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- Herausgeber: John Wiley & Sons
- Kategorie: Wissenschaft und neue Technologien
- Sprache: Englisch
Photosynthesis and the complex network within plants is becoming more important than ever, because of the earth's changing climate. In addition, the concepts can be used in other areas, and the science itself is useful in practical applications in many branches of science, including medicine, biology, biophysics, and chemistry. This original, groundbreaking work by two highly experienced and well-known scientists introduces a new and different approach to thinking about living organisms, what we can learn from them, and how we can use the concepts within their scientific makeup in practice. This book describes the principles of complex signaling networks enabling spatiotemporally-directed macroscopic processes by the coupling of systems leading to a bottom-up information transfer in photosynthetic organisms. Top-down messengers triggered by macroscopic actuators like sunlight, gravity, environment or stress lead to an activation of the gene regulation on the molecular level. Mainly the generation and monitoring, as well the role of reactive oxygen species in photosynthetic organisms as typical messengers in complex networks, are described. A theoretical approach according to the principle of synergetics is presented to model light absorption, electron transfer and membrane dynamics in plants. A special focus will be attended to nonlinear processes that form the basic principle for the accumulation of energy reservoirs and large forces enabling the dynamics of macroscopic devices. This volume is a must-have for any scientist, student, or engineer working with photosynthesis. The concepts herein are not available anywhere else, in any other format, and it is truly a groundbreaking work with sure to be long-lasting effects on the scientific community.
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Contents
Cover
Title page
Copyright page
Abstract
Foreword 1
Foreword 2
Preface
Chapter 1: Multiscale Hierarchical Processes
1.1 Coupled Systems, Hierarchy and Emergence
1.2 Principles of Synergetics
1.3 Axiomatic Motivation of Rate Equations
1.4 Rate Equations in Photosynthesis
1.5 Top down and Bottom up Signaling
Chapter 2: Photophysics, Photobiology and Photosynthesis
2.1 Light Induced State Dynamics
2.2 Rate Equations and Excited State Dynamics in Coupled Systems
2.3 Light-Harvesting, Energy and Charge Transfer and Primary Processes of Photosynthesis
2.4 Antenna Complexes in Photosynthetic Systems
2.5 Fluorescence Emission as a Tool for Monitoring PS II Function
2.6 Excitation Energy Transfer and Electron Transfer Steps in Cyanobacteria Modeled with Rate Equations
2.7 Excitation Energy and Electron Transfer in Higher Plants Modelled with Rate Equations
2.8 Nonphotochemical Quenching in Plants and Cyanobacteria
2.9 Hierarchical Architecture of Plants
Chapter 3: Formation and Functional Role of Reactive Oxygen Species (ROS)
3.1 Generation, Decay and Deleterious Action of ROS
3.2 Monitoring of ROS
3.3 Signaling Role of ROS
Chapter 4: ROS Signaling in Coupled Nonlinear Systems
4.1 Signaling by Superoxide and Hydrogen Peroxide in Cyanobacteria
4.2 Signaling by Singlet Oxygen and Hydrogen Peroxide in Eukaryotic Cells and Plants
4.3 ROS and Cell Redox Control and Interaction with the Nuclear Gene Expression
4.4 ROS as Top down and Bottom up Messengers
4.5 Second Messengers and Signaling Molecules in H2O2 Signaling Chains and (Nonlinear) Networking
4.6 ROS-Waves and Prey-Predator Models
4.7 Open questions on ROS Coupling in Nonlinear Systems
Chapter 5: The Role of ROS in Evolution
5.1 The Big Bang of the Ecosphere
5.2 Complicated Patterns Result from Simple Rules but Only the Useful Patterns are Stable
5.3 Genetic Diversity and Selection Pressure as Driving Forces for Evolution
Chapter 6: Outlook: Control and Feedback in Hierarchic Systems in Society, Politics and Economics
Bibliography
Appendix
Index
End User License Agreement
Guide
Cover
Copyright
Contents
Begin Reading
List of Tables
Chapter 2
Table 1.
Values of parameters used for the fitting of SFITFY data (see Figure 48) according to the model of PS II shown in Figure 47 as published in (Natalya, 2011). (PPFD stands for photosynthetic photon flux density; all other variables are described in the text).
Table 2.
Values of parameters used for quantitative fits with the PS II model (Figure 47) simulations of SFITFY curves for whole leaves of
Arabidopsis thaliana
plants (see Figure 48).
Chapter 3
Table 3.
Compilation of ROS-sensitive exogenous fluorescence probes.
Table 4.
Spin traps suitable for imaging ROS.
Table 5.
Genetically encoded fluorescence proteins applicable for ROS monitoring.
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Scrivener Publishing100 Cummings Center, Suite 541JBeverly, MA 01915-6106
Publishers at ScrivenerMartin Scrivener ([email protected])Phillip Carmical ([email protected])
Reactive Oxygen Species
Signaling Between Hierarchical Levels in Plants
Edited by
Franz-Josef Schmitt
Suleyman I. Allakhverdiev
This edition first published 2017 by John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, USA and Scrivener Publishing LLC, 100 Cummings Center, Suite 541J, Beverly, MA 01915, USA© 2017 Scrivener Publishing LLCFor more information about Scrivener publications please visit www.scrivenerpublishing.com.
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Library of Congress Cataloging-in-Publication DataISBN 978-1-119-18488-1
Abstract
Reactive oxygen species (ROS) play different roles in oxidative degradation and signal transduction in photosynthetic organisms. This book introduces basic principles of light-matter interaction, photophysics and photosynthesis to elucidate complex signaling networks that enable spatiotemporally directed macroscopic processes. Reaction schemes are presented for the formation and monitoring of ROS and their participation in stress signal transduction pathways within prokaryotic cyanobacteria as well as from chloroplasts to the nuclear genome in plants. Redoxregulated systems, mitogen-activated protein kinase cascades and transcription factor networks play a key role in ROS-dependent signaling systems in plant cells and for their spatiotemporal morphology and lifespan. ROS are understood as bottom up messengers and as targets of top down communication in plants. The role of the chemical environment in introducing genetic diversity as a prerequisite for efficient adaption is elucidated. Finally, it is suggested how the presented concepts can be used to describe other biological principles and multiscale hierarchical systems in society, politics and economics.
We hope that this book will be an invaluable reference source for university and research institute libraries, as well as for individual research groups and scientists working in the fields. It will be helpful not only for photo–biophysicists, biochemists, and plant physiologists, but also for a wider group of physicists and biologists. Lastly, and most importantly, it will serve to educate undergraduate, graduate and post-graduate students around the world.
Foreword 1
This book introduces basic principles of light-matter interaction, photophysics and photosynthesis in a brief manner in order to elucidate complex signaling networks that enable spatiotemporally directed macroscopic processes. The roles of reactive oxygen species (ROS) are explained both as bottom up messengers and as targets of top down communication. Starting with Hermann Haken’s Principles of Synergetics, the role of ROS is investigated in order to explain emergent phenomena that occur during light-driven chemical reactions. Rate equations are used to describe energy transfer processes in photosynthesis, nonlinear phenomena that fill up energy reservoirs, and drive forces that are able to control macroscopic dynamics. The second chapter describes the basic principles of the light reaction in photosynthesis from light absorption to the storage of free Gibbs energy in the form of energy rich chemical compounds. The roles of different processes that support light energy transduction, on the one hand, and non-photochemical quenching, on the other hand, are elucidated with special focus on the context of a highly adapted system that has developed as an advanced structure for energy conversion during evolution in its local environment. Rate equations are not only used to understand optical transitions, excitation energy and electron transfer processes, and chemical reactions but are used to much more generally describe information processing in complex networks.
In the third and fourth chapters, the messenger role of ROS is described including formation, decay, monitoring and functional role of ROS – mainly H2O2, 1O2, O•2– – in both oxidative degradation and signal transduction during exposure of oxygen-evolving photosynthetic organisms to oxidative stress. These chapters focus on phenomena and mechanisms of ROS signaling. Reaction schemes are presented for the for mation and monitoring of ROS and their participation in stress signal transduction pathways, both within prokaryotic cyanobacteria as well as from chloroplasts to the nuclear genome in plants. It is suggested that redox-regulated systems, mitogen-activated protein kinase cascades, and transcription factor networks play a key role in the ROS-dependent signaling systems in plant cells and for their spatiotemporal morphology and lifespan.
Vladimir A. Shuvalov,Academician (Russia)
Foreword 2
Reactive oxygen species (ROS) play different roles in oxidative degradation and signal transduction in photosynthetic organisms. Since modern microscopic, genetic, and chemical techniques for ROS detection and controlled generation have improved significantly in recent years, our knowledge of the complex interaction patterns of ROS has significantly increased. This book introduces basic principles of light-matter interaction, photophysics and photosynthesis in a brief manner in order to generally elucidate complex signaling networks that enable spatiotemporally directed macroscopic processes. ROS are understood as bottom up messengers and as targets of top down communication. Reaction schemes are presented for the formation and monitoring of ROS and their participation in stress signal transduction pathways, both within prokaryotic cyanobacteria as well as from chloroplasts to the nuclear genome in plants. It is suggested that redox-regulated systems, mitogen-activated protein kinase cascades, and transcription factor networks play a key role in the ROS-dependent signaling systems in plant cells and for their spatiotemporal morphology and lifespan.
Rate equations are used to explain the dynamics of excitation energy and electron transfer during light-driven reactions. Energy transfer processes and subsequent chemical reactions in photosynthesis are nonlinearly coupled. They fill up energy reservoirs and drive forces able to control macroscopic dynamics.
Photosynthetic organisms (as all organisms) represent highly adapted systems that have developed advanced structures for energy conversion during evolution in their local environment. Basic principles of evolution as the continuous adaption to environmental constraints are derived from considerations based on state transitions as basic theory and ROS as an example for a chemical reaction partner that contributes to selection and mutation. It will be shown that the structure of the environment mainly allows for genetic diversity as a prerequisite for efficient adaption and that mutations are of minor relevance in that context.
Finally, it is suggested how the presented concepts can be used to describe other biological principles and multiscale hierarchical systems in society, politics and economics.
This book is intended for a broad range of researchers and students, and all who are interested in learning more about the most important global process on our planet – the process of photosynthesis.
Tatsuya Tomo,Professor (Japan)
Preface
To my family and my friends
Franz-Josef Schmitt
To my mother, my wife and my son
Suleyman I. Allakhverdiev
This book introduces basic principles of light-matter interaction, photophysics, and photosynthesis in a brief manner in order to elucidate principles of complex signaling networks that enable spatiotemporally directed macroscopic processes. We will start with random walk processes typically used to describe excitation energy transfer in plant lightharvesting complexes and later focus on coupled systems such as the communication network of reactive oxygen species (ROS) which are embedded into the plant metabolism and enable an information transfer from molecules to the overall organism as a bottom up process. In addition the microscale dynamics always accepts signals on the bottom level that can be understood as a top down communication. One example is the activation of genes by ROS caused by macroscopic events like strong sunlight or atmospheric variations that activate a change in composition of the microscopic environment by producing new proteins.
Typical bottom up processes are cascades that start with gene activation and protein translation regulating plant growth and morphology. Top down messengers triggered by macroscopic actuators like sunlight, gravity, environment or any forms of stress, on the other hand, activate gene regulation on the molecular level and therefore concern the dynamics of single molecules under the constraints of macroscopic factors. In this book the generation and monitoring as well as the role of ROS in photosynthetic organisms as typical messengers in complex networks are primarily treated in a scientific manner. All findings are supported by our own research results and recent publications. Additionally, the principles of top down and bottom up messaging are presented in the form of a philosophical discussion.
The first chapter focuses on a theoretical approach according to the Principle of Synergetics (Haken, 1990) to understand coupling, networks, and emergence of unpredictable phenomena. The approach is used to model light absorption, electron transfer and membrane dynamics in plants. Special focus will be placed on nonlinear processes that form the basic principle for the accumulation of energy reservoirs and on the formation of forces that are able to control the dynamics of macroscopic devices.
The formalism of rate equations is presented as a general scheme to formulate dynamical equations for arbitrarily complex systems. Key is the definition of “states” as an intensity level or a pattern that carries a certain amount of information, and their dynamics which are assessed by evaluating the probability of transfer from one state to another. In fact, rate equations are not only used to describe energy transfer processes in photosynthesis but in many systems, for instance, optical transitions, particle reactions, complex chemical reactions and more general information processing in complex networks. Rate equations are also used to describe complex systems such as sociological networks.
The second chapter describes the basic principles of the light reaction in photosynthesis from absorption to the storage of free Gibbs energy in the form of energy rich chemical compounds. The roles of different processes that support light energy transduction, on the one hand, and nonphotochemical quenching, on the other hand, are elucidated with special focus on the context of a highly adapted system that has developed as an advanced structure for energy conversion during evolution in its local environment.
In the third chapter the formation, decay, monitoring, and the functional role of ROS – mainly H2O2, 1O2, O•2– are described and the fourth chapter especially focuses on the messenger role of ROS. The ambivalent picture of oxidative degradation and signal transduction during exposure of oxygen-evolving, photosynthetic organisms to oxidative stress istelucidated. Both degradation and activation are important mechanisms of ROS signaling. Reaction schemes are presented for the formation and monitoring of ROS and their participation in stress signal transduction pathways both within prokaryotic cyanobacteria as well as from chloroplasts to the nuclear genome in plants. It is suggested that redoxregulated systems, mitogen-activated protein kinase cascades and transcription factor networks play a key role in the ROS-dependent signaling systems in plant cells and for their spatiotemporal morphology and lifespan.
Chapter five focuses on evolution. It is emphasized that mainly the local environment of evolving organisms enforces directed evolution resulting in quick changes of the phenotype if the genetic diversity of the organisms is large enough. In that sense leaps in evolution necessarily follow volatile changes of the environment. It might be possible that ROS are the most important driving forces in evolution.
The last chapter finally offers a glance at how the described concepts can be used to describe other biological principles and multiscale hierarchical systems in society, politics and economics. The book is intended for a broad range of researchers and students, and everyone who is interested in learning about the most important global process on our planet – the process of photosynthesis. We would like to believe that this book will stimulate future researchers of photosynthesis and lead to progress in our understanding of the mechanisms of photosynthesis and their practical use in biotechnology and in human life.
We express our sincere gratitude to the two referees: the Academician of the Russian Academy of Sciences (RAS) Prof. V.A. Shuvalov and Prof. T. Tomo of Tokyo University of Science, Tokyo, Japan. We are extremely grateful to Corresponding Member of RAS Vl.V. Kuznetsov, Corresponding Member of RAS A.B. Rubin, and Professors D.A. Los, A.M. Nosov, V.Z. Paschenko, A.N. Tikhonov, G.V. Maksimov, V.V. Klimov, A.A. Tsygankov, and Drs. V.D. Kreslavski, S.K. Zharmukhamedov, I.R. Fomina, J. Karakeyan for their permanent help and fruitful advice. We are also indebted to Professors T. Friedrich, N. Budisa, P. Hildebrandt, L. Kroh, H.J. Eichler, Drs. M. Vitali, V. Tejwani, C. Junghans, N. Tavraz, J. Laufer, and J. Märk from TU Berlin and Drs. E.G. Maksimov and N. Belyaeva from Moscow State University, Prof. J. Pieper from University of Tartu, Prof. H. Paulsen from Johannes Gutenberg-Universität Mainz, Prof. F. Zappa and Dr. D. Bronzi from Politecnico di Milano, and Prof. R. Rigler, Drs. J. Jarvet, and V. Vukojević from the Karolinska Institute in Stockholm.
We express our deepest gratitude to Russian Science Foundation (№ 14-04-00039) and the German Research Foundation DFG (cluster of excellence “Unifying Concepts in Catalysis”) and the Federal Ministry of Education and Research for funding bilateral cooperation between Germany and Russia (RUS 10/026 and 11/014). We acknowledge COST for financial support in the framework of COST action MP1205. We thank F. Schmitt for preparing Figs. 4, 5, 7, 10, 11, 18, 27A, 50, 51, 71, 75, 79 and 80. Further gratitude belongs to M. Nabugodi and J.M. Zinn for proofreading of the manuscript. F.-J. Schmitt especially thanks Joachim Herz Stiftung and Stifterverband für die Deutsche Wissenschaft for the fellowship IGT-educationTUB.
We are grateful to Scrivener Publishing, Wiley and Izhevsk Institute of Computer Sciences for their cooperation in producing this book.
Franz-Josef SchmittInstitute of Physical Chemistry,Max-Volmer-Laboratory for Biophysical Chemistry,Technische Universität Berlin(e-mail: [email protected])
Suleyman I. AllakhverdievControlled Photobiosynthesis Laboratory,Institute of Plant Physiology, Russian Academy of Sciences, Moscow;Institute of Basic Biological Problems,Russian Academy of Sciences, Pushchino, Moscow Region;Department of Plant Physiology, Faculty of Biology,M.V. Lomonosov Moscow State University;Department of Biological and Medical Physics,Moscow Institute of Physics and Technology (State University),Moscow, Russia;Bionanotechnology Laboratory, Institute of Molecular Biology and Biotechnology, Azerbaijan National Academy of Sciences,Baku, Azerbaijan;Department of New Biology, Daegu Gyeongbuk Institute of Science & Technology (DGIST), Daegu, Republic of Korea(e-mail: [email protected])
Franz-Josef Schmitt is a research assistant at the Institute of Physical Chemistry, Technische Universität Berlin (TU Berlin). He finished his doctoral thesis with “summa cum laude” in physics in 2011 in Prof. Hans-Joachim Eichler’s working group on Laser Physics under the supervision of Prof. Gernot Renger. The thesis is entitled “Picobiophotonics for the investigation of Pigment-Pigment and Pigment-Protein interactions in Photosynthetic Complexes”. Dr. Schmitt holds a series of scientific awards including the Chorafas award for extraordinary scientific results (2009) and the Stifterverb and Fellowship for excellence in teaching (2014) awarded by Joachim Herz Stiftung for his teaching project IGT-education TUB. He was recently awarded twice with a young talents award (2013) and received best poster awards (2014) for his invited presentations at the conference on Photosynthesis research for Sustainability in Baku, Azerbaijan and Moscow, Russia, respectively. More than 80 research papers, two patents, one book chapter and 200 partially invited talks on international conferences summarize his research in Photosynthesis, Nanobiophotonics, Environmental Spectroscopy and didactics. Dr. Schmitt was group leader of the reform project “educationZEN” that developed new teaching formats for Mathematics education and internships in the Nature Sciences and Engineering. His research fields comprise protein dynamics and protein-cofactor interaction, energy transfer and conversion in organic systems, information processing in complex networks and general biophysics and biotechnology. Dr. Schmitt is coordinating editor of the topical issue on “Optofluidics and Biological Materials” of the open access journal “Optofluidics, Microfluidics and Nanofluidics” (de Gruyter open) and guest editor of the open access journal SOAJ NanoPhotoBioSciences. He was substitutional Management Committee member of COST action MP 1205 and member of the Faculty Council of the Department of Mathematics and Nature Sciences (2007–2017). He is a member of the Academic Senate (since 2010), and Chairman of the Extended Academic Senate of TU Berlin (since 2015).
Suleyman I. Allakhverdiev is the Head of the Controlled Photobiosynthesis Laboratory at the Institute of Plant Physiology of the Russian Academy of Sciences (RAS), Moscow; Chief Research Scientist at the Institute of Basic Biological Problems RAS, Pushchino, Moscow Region; Professor at M.V. Lomonosov Moscow State University, Moscow; Professor at Moscow Institute of Physics and Technology (State University), Moscow, Russia; Head of Bionanotechnology Laboratory at the Institute of Molecular Biology and Biotechnology of the Azerbaijan National Academy of Sciences, Baku, Azerbaijan, and Invited-Adjunct Professor at the Department of New Biology, Daegu Gyeongbuk Institute of Science & Technology (DGIST), Daegu, Republic of Korea. He is originally from Chaykend (Karagoyunly/Dilichanderesi), Armenia, and he obtained both his B.S. and M.S. in Physics from the Department of Physics, Azerbaijan State University, Baku. He obtained his Dr.Sci. degree (highest/top degree in science) in Plant Physiology and Photobiochemistry from the Institute of Plant Physiology, RAS (2002, Moscow), and Ph.D. in Physics and Mathematics (Biophysics), from the Institute of Biophysics, USSR (1984, Pushchino). His Ph.D. advisors were Academician Alexander A. Krasnovsky and Dr. Sci. Vyacheslav V. Klimov. He worked for many years (1990–2007) as visiting scientist at the National Institute for Basic Biology (with Prof. Norio Murata), Okazaki, Japan, and in the Department de Chimie-Biologie, Universite du Quebec at Trois Rivieres (with Prof. Robert Carpentier), Quebec, Canada (1988–1990). He has been a guest editor of more than thirty special issues in international peer-reviewed journals. At present, he is a member of the Editorial Board of more than fifteen international journals. Besides being editor-in-chief of SOAJ NanoPhotoBioSciences, associate editor of the International Journal of Hydrogen Energy, section editor of the BBA Bioenergetics, associate editor of the Photosynthesis Research, associate editor of the Functional Plant Biology, and associate editor of the Photosynthetica, he also acts as a referee for major international journals and grant proposals. He has authored (or co-authored) more than 400 research papers, six patents and eight books. He has organized more than ten international conferences on photosynthesis. His research interests include the structure and function of photosystem II, water-oxidizing complex, artificial photosynthesis, hydrogen photoproduction, catalytic conversion of solar energy, plants under environmental stress, and photoreceptor signaling.
Chapter 1Multiscale Hierarchical Processes
Träumen wir uns für einen Moment in einen zukünftigen Zustand der Naturwissenschaft, in dem die Biologie ebenso vollständig mit Physik und Chemie verschmolzen sein wird, wie in der heutigen Quantenmechanik Physik und Chemie miteinander verschmolzen sind. Glaubst du, dass die Naturgesetze in dieser gesamten Wissenschaft dann einfach die Gesetze der Quantenmechanik sein werden, denen man noch biologische Begriffe zugeordnet hat, so wie man den Gesetzen der Newtonschen Mechanik noch statistische Begriffe wie Temperatur und Entropie zuordnen kann; oder meinst du, in dieser einheitlichen Naturwissenschaft gelten dann umfassendere Naturgesetze, von denen aus die Quantenmechanik nur als ein spezieller Grenzfall erscheint, so wie die Newtonsche Mechanik als Grenzfall der Quantenmechanik betrachtet werden kann ?
Werner Heisenberg (1901–1976),Deutscher Physiker (Heisenberg, 1986)
Multiscale hierarchical processes are understood as information transduction in networks which are hierarchically structured. The most simple assumption might be a house which is structured into rooms, rooms are structured into furnishings but also people that move from one room to another. Of course cupboards and chairs, computers and TVs as well as human beings are hierarchically structured in a somehow comparable way. We would call our house a hierarchically structured system. If information flows from one room to another – and everyone would agree that this is the case when people live in that house and move objects or direct information – we can speak about hierarchical processes. These processes might comprise the information conveyed by the parents that the food is prepared which leads to a movement of the children towards the kitchen and the covering of the table by dishes, not to mention all the processes that are correlated with eating and enjoying the wonderful meal.
If we agree that the type of hierarchical structure might additionally vary if elucidated from different aspects we speak about multiscale hierarchical processes. Such different aspects can be aspects of spatial organization as it is the case in our example, the house. But in addition also other, for example temporal, organization principles are possible. To summarize all these organization principles we generalize the hierarchical systems to multiscale hierarchical systems housing the dynamics of multiscale hierarchical processes.
Living systems are always spatially hierarchically organized: in this case molecules are the basic entities that form genes and proteins as an intermediate structure on a mesoscale. The proteins aggregate in a quaternary structure to form higher ordered systems that do not necessarily need to be stable in time. The network of interacting proteins is in its turn forming a metastructure that can be understood as a network formed from single proteins. However, also on the temporal scale multiscale hierarchical processes arise. For example, a reaction scheme may represent the dynamics of the chemical reaction of two compounds on the temporal microscale. However, if a certain threshold of concentration of its output is present, another chemical reaction may start and is therefore triggered by the first reaction scheme. Long-term effects like the active movement of our extremities, circadian rhythms, the growth of an organism and senescence are typical examples of processes that change their appearance over time and are therefore a hierarchical metastructure that arises on the network of microscale processes.
1.1 Coupled Systems, Hierarchy and Emergence
Naturally, coupled systems are generally nonlinear. That is always the case if two compounds form a special reaction pathway that is not possible if only a single compound is present. If two molecules of two different compounds interact, then the reaction is bilinear or bimolecular, which is a nonlinearity. If two molecules (or two photons) of the same kind are able to reach a state that is not accessible by a single molecule (or photon) then the outcome is typically in a nonlinear dependence on the input. One prominent example of nonlinear optics in physics is the two photon absorption where the absorbing state is reached by interaction of two photons with the ground state within a certain time interval. If the photon density is too low for that to happen then the output is zero, but when the photon density increases the probability for the two photon absorption increases with the square of the photon density. Therefore two (or more) photons are needed to activate a state transition. Only spontaneous population and depopulation of certain states, which is not the typical situation for characteristic biochemical reactions, are truly linear. If several molecules of one or several compounds have to interact within a certain time interval, then the reaction scheme is nonlinear and characterized by the typical mathematical problems and challenges of nonlinear systems.
Photosynthesis is a truly nonlinear reaction as at least eight photons have to be absorbed by two different photosystems to split two molecules of water and release one molecule of oxygen. Photon absorption drives an electron transfer in photosynthesis. However, the involved molecules are reduced and/or oxidized by more than one electron and the coupled proton transfer again forms ATP from ADP and phosphate in a nonlinear process. Biochemistry is truly a hierarchy of nonlinear processes.
The “cycles” of nonlinearities that form the overall, hierarchical structure also include loss processes. After photon absorption excitation-energy can be lost and the following electron transfer processes are likewise restricted by loss processes that limit the production of one molecule of oxygen with a demand of at least 11–12 photons. Other sources report 60 photons per molecule glucose (Häder, 1999; Campbell and Reece, 2009) which would equal 10 photons per molecule glucose according to the basic equation of photosynthesis understood as the light-induced chemical reaction of water with carbon dioxide to glucose:
chemical equation 1
The energetic stoichiometry of light and dark reactions in photosynthesis are again discussed in chap. 4.4.1 as well as in the literature (Häder, 1999). This also features discussions of coupled reaction schemes like the proton assisted electron transfer (Renger, 2008, 2012; Renger and Ludwig, 2011). This question shall therefore not be discussed here in more detail. The basic principles of the photosynthetic light reaction are presented in chapter two.
