers in Plant Science 7 : 1849 .

Kautsky H , Hirsch A . 1931 . Neue versuche zur kohlensaureassimilation . Naturwissenschaften 19 : 964 .

Kitajima M , Butler WL . 1975 . Quenching of chlorophyll fluorescence and primary photochemistry in chloroplasts by dibromothymoquinone . Biochimica et Biophysica Acta 723 : 105 – 115 .

Klimov VV , Klevanik AV , Shuvalov VA , Krasnovsky AA . 1977 . Reduction of pheophytin in primary light reaction of photosystem II . FEBS Letters 82 : 183 – 186 .

Klimov VV , Dolan E , Ke B . 1980 . EPR properties of an intermediary electron acceptor (pheophytin) in photosystem II reaction centers at cryogenic temperatures . FEBS Letters 112 : 97 – 100 .

Klughammer C , Schreiber U . 1994 . An improved method, using saturating light pulses, for the determination of photosystem I quantum yield via P700+-absorbance changes at 830 nm . Planta 192 : 261 – 268 .

Kodru S , Malavath T , Devadasu E , et al.  2015 . The slow S to M rise of chlorophyll a fluorescence induction reflects transition from state 2 to state 1 in the green alga Chlamydomonas reinhardtii . Photosynthesis Research 125 : 219 – 231 .

Kok B . 1956 . On the reversible absorption change at 705 μm in photosynthetic organisms . Biochimica et Biophysica Acta 22 : 399 – 401 .

Kok B , Forbush B , McGloin M . 1970 . Cooperation of charges in photosynthetic O 2 evolution. 1. A linear four step mechanism . Photochemistry and Photobiology 11 : 457 – 475 .

Kramer DM , Sacksteder CA , Cruz JA . 1999 . How acidic is the lumen? Photosynthesis Research 60 : 151 – 163 .

Krause H , Weis W . 1991 . Chlorophyll fluorescence and photosynthesis: the basics . Annual Review of Plant Physiology and Plant Molecular Biology 42 : 313 – 349 .

Krey A , Govindjee . 1964 . Fluorescence changes in Porphyridium exposed to green light of different Intensity: A new emission band at 693 nm and its significance to photosynthesis . Proceedings of the National Academy of Sciences of the USA 52 : 1568 – 1572 .

Krieger A , Weis E . 1993 . The role of calcium in the pH-dependent control of photosystem II . Photosynthesis Research 37 : 117 – 130 .

Krogmann DW , Jagendorf AT , Avron M . 1959 . Uncouplers of spinach chloroplast photosynthetic phosphorylation . Plant Physiology 34 : 272 – 277 .

Kromdijk J , Głowacka K , Leonelli L , et al.  2016 . Improving photosynthesis and crop productivity by accelerating recovery from photoprotection . Science 354 : 857 – 861 .

Kroon BMA , Thoms S . 2006 . From electron to biomass: a mechanistic model to describe phytoplankton photosynthesis and steady-state growth mates . Journal of Phycology 42 : 593 – 609 .

Kuvykin IV , Vershubskii AV , Priklonskii VI , Tikhonov AN . 2009 . Computer simulation study of pH-dependent regulation of electron transport in chloroplasts . Biophysics 54 : 455 – 464 .

Laisk A , Oja V . 2018 . Kinetics of photosystem II electron transport: a mathematical analysis based on chlorophyll fluorescence induction . Photosynthesis Research 136 : 63 – 82 .

Laisk A , Oja V , Rasulov B , Eichelmann H , Sumberg A . 1997 . Quantum yields and rate constants of photochemical and nonphotochemical excitation quenching. Experiment and model . Plant Physiology 115 : 803 – 815 .

Laisk A , Eichelmann H , Oja V . 2006 . C3 photosynthesis in silico . Photosynthesis Research 90 : 45 – 66 .

Laisk A , Eichelmann H , Oja V . 2009 . Leaf C 3 photosynthesis in silico : Integrated carbon/nitrogen metabolism. In: Laisk A , Nedbal AL , Govindjee , eds. Photosynthesis in silico: understanding complexity from molecules to ecosystems. Advances in photosynthesis and respiration , Vol. 29. Dordrecht : Springer , 295 – 322 .

Latimer P , Bannister TT , Rabinowitch E . 1956 . Quantum yields of fluorescence of plant pigments . Science 124 : 585 – 586 .

Lavergne J , Trissl H-W . 1995 . Theory of fluorescence induction in photosystem II: Derivation of analytical expressions in a model including exciton-radical-pair equilibrium and restricted energy transfer between photosynthetic units . Biophysical Journal 68 : 2474 – 2492 .

Lazár D . 1999 . Chlorophyll a fluorescence induction . Biochimica et Biophysica Acta 1412 : 1 – 28 .

Lazár D . 2003 . Chlorophyll a fluorescence rise induced by high light illumination of dark-adapted plant tissue studied by means of a model of photosystem II and considering photosystem II heterogeneity . Journal of Theoretical Biology 220 : 469 – 503 .

Lazár D . 2006 . The polyphasic chlorophyll a fluorescence rise measured under high intensity of exciting light . Functional Plant Biology 33 : 9 – 30 .

Lazár D . 2009 . Modelling of light-induced chlorophyll a fluorescence rise (O-J-I-P transient) and changes in 820 nm-transmittance signal of photosynthesis . Photosynthetica 47 : 483 – 498 .

Lazár D . 2013 . Simulations show that a small part of variable chlorophyll a fluorescence originates in photosystem I and contributes to overall fluorescence rise . Journal of Theoretical Biology 335 : 249 – 264 .

Lazár D . 2015 . Parameters of photosynthetic energy partitioning . Journal of Plant Physiology 175 : 131 – 147 .

Lazár D , Jablonský J . 2009 . On the approaches applied in formulation of a kinetic model of photosystem II: different approaches lead to different simulations of the chlorophyll a fluorescence transients . Journal of Theoretical Biology 257 : 260 – 269 .

Lazár D , Pospíšil P . 1999 . Mathematical simulation of chlorophyll a fluorescence rise measured with 3-(3′,4′-dichlorophenyl)-1,1-dimethylurea-treated barley leaves at room and high temperatures . European Biophysics Journal 28 : 468 – 477 .

Lazár D , Schansker G . 2009 . Models of chlorophyll a fluorescence transients. In: Laisk A , Nedbal L , Govindjee , eds. Photosynthesis in silico: understanding complexity from molecules to ecosystems. Advances in photosynthesis and respiration , Vol. 29. Dordrecht : Springer , 85 – 123 .

Lazár D , Nauš J , Matoušková M , Flašarová M . 1997 . Mathematical modeling of changes in chlorophyll fluorescence induction caused by herbicides . Pesticide Biochemistry and Physiology 57 : 200 – 210 .

Lazár D , Brokeš M , Nauš J , Dvořák L . 1998 . Mathematical modelling of 3-(3′,4′-dichlorophenyl)-1,1-dimethylurea action in plant leaves . Journal of Theoretical Biology 191 : 79 – 86 .

Lazár D , Tomek P , Ilík P , Nauš J . 2001 . Determination of the antenna heterogeneity of Photosystem II by direct simultaneous fitting of several fluorescence rise curves measured with DCMU at different light intensities . Photosynthesis Research 68 : 247 – 257 .

Lazár D , Ilík P , Kruk J , Strzalka K , Nauš J . 2005 . A theoretical study on effect of the initial redox state of cytochrome b559 on maximal chlorophyll fluorescence level (F M ). Implications for photoinhibition of photosystem II . Journal of Theoretical Biology 233 : 287 – 300 .

Lebedeva GV , Belyaeva NE , Demin OV , Riznichenko GYu , Rubin AB . 2002 . Kinetic model of primary photosynthetic processes in chloroplasts. Description of the fast phase of chlorophyll fluorescence induction under different light intensities . Biophysics (Russia) 47 : 968 – 980 .

Lemeille S , Rochaix JD . 2010 . State transitions at the crossroad of thylakoid signalling pathways . Photosynthesis Research 106 : 33 – 46 .

Li X-P , Björkman O , Shih C , et al.  2000 . A pigment-binding protein essential for regulation of photosynthetic light harvesting . Nature 403 : 391 – 395 .

Long SP , Zhu XG , Naidu SL , Ort DR . 2006 . Can improvement in photosynthesis increase crop yields? Plant, Cell and Environment 29 : 315 – 330 .

Long SP , Marshall-Colon A , Zhu XG . 2015 . Meeting the global food demand of the future by engineering crop photosynthesis and yield potential . Cell 161 : 56 – 66 .

Lubitz W , Chrysina M , Cox N . 2019 . Water oxidation in photosystem II . Photosynthesis Research 142 : 105 – 125 .

Lyu H , Lazár D . 2017 a . Modeling the light-induced electric potential difference (ΔΨ), the pH difference (ΔpH) and the proton motive force across the thylakoid membrane in C3 leaves . Journal of Theoretical Biology 413 : 11 – 23 .

Lyu H , Lazár D . 2017 b . Modeling the light-induced electric potential difference ΔΨ across the thylakoid membrane based on the transition state rate theory . Biochimica et Biophysica Acta 1858 : 239 – 248 .

Magyar M , Sipka G , Kovács L , et al.  2018 . Rate-limiting steps in the dark-to-light transition of Photosystem II - revealed by chlorophyll- a fluorescence induction . Scientific Reports 8 : 2755 .

Makarov S , Grachev EA , Antal TK . 2012 . Mathematical modeling of photosynthetic electron transport chain considering spatial heterogeneity of the thylakoid membrane . Mathematical Biology and Bioinformatics 7 : 508 – 528 .

Malkin S . 1966 . Fluorescence induction studies in isolated chloroplasts. II. Kinetic analysis of the fluorescence intensity dependence on time . Biochimica et Biophysica Acta 123 : 433 – 442 .

Malkin S , Kok B . 1966 . Fluorescence induction studies in isolated chloroplasts. I. Number of components involved in the reaction and quantum yields . Biochimica et Biophysica Acta 123 : 413 – 432 .

Malnoë A . 2018 . Photoinhibition or photoprotection of photosynthesis? Update on the (newly termed) sustained quenching component qH . Environmental and Experimental Botany 154 : 123 – 133 .

Mar T , Govindjee . 1972 . Kinetic models of oxygen evolution in photosynthesis . Journal of Theoretical Biology 36 : 427 – 446 .

Marshall-Colón A , Kliebenstein DJ . 2019 . Plant networks as traits and hypotheses: moving beyond description . Trends of Plant Science 24 : 840 – 852 .

Marshall-Colón A , Long SP , Douglas K , et al.  2017 . Crops in silico: generating virtual crops using an integrative and multi-scale modeling platform . Frontiers in Plant Science 8 : 786 .

Maslakov AS , Antal TK , Riznichenko GY , Rubin AB . 2016 . Modeling of primary photosynthetic processes using the kinetic Monte Carlo method . Biophysics 61 : 387 – 399 .

Matsuoka T , Tanaka S , Ebina K . 2015 . Systems approach to excitation-energy and electron transfer reaction networks in photosystem II complex: model studies for chlorophyll a fluorescence induction kinetics . Journal of Theoretical Biology 380 : 220 – 237 .

Matuszyńska A , Ebenhöh O . 2015 . A reductionist approach to model photosynthetic self-regulation in eukaryotes in response to light . Biochemical Society Transactions 43 : 1133 – 1139 .

Matuszyńska A , Heidari S , Jahns P , Ebenhöh O . 2016 . A mathematical model of non-photochemical quenching to study short-term light memory in plants . Biochimica et Biophysica Acta 1857 : 1860 – 1869 .

Matuszyńska A , Saadat NP , Ebenhöh O . 2019 . Balancing energy supply during photosynthesis - a theoretical perspective . Physiologia Plantarum 166 : 392 – 402 .

McAlister ED , Myers J . 1940 . Time course of photosynthesis and fluorescence . Science 92 : 241 – 243 .

McDonald AE , Ivanov AG , Bode R , Maxwell DP , Rodermel SR , Hüner NP . 2011 . Flexibility in photosynthetic electron transport: the physiological role of plastoquinol terminal oxidase (PTOX) . Biochimica et Biophysica Acta 1807 : 954 – 967 .

McGrath JM , Long SP . 2016 . Can the cyanobacterial carbon-concentrating mechanism increase photosynthesis in crop species? A theoretical analysis . Plant Physiology 164 : 2247 – 2261 .

Mehler AH . 1951 . Studies on reactions of illuminated chloroplasts. I. Mechanisms of the reduction of oxygen and other Hill reagents . Archives of Biochemistry and Biophysics 33 : 65 – 77 .

Melis A , Homann PH . 1975 . Kinetic analysis of the fluorescence induction in 3-(3′,4′-dichlorophenyl)-1,1-dimethylurea poisoned chloroplasts . Photochemistry and Photobiology 21 : 431 – 437 .

Mirkovic T , Ostroumov , Anna JM , van Grondelle R , Govindjee , Scholes GD . 2017 . Light absorption and energy transfer in the antenna complexes of photosynthetic organisms . Chemical Reviews 117 : 249 – 293 .

Mishra KB , Mishra A , Kubásek J , Urban O , Heyer AG , Govindjee . 2019 . Low temperature induced modulation of photosynthetic induction in non-acclimated and cold-acclimated Arabidopsis thaliana : chlorophyll a fluorescence and gas-exchange measurements . Photosynthesis Research 139 : 123 – 143 .

Mitchell P . 1961 a . Coupling of phosphorylation to electron and hydrogen transfer by a chemiosmotic type of mechanism . Nature 191 : 144 – 148 .

Mitchell P . 1961 b . Chemiosmotic coupling in oxidative and photosynthetic phosphorylation . Bodmin : Glynn Research .

Mitchell P . 1975 . Protonmotive Q-cycle-general formulation . FEBS Letters 59 : 137 – 139 .

Miyake C . 2010 . Alternative electron flows (water–water cycle and cyclic electron flow around PSI) in photosynthesis: molecular mechanisms and physiological functions . Plant and Cell Physiology 51 : 1951 – 1963 .

Morales A , Kaiser E , Yin X , et al.  2018 a . Dynamic modelling of limitations on improving leaf CO 2 assimilation under fluctuating irradiance . Plant, Cell & Environment 41 : 589 – 604 .

Morales A , Yin X , Harbinson J , et al.  2018 b . In silico analysis of the regulation of the photosynthetic electron transport chain in C3 plants . Plant Physiology 176 : 1247 – 1261 .

Müh F , Glöckner C , Hellmich J , Zouni A . 2012 . Light-induced quinone reduction in photosystem II . Biochimica et Biophysica Acta 1817 : 44 – 65 .

Müller P , Li X , Niyogi KK . 2001 . Non-photochemical quenching. A response to excess light energy . Plant Physiology 125 : 1558 – 1566 .

Munday JC , Govindjee . 1969 . Light-induced changes in the fluorescence yield of chlorophyll a in vivo. III. The dip and the peak in the fluorescence transient of Chlorella pyrenoidosa . Biophysical Journal 9 : 1 – 21 .

Murata N . 1969 a . Control of excitation transfer in photosynthesis. I. Light-induced change of chlorophyll a fluorescence in Porphyridium cruentum . Biochimica et Biophysica Acta 172 : 242 .

Murata N . 1969 b . Control of excitation transfer in photosynthesis. II. Magnesium ion-dependent distribution of excitation energy between two pigment systems in spinach chloroplasts . Biochimica et Biophysica Acta 189 : 171 – 181 .

Murata N , Allakhverdiev SI , Nishiyama Y . 2012 . The mechanism of photoinhibition in vivo: re-evaluation of the roles of catalase, α-tocopherol, non-photochemical quenching, and electron transport . Biochimica et Biophysica Acta 1817 : 1127 – 1133 .

Myers J . 1994 . The 1932 experiments . Photosynthesis Research 40 : 303 – 310 .

Najafpour MM , Moghaddam NA , Allakhverdiev SI , Govindjee . 2012 . Biological water oxidation: Lessons from nature . Biochimica et Biophysica Acta 1817 : 1110 – 1121 .

Nawrocki WJ , Bailleul B , Picot D , et al.  2019 . The mechanism of cyclic electron flow . Biochimica et Biophysica Acta 1860 : 433 – 438 .

Nedbal L , Samson G , Whitmarsh J . 1992 . Redox state of one-electron component controls the rate of photoinhibition of photosystem II . Proceedings of the National Academy of Sciences of the USA 89 : 7929 – 7933 .

Nedbal L , Červený J , Schmidt H . 2009 . Scaling and integration of kinetic models of photosynthesis: towards comprehensive e-photosynthesis. In: Laisk A , Nedbal AL , Govindjee , eds. Photosynthesis in silico: understanding complexity from molecules to ecosystems. Advances in photosynthesis and respiration , Vol. 29. Dordrecht : Springer , 17 – 29 .

Nelson N , Junge W . 2015 . Structure and energy transfer in photosystems of oxygenic photosynthesis . Annual Review of Biochemistry 84 : 659 – 683 .

Nickelsen K . 2016 . Explaining photosynthesis: models of biochemical mechanisms, 1840–1960 . Dordrecht : Springer .

Nickelsen K , Govindjee . 2011 . The maximum quantum yield controversy: Otto Warburg and the Midwest Gang . Bern Studies in the History and Philosophy of Science, Switzerland: Berne : University of Bern, Institute für Philosophie .

Nikkanen L , Rintamäki E . 2019 . Chloroplast thioredoxin systems dynamically regulate photosynthesis in plants . Biochemical Journal 476 : 1159 – 1172 .

Nishiyama Y , Allakhverdiev SI , Murata N . 2006 . A new paradigm for the action of reactive oxygen species in the photoinhibition of photosystem II . Biochimica et Biophysica Acta 1757 : 742 – 749 .

Nižnan J . 2014 . Compact representation of photosynthesis biochemical processes . Diploma Thesis, Masaryk University .

Noctor G , Foyer CH . 2000 . Homeostasis of adenylate status during photosynthesis in a fluctuating environment . Journal of Experimental Botany 51 : 347 – 356 .

Oettmeier W , Masson K , Johanningmeier U . 1980 . Photoaffinity labelling of the photosystem II herbicide binding protein . FEBS Letters 118 : 267 – 270 .

Okayama S , Butler WL . 1972 . The influence of cytochrome b 559 on the fluorescence yield of chloroplasts at low temperature . Biochimica et Biophysica Acta 267 : 523 – 527 .

Ono T , Inoue Y . 1988 . Discrete extraction of the Ca atom functional for O 2 evolution in higher plant Photosystem II by a simple low pH treatment . FEBS Letters 227 : 147 – 152 .

Ort DR , Merchant SS , Alric J , et al.  2015 . Redesigning photosynthesis to sustainably meet global food and bioenergy demand . Proceedings of the National Academy of Sciences of the USA 112 : 8529 – 8536 .

Osmond B , Chow WS , Wyber R , et al.  2017 . Relative functional and optical absorption cross-sections of PSII and other photosynthetic parameters monitored in situ, at a distance with a time resolution of a few seconds, using a prototype light induced fluorescence transient (LIFT) device . Functional Plant Biology 44 : 985 – 1006 .

Page CC , Moser CC , Chen X , Dutton PL . 1999 . Natural engineering principles of electron tunnelling in biological oxidation-reduction . Nature 402 : 47 – 52 .

Paillotin G . 1976 . Movement of excitations in the photosynthetic domains of photosystem II . Journal of Theoretical Biology 58 : 237 – 252 .

Papageorgiou GC . 1975 . Chlorophyll fluorescence: an intrinsic probe of photosynthesis. In: Govindjee , ed. Bioenergetics of photosynthesis . New York : Academic Press , 319 – 372 .

Papageorgiou GC , Govindjee . 1968 a . Light-induced changes in the fluorescence yield of chlorophyll a in vivo. I. Anacystis nidulans . Biophysical Journal 8 : 1299 – 1315 .

Papageorgiou GC , Govindjee . 1968 b . Light induced changes in the fluorescence yield of chlorophyll a in vivo. II. Chlorella pyrenoidosa . Biophysical Journal 8 : 1316 – 1328 .

Papageorgiou GC , Govindjee , eds. 2004 . Chlorophyll a fluorescence: a signature of photosynthesis. Advances in photosynthesis and respiration , Vol. 19. Dordrecht : Springer .

Papageorgiou GC , Govindjee . 2011 . Photosystem II fluorescence: slow changes–scaling from the past . Journal of Photochemistry and Photobiology B: Biology 104 : 258 – 270 .

Papageorgiou GC , Govindjee . 2014 . The non-photochemical quenching of the electronically excited state of chlorophyll a in plants: definitions, timelines, viewpoints, open questions. In: Demmig-Adams B , Garab G , Adams WW III , Govindjee , Sharkey TD , eds. Nonphotochemical quenching and energy dissipation in plants, algae and cyanobacteria. Advances in photosynthesis and respiration , vol. 40. Dordrecht : Springer , 1 – 44 .

Papageorgiou GC , Tsimilli-Michael M , Stamatakis K . 2007 . The fast and slow kinetics of chlorophyll a fluorescence induction in plants, algae and cyanobacteria: a viewpoint . Photosynthesis Research 94 : 275 – 290 .

Pearcy RW . 1990 . Sunflecks and photosynthesis in plant canopies . Annual Review of Plant Biology 41 : 421 – 453 .

Peers G , Truong TB , Ostendorf E , et al.  2009 . An ancient light-harvesting protein is critical for the regulation of algal photosynthesis . Nature 462 : 518 – 521 .

Pettersson G , Ryde-Pettersson U . 1988 . A mathematical model of the Calvin photosynthesis cycle . European Journal of Biochemistry 175 : 661 – 672 .

Petrouleas V , Crofts AR . 2005 . The quinone iron acceptor complex. In: Wydrzynski T , Satoh K . eds. Photosystem II: the light-driven water: plastoquinone oxidoreductase. Advances in photosynthesis and respiration , Vol. 22. Dordrecht : Springer , 177 – 206 .

Pfündel E . 1998 . Estimating the contribution of photosystem I to total leaf chlorophyll fluorescence . Photosynthesis Research 56 : 185 – 195 .

Poolman MG , Fell DA , Thomas S . 2000 . Modelling photosynthesis and its control . Journal of Experimental Botany 51 : 319 – 328 .

Pribil M , Sandoval-Ibáñez O , Xu W. et al.  2018 . Fine-tuning of photosynthesis requires CURVATURE THYLAKOID1-mediated thylakoid plasticity . Plant Physiology 176 : 2351 – 2364 .

Rabinowitch EI . 1945 . Photosynthesis and related processes, vol 1. Chemistry of photosynthesis, chemosynthesis and related processes in vitro and in vivo . New York : Interscience Publishers .

Rabinowitch EI , Govindjee . 1969 . Photosynthesis . Chichester : Wiley & Sons .

Rees D , Young A , Noctor G , Britton G , Horton P . 1989 . Enhancement of the pH-dependent dissipation of excitation energy in spinach chloroplasts by light-activation: correlation with the synthesis of zeaxanthin . FEBS Letters 256 : 85 – 90 .

Rees D , Noctor G , Ruban AV , Crofts J , Young A , Horton P . 1992 . pH dependent chlorophyll fluorescence quenching in spinach thylakoids from light treated or dark adapted leaves . Photosynthesis Research 31 : 11 – 19 .

Reinhold C , Niczyporuk S , Beran K , Jahns P . 2008 . Short-term down-regulation of zeaxanthin epoxidation in Arabidopsis thaliana in response to photo-oxidative stress conditions . Biochimica et Biophysica Acta 1777 : 462 – 469 .

Renger G , Schulze A . 1985 . Quantitative analysis of fluorescence induction curves in isolated spinach chloroplasts . Photobiochemistry and Photobiophysics 9 : 79 – 87 .

Renger G , Govindjee , eds. 1993 . How plants and cyanobacteria make oxygen: 25 years of period four oscillations . Photosynthesis Research 38 : 211 – 469 .

Robinson HH , Crofts AR , 1983 . Kinetics of the changes in oxidation-reduction reactions of the photosystem II quinone acceptor complex, and the pathway for deactivation . FEBS Letters 153 : 221 – 226 .

Rochaix J-D . 2014 . Regulation and dynamics of the light-harvesting system . Annual Review of Plant Biology 65 : 287 – 309 .

Rochaix J-D . 2016 . The dynamics of the photosynthetic apparatus in algae. In: Najafpour MM , ed. Applied photosynthesis - new progress . London : IntechOpen, 23 – 52 .

Rochaix JD , Lemeille S , Shapiguzov A , et al.  2012 . Protein kinases and phosphatases involved in the acclimation of the photosynthetic apparatus to a changing light environment . Philosophical Transactions of the Royal Society B: Biological Sciences 367 : 3466 – 3474 .

Roden JJJ , Bennett DIG , Whaley KB . 2016 . Long-range energy transport in photosystem II . The Journal of Chemical Physics 144 : 245101 .

Roelofs TA , Lee C-H , Holzwarth AR . 1992 . Global target analysis of picosecond fluorescence kinetics from pea chloroplasts. A new approach to the characterization of the primary processes in photosystem II α- and β-units . Biophysical Journal 61 : 1147 – 1163 .

Rosenthal DM , Locke AM , Khozaei M , Raines CA , Long SP , Ort DR . 2011 . Over-expressing the C3 photosynthesis cycle enzyme sedoheptulose-1–7 bisphosphatase improves photosynthetic carbon gain and yield under fully open air CO 2 fumigation (FACE) . BMC Plant Biology 11 : 123 .

Ruban AV , Johnson MP , Duffy CD . 2012 . The photoprotective molecular switch in the photosystem II antenna . Biochimica et Biophysica Acta 1817 : 167 – 181 .

Ruben S , Kamen MD . 1941 . Long-lived radioactive carbon: C14 . Physics Reviews 59 : 349 – 354 .

Ruben S , Hassid WZ , Kamen MD . 1939 . Radioactive carbon in the study of photosynthesis . Journal of the American Chemical Society 61 : 661 – 663 .

Ruben S , Randall M , Kamen M , Logan Hyde JL . 1941 . Heavy oxygen ( 18 O) as a tracer in the study of photosynthesis . Journal of the American Chemical Society 63 : 877 – 879 .

Rubin A , Riznichenko G . 2009 . Modeling of the primary processes in a photosynthetic membrane. In: Laisk A , Nedbal AL , Govindjee , eds. Photosynthesis in silico: understanding complexity from molecules to ecosystems. Advances in photosynthesis and respiration , Vol. 29. Dordrecht : Springer , 151 – 176 .

Šafránek D , Červený J , Klement M , Pospíšilová J , Brim L , Lazár D , Nedbal L . 2011 . E-photosynthesis: Web-based platform for modeling of complex photosynthetic processes . BioSystems 103 : 115 – 124 .

Sapozhnikov DI , Krasnovskaya TA , Maevskaya AN . 1957 . Change in the interrelationship of the basic carotenoids of the plastids of green leaves under the action of light . Doklady Akademii Nauk SSSR 113 : 465 – 467 .

Schansker G , Srivastava A , Govindjee , Strasser RJ . 2003 . Characterization of the 820-nm transmission signal paralleling the chlorophyll a fluorescence rise (OJIP) in pea leaves . Functional Plant Biology 30 : 785 – 796

Schansker G , Tóth SZ , Strasser RJ . 2005 . Methylviologen and dibromorhymoquinone treatments of pea leaves reveal the role of photosystem I in the Chl a fluorescence rise OJIP . Biochimica et Biophysica Acta 1706 : 250 – 261 .

Schansker G , Tóth SZ , Kovács L , Holzwarth AR , Garab G . 2011 . Evidence for a fluorescence yield change driven by a light-induced conformational change within photosystem II during the fast chlorophyll a fluorescence rise . Biochimica et Biophysica Acta 1807 : 1032 – 1043 .

Schansker G , Tóth SZ , Holzwarth AR , Garab G . 2014 . Chlorophyll a fluorescence: beyond the limits of the Q A model . Photosynthesis Research 120 : 43 – 58 .

Schatz GH , Brock H , Holzwarth AR . 1988 . Kinetic and energetic model for the primary processes in photosystem II . Biophysical Journal 54 : 397 – 405 .

Schlodder E , Meyer B . 1987 . pH-dependence of oxygen evolution and reduction kinetics of photooxidized chlorophyll a II (P-680) in Photosystem II particles from Synechococcus sp . Biochimica et Biophysica Acta 890 : 23 – 31 .

Schreiber U . 1986 . Detection of rapid induction kinetics with a new type of high-frequency modulated chlorophyll fluorometer . Photosynthesis Research 9 : 261 – 272 .

Schreiber U , Schliwa U , Bilger W . 1986 . Continuous recording of photochemical and nonphotochemical chlorophyll fluorescence quenching with a new type of modulation fluorometer . Photosynthesis Research 10 : 51 – 62 .

Schreiber U , Neubauer C , Klughammer C . 1989 . Devices and methods for room-temperature fluorescence analysis . Philosophical Transactions of the Royal Society B 323 : 241 – 251 .

Schreiber U , Klughammer C , Schansker G . 2019 . Rapidly reversible chlorophyll fluorescence quenching induced by pulses of supersaturating light in vivo . Photosynthesis Research 142 : 35 – 50 .

Semer J , Štroch M , Špunda V , Navrátil M . 2018 . Partitioning of absorbed light energy within photosystem II in barley can be affected by chloroplast movement . Journal of Photochemistry and Photobiology B: Biology 186 : 98 – 106 .

Semer J , Navrátil M , Špunda V , Štroch M . 2019 . Chlorophyll fluorescence parameters to assess utilization of excitation energy in photosystem II independently of changes in leaf absorption . Journal of Photochemistry and Photobiology B: Biology 197 : 111535 .

Sétif P . 2015 . Electron-transfer kinetics in cyanobacterial cells: Methyl viologen is a poor inhibitor of linear electron flow . Biochimica et Biophysica Acta 1847 : 212 – 222 .

Shen JR . 2015 . The structure of photosystem II and the mechanism of water oxidation in photosynthesis . Annual Review of Plant Biology 66 : 23 – 48 .

Shevela D , Eaton-Rye JJ , Shen JR , Govindjee . 2012 . Photosystem II and the unique role of bicarbonate: a historical perspective . Biochimica et Biophysica Acta 1817 : 1134 – 1151 .

Shevela D , Björn L , Govindjee . 2019 . Photosynthesis: solar energy for life . Singapore : World Scientific .

Shikanai TI , Yamamoto H . 2017 . Contribution of cyclic and pseudo-cyclic electron transport to the formation of proton motive force in chloroplasts . Molecular Plant 10 : 20 – 29 .

Shinkarev VP , Govindjee . 1993 . Insight into the relationship of chlorophyll a fluorescence yield to the concentration of its natural quenchers in oxygenic photosynthesis . Proceedings of the National Academy of Sciences of the USA 90 : 7466 – 7469 .

Simkin AJ , McAusland L , Headland LR , Lawson T , Raines CA . 2015 . Multigene manipulation of photosynthetic carbon assimilation increases CO 2 fixation and biomass yield in tobacco . Journal of Experimental Botany 66 : 4075 – 4090 .

Simkin AJ , McAusland L , Lawson T , Raines CA . 2017 . Overexpression of the RieskeFeS protein increases electron transport rates and biomass yield . Plant Physiology 175 : 134 – 145 .

Simkin AJ , López-Calcagno PE , Raines CA . 2019 . Feeding the world: improving photosynthetic efficiency for sustainable crop production . Journal of Experimental Botany 70 : 1119 – 1140 .

Snellenburg J , Johnson MP , Ruban AV , van Grondelle R , van Stokkum IHM . 2017 . A four state parametric model for the kinetics of the non-photochemical quenching in Photosystem II . Biochimica et Biophysica Acta 1858 : 854 – 864 .

South PF , Cavanagh AP , Lopez-Calcagno PE , Raines CA , Ort DR . 2018 . Optimizing photorespiration for improved crop productivity . Journal of Integrative Plant Biology 60 : 1217 – 1230 .

Srivastava A , Guissé B , Greppin H , Strasser RJ . 1997 . Regulation of antenna structure and electron transport in photosystem II of Pisum sativum under elevated temperature probed by the fast polyphasic chlorophyll a fluorescence transient: OKJIP . Biochimica et Biophysica Acta 1320 : 95 – 106 .

Steffen R , Christen G , Renger G . 2001 . Time-resolved monitoring of flash-induced changes of fluorescence quantum yield and decay of delayed light emission in oxygen-evolving photosynthetic organisms . Biochemistry 40 : 173 – 180 .

Steffen R , Eckert H-J , Kelly AA , Dörmann P , Renger G . 2005 . Investigation on the reaction pattern of photosystem II in leaves from Arabidopsis thaliana by time resolved fluorometric analysis . Biochemistry 44 : 3123 – 3133 .

Stiehl HH , Witt HT . 1968 . Die kurzzeitigen ultravioletten Differenzspektren bei der Photosynthese . Zeitschrift für Naturforschung 23b : 220 – 224 .

Stiehl HH , Witt HT . 1969 . Quantitative treatment of the function of plastoquinone in photosynthesis . Zeitschrift für Naturforschung 24b : 1588 – 1598 .

Stirbet A . 2013 . Excitonic connectivity between photosystem II units: what is it, and how to measure it? Photosynthesis Research 116 . 189 – 214 .

Stirbet A , Govindjee . 2011 . On the relation between the Kautsky effect (chlorophyll a fluorescence induction) and photosystem II: basics and applications of the OJIP fluorescence transient . Journal of Photochemistry and Photobiology B: Biology 104 : 236 – 257 .

Stirbet A , Govindjee . 2012 . Chlorophyll a fluorescence induction: a personal perspective of the thermal phase, the J–I–P rise . Photosynthesis Research 113 : 15 – 61 .

Stirbet A , Govindjee . 2016 . The slow phase of chlorophyll a fluorescence induction in silico: origin of the S-M fluorescence rise . Photosynthesis Research 130 : 193 – 213 .

Stirbet A , Strasser RJ . 1995 . Numerical simulation of the fluorescence induction in plants . Archives des Sciences – Université de Genève 48 : 41 – 60 .

Stirbet A , Strasser RJ . 1996 . Numerical simulation of the in vivo fluorescence in plants . Mathematics and Computers in Simulation 42 : 245 – 253 .

Stirbet A , Govindjee , Strasser BJ , Strasser RJ . 1998 . Chlorophyll a fluorescence induction in higher plants: modeling and numerical simulation . Journal of Theoretical Biology 193 : 131 – 151 .

Stirbet A , Rosenau P , Strőder AC , Strasser RJ . 2001 . Parameter optimisation of fast chlorophyll fluorescence induction model . Mathematics and Computers in Simulation 56 : 443 – 450 .

Stirbet A , Riznichenko GY , Rubin AB , Govindjee . 2014 . Modeling chlorophyll a fluorescence transient: relation to photosynthesis . Biochemistry (Mosc.) 79 : 291 – 323 .

Stirbet A , Lazár D , Kromdijk J , Govindjee . 2018 . Chlorophyll a fluorescence induction: can just a one-second measurement be used to quantify abiotic stress responses? Photosynthetica 56 : 86 – 104 .

Stirbet A , Lazár D , Papageorgiou CG , Govindjee . 2019 . Chlorophyll a fluorescence in cyanobacteria: relation to photosynthesis . In: Mishra AK , Tiwari DN , Rai AN . eds. Cyanobacteria – from basic science to applications . London : Academic Press , 79 – 130 .

Strand DD , Kramer DM . 2014 . Control of non-photochemical exciton quenching by the proton circuit of photosynthesis. In: Demmig-Adams B , Garab G , Adams WW III , Govindjee , Sharkey TD , eds. Nonphotochemical quenching and energy dissipation in plants, algae and cyanobacteria. Advances in photosynthesis and respiration , vol. 40. Dordrecht : Springer , 387 – 408 .

Strand DD , Fisher N , Davis GA , Kramer DM . 2016 . Redox regulation of the antimycin A sensitive pathway of cyclic electron flow around photosystem I in higher plant thylakoids . Biochimica et Biophysica Acta 1857 : 1 – 6

Strand DD , Fisher N , Kramer DM . 2017 . The higher plant plastid NAD(P)H dehydrogenase-like complex (NDH) is a high efficiency proton pump that increases ATP production by cyclic electron flow . The Journal of Biological Chemistry 292 : 11850 – 11860 .

Strasser RJ . 1978 . The grouping model of plant photosynthesis. In: Argyroudi-Akoyunoglou JH , Akoyunoglou G , eds. Chloroplast development . Amsterdam : Elsevier Biomedical , 513 – 515 .

Strasser RJ , Govindjee . 1991 . The F 0 and the O-J-I-P fluorescence rise in higher plants and algae. In: Argyroudi-Akoyunoglou JH , ed. Regulation of chloroplast biogenesis . New York : Plenum Press , 423 – 426 .

Strasser RJ , Stirbet A , 1998 . Heterogeneity of photosystem II probed by the numerically simulated chlorophyll a fluorescence rise (O-J-I-P) . Mathematics and Computers in Simulation 48 : 3 – 9 .

Strasser RJ , Stirbet A . 2001 . Estimation of the energetic connectivity of PS II centres in plants using the fluorescence rise O-J-I-P. Fitting of experimental data to three different PS II models . Mathematics and Computers in Simulation 56 : 451 – 461 .

Strasser RJ , Srivastava A , Govindjee . 1995 . Polyphasic chlorophyll a fluorescence transient in plants and cyanobacteria . Photochemistry and Photobiology 61 : 32 – 42 .

Strasser RJ , Tsimilli-Michael M , Srivastava A . 2004 . Analysis of the chlorophyll fluorescence transient. In: Papageorgiou GC , Govindjee . eds. Chlorophyll a fluorescence: a signature of photosynthesis. Advances in photosynthesis and respiration , vol. 19. Dordrecht : Springer , 321 – 362 .

Sušila P , Lazár D , Ilík P , Tomek P and Nauš J . 2004 . The gradient of exciting radiation within a sample affects relative heights of steps in the fast chlorophyll a fluorescence rise . Photosynthetica 42 : 161 – 172 .

Sylak-Glassman EJ , Zaks J , Amarnath K , Leuenberger M , Fleming GR . 2016 . Characterizing non-photochemical quenching in leaves through fluorescence lifetime snapshots . Photosynthesis Research 127 : 69 – 76 .

Tagawa K , Tsujimoto HY , Arnon DI . 1963 . Role of chloroplast ferredoxin in the energy conversion process of photosynthesis . Proceedings of the National Academy of Sciences of the USA 49 : 567 – 572 .

Thompson LK , Brudvig GW . 1988 . Cytochrome b-559 may function to protect photosystem II from photoinhibitin . Biochemistry 27 : 6653 – 6658 .

Tian L , Xu P , Chukhutsina VU , Holzwarth AR , Croce R . 2017 . Zeaxanthin-dependent nonphotochemical quenching does not occur in photosystem I in the higher plant Arabidopsis thaliana . Proceedings of the National Academy of Sciences of the USA 114 : 4828 – 4832 .

Tikhonov AN . 2013 . pH-Dependent regulation of electron transport and ATP synthesis in chloroplasts . Photosynthesis Research 116 : 511 – 534 .

Tikhonov AN , Vershubskii AV . 2014 . Computer modeling of electron and proton transport in chloroplasts . Biosystems 121 : 1 ‒ 21 .

Tokarčík A . 2012 . Rewriting complex biological models in stochastic process algebras. A case study . Bachelor Thesis, Masaryk University .

Tomek P , Lazár D , Ilík P , Nauš J . 2001 . On the intermediate steps between the O and P steps in chlorophyll a fluorescence rise measured at different intensities of exciting light . Australian Journal of Plant Physiology 28 : 1151 – 1160 .

Tomek P , Ilík P , Lazár D , Štroch M , Nauš J . 2003 . On the determination of Q B -non-reducing photosystem II centers from chlorophyll a fluorescence induction . Plant Science 164 : 665 – 670 .

Trebst A , Reimer S . 1973 . Energy conservation in photoreductions by Photosystem II. Reversal of dibromothymoquinone inhibition of Hill-reactions by phenylenediamines . Zeitschrift für Naturforschung 28c : 710 .

Trissl H-W , Lavergne J . 1995 . Fluorescence induction from photosystem II: analytical equations for the yields of photochemistry and fluorescence derived from analysis of a model including exciton-radical pair equilibrium and restricted energy transfer between units . Australian Journal of Plant Physiology 22 : 183 – 193 .

Trissl H-W , Gao Y , Wulf K . 1993 . Theoretical fluorescence induction curves derived from coupled differential equations describing the primary photochemistry of photosystem II by an exciton-radical pair equilibrium . Biophysical Journal 64 : 974 – 988 .

Tyystjärvi E . 2013 . Photoinhibition of photosystem II . International Review of Cell and Molecular Biology 300 : 243 – 303 .

Tyystjärvi E , Hakala M , Sarvikas P . 2005 . Mathematical modelling of the light response curve of photoinhibition of photosystem II . Photosynthesis Research 84 : 21 – 27 .

Valero E , Gonzalez-Sanchez MI , Macia H , Garcıa-Carmona F . 2009 . Computer simulation of the dynamic behavior of the glutathione-ascorbate redox cycle in chloroplasts . Plant Physiology 149 : 1958 – 1969 .

van Amerongen H , Croce R . 2013 . Light-harvesting in photosystem II . Photosynthesis Research 116 : 251 – 263 .

van Gorkom HJ . 1974 . Identification of the reduced primary electron acceptor of Photosystem II as a bound semiquinone anion . Biochimica et Biophysica Acta 347 : 439 – 442 .

van Gorkom HJ , Pulles MPJ , Etienne A-L . 1978 . Fluorescence and absorbance changes in Tris-washed chloroplasts. In: Metzner H , ed. Photosynthetic oxygen evolution . London : Academic Press , 135 – 145 .

van Kooten O , Snel JFH , Vredenberg VJ . 1986 . Photosynthetic free energy transduction related to the electric potential changes across the thylakoid membrane . Photosynthesis Research 9 : 211 – 227 .

van Rensen JJS . 2002 . Role of bicarbonate at the acceptor side of Photosystem II . Photosynthesis Research 73 : 185 – 192 .

Vavilin DV , Tyystjärvi E , Aro E-M . 1998 . Model for the fluorescence induction curve of photoinhibited thylakoids . Biophysical Journal 75 : 503 – 512 .

Velthuys BR , Amesz J . 1974 . Charge accumulation at the reducing side of Photosystem 2 of photosynthesis . Biochimica et Biophysica Acta 333 : 85 – 94 .

Vermaas WFJ . 2007 . Targeted genetic modification of cyanobacteria: new biotechnological applications. In: Richmond A , ed. Handbook of microalgal culture . Oxford : Blackwell Science , 457 – 470 .

Vermeglio A . 2002 . The two-electron gate in photosynthetic bacteria . Photosynthesis Research 73 : 83 – 86 .

Vink M , Zer H , Alumot N , et al.  2004 . Light modulated exposure of the light-harvesting complex II (LHCII) to protein kinase(s) and state transition in Chlamydomonas reinhardtii xanthophyll mutants . Biochemistry 43 : 7824 – 7833 .

Visser D , Heijnen J . 2002 . The mathematics of metabolic control analysis revisited . Metabolic Engineering 4 : 114 – 123 .

Vredenberg WJ . 2000 . A three-state model for energy trapping and chlorophyll fluorescence in photosystem II incorporating radical pair recombination . Biophysical Journal 79 : 26 – 38 .

Vredenberg WJ . 2008 . Algorithm for analysis of OJDIP fluorescence induction curves in terms of photo- and electrochemical events in photosystems of plant cells. Derivation and application . Journal of Photochemistry and Photobiology B: Biology 91 : 58 – 65 .

Vredenberg WJ . 2011 . Kinetic analyses and mathematical modeling of primary photochemical and photoelectrochemical processes in plant photosystems . BioSystems 103 : 138 – 151 .

Vredenberg WJ , Duysens LNM . 1963 . Transfer of energy from bacteriochlorophyll to a reaction centre during bacterial photosynthesis . Nature 197 : 355 – 357 .

Wang X , Cao J , Maroti P , et al.  1992 . Is bicarbonate in photosystem II the equivalent of the glutamate ligand to the iron atom in bacterial reaction centers? Biochimica et Biophysica Acta 1100 : 1 – 8 .

Warburg O , Uyesugi T . 1924 . Über die Blackmansche Reaktion . Biochemische Zeitschrift 146 : 486 – 492 .

Werdan K , Heldt HW , Milovancev M . 1975 . The role of pH in the regulation of carbon fixation in the chloroplast stroma. Studies on CO 2 fixation in the light and dark . Biochimica et Biophysica Acta 396 : 276 – 292 .

Wientjes E , Croce R . 2012 . PMS: photosystem I electron donor or fluorescence quencher . Photosynthesis Research 111 : 185 – 191 .

Willstätter R , Stoll A . 1913 . Untersuchungen über Chlorophyll . Berlin : Justus Springer .

Witt HT . 2004 . Steps on the way to building blocks, topologies, crystals and X-ray structural analysis of Photosystems I and II of water-oxidizing photosynthesis . Photosynthesis Research 80 : 85 – 107 .

Witt HT , Müller A , Rumberg B . 1961 a . Experimental evidence for the mechanism of photosynthesis . Nature 191 : 194 – 195 .

Witt HT , Müller A , Rumberg B . 1961 b . Oxidized cytochrome and chlorophyll in photosynthesis . Nature 192 : 967 – 969 .

Wood WH , Barnett SFH , Flannery S , Hunter CN , Johnson MP . 2019 . Dynamic thylakoid stacking is regulated by LHCII phosphorylation but not its interaction with photosystem I . Plant Physiology 180 : 2152 – 2166 .

Wraight CA , Crofts AR . 1970 . Energy-dependent quenching of chlorophyll a fluorescence in isolated chloroplasts . European Journal of Biochemistry 17 : 319 – 327 .

Wydrzynski T , Govindjee . 1975 . A new site of bicarbonate effect in Photosystem II of photosynthesis; evidence from chlorophyll fluorescence transients in spinach chloroplasts . Biochimica et Biophysica Acta 387 : 403 – 408 .

Wydrzynski T , Satoh K , eds. 2005 . Photosystem II: the light-driven water-plastoquinone oxidoreductase. Advances in photosynthesis and respiration , Vol. 22. Dordrecht : Springer .

Xia Q , Tan J , Ji X , Jiang Y , Guo Y . 2018 . Modelling and simulation of chlorophyll fluorescence from photosystem II as affected by temperature . IET Systems Biology 12 : 304 – 310 .

Xin CP , Yang J , Zhu XG . 2013 . A model of chlorophyll a fluorescence induction kinetics with explicit description of structural constraints of individual photosystem II units . Photosynthesis Research 117 : 339 – 354 .

Yamamoto HY , Higashi RM . 1978 . Violaxanthin deepoxidase. Lipid composition and substrate specificity . Archives of Biochemistry and Biophysics 190 : 514 – 522 .

Yamamoto HY , Nakayama T , Chichester C . 1962 . Studies on the light and dark interconversions of leaf xanthophylls . Archives of Biochemistry and Biophysics 97 : 168 – 173 .

Yamori W , Makino A , Toshiharu Shikanai T . 2016 . A physiological role of cyclic electron transport around photosystem I in sustaining photosynthesis under fluctuating light in rice . Scientific Reports 6 : 20147 .

Yin X , Harbinson J , Struik PC . 2009 . A model of the generalized stoichiometry of electron transport limited C3 photosynthesis: development and applications. In: Laisk A , Nedbal AL , Govindjee , eds. Photosynthesis in silico: understanding complexity from molecules to ecosystems. Advances in photosynthesis and respiration , Vol. 29. Dordrecht : Springer , 247 – 273 .

Zaks J , Amarnath K , Kramer DM , Niyogi KK , Fleming GR . 2012 . A kinetic model of rapidly reversible nonphotochemical quenching . Proceedings of the National Academy of Sciences of the USA 109 : 15757 – 15762 .

Zaks J , Amarnath K , Sylak-Glassman EJ , Fleming GR . 2013 . Models and measurements of energy-dependent quenching . Photosynthesis Research 116 : 389 – 409 .

Zhou Y , Schideman LC , Park DS , et al.  2015 . Characterization of a Chlamydomonas reinhardtii mutant strain with improved biomass production under low light and mixotrophic conditions . Algal Research 11 : 134 – 147 .

Zhu XG , Govindjee , Baker NR , deSturler E , Ort DR , Long SP . 2005 . Chlorophyll a fluorescence induction kinetics in leaves predicted from a model describing each discrete step of excitation energy and electron transfer associated with photosystem II . Planta 223 : 114 – 133 .

Zhu XG , de Sturler E , Long SP . 2007 . Optimizing the distribution of resources between enzymes of carbon metabolism can dramatically increase photosynthetic rate: a numerical simulation using an evolutionary algorithm . Plant Physiology 145 : 513 – 526 .

Zhu XG , Long SP , Ort DR . 2010 . Improving photosynthetic efficiency for greater yield . Annual Review of Plant Biology 61 : 235 – 261 .

Zhu XG , Wang Y , Ort DR , Long SP . 2013 . e-Photosynthesis: a comprehensive dynamic mechanistic model of C3 photosynthesis: from light capture to sucrose synthesis . Plant, Cell & Environment 36 : 1711 – 1727 .

Zhu XG , Lynch JP , LeBauer DS , Millar AJ , Stitt M , Long SP . 2016 . Plants in silico: why, why now and what? – an integrative platform for plant systems biology research . Plant, Cell & Environment 39 : 1049 – 1057 .

Zito F , Finazzi G , Delosme R , Nitschke W , Picot D , Wollman FA . 1999 . The Qo site of cytochrome b6f complexes controls the activation of the LHCII kinase . EMBO Journal 18 : 2961 – 2969 .

Zouni A , Witt HT , Kern J , et al.  2001 . Crystal structure of photosystem II from Synechococcus elongatus at 3.8 Å resolution . Nature 409 , 739 – 743 .

Author notes

Month:	Total Views:
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September 2020	1,233
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March 2021	735
April 2021	603
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July 2021	296
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