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  • Metabolic Pathway Analysis 2015Mini Review

    A reductionist approach to model photosyntheticself-regulation in eukaryotes in response to lightAnna B. Matuszynska1, Oliver Ebenhoh1,2*

    AbstractAlong with the development of several large-scale methods such as mass spectrometry or micro arrays, genomewide models became not only a possibility but an obvious tool for theoretical biologists to integrate and analysecomplex biological data. Nevertheless, incorporating the dynamics of photosynthesis remains one of the majorchallenges while reconstructing metabolic networks of plants and other photosynthetic organisms. In this review,we aim to provide arguments that small-scale models are still a suitable choice when it comes to discoverorganisational principles governing the design of biological systems. We give a brief overview of recent modellingefforts in understanding the interplay between rapid, photoprotective mechanisms and the redox balance withinthe thylakoid membrane, discussing the applicability of a reductionist approach in modelling self-regulation inplants, and outline possible directions for further research.

    Keywordsphotosynthesis, non-photochemical quenching, self-regulation, redox balance, mathematical model, acclimation

    1Institute for Quantitative and Theoretical Biology, Cluster of Excellence on Plant Sciences, Heinrich- Heine-University, 40225 Dusseldorf,Germany2Institute for Complex Systems and Mathematical Biology, University of Aberdeen, AB24 3UE Aberdeen, United Kingdom*Corresponding author: oliver.ebenhoeh@hhu.de

    Abbreviations

    LHC light harvesting complex

    NPQ non-photochemical quenching

    PSI photosystem I

    PSII photosystem II

    qE high-energy dependent quenching

    qT state transitions

    RC reaction centre

    VAZ violaxanthin-antheraxanthin-zeaxanthin cycle

    .CC-BY-NC 4.0 International licensepeer-reviewed) is the author/funder. It is made available under aThe copyright holder for this preprint (which was not. http://dx.doi.org/10.1101/033894doi: bioRxiv preprint first posted online Dec. 7, 2015;

    http://dx.doi.org/10.1101/033894http://creativecommons.org/licenses/by-nc/4.0/

  • A reductionist approach to model photosynthetic self-regulation in eukaryotes in response to light 2/9

    IntroductionIn the process of photosynthesis solar energy is harvestedby chlorophyll pigments and converted into chemical energyby a series of redox reactions. High light intensities mayseverely impair the photosynthetic apparatus and damage thereaction centres, where charge separation occurs. In orderto protect themselves against photodamage, plants and otherphotosynthetic organisms are capable of switching from aphotosynthetic, light-harvesting to a protective status, in whichexcess absorbed radiant energy is dissipated as heat [1].

    Through the reorganisation of light harvesting complexesplants gain the ability to dynamically react to external stimuliand to keep the redox balance within the thylakoid mem-brane [2]. However, what is a desired and even essentialmechanism in natural, fluctuating environments, becomes anunwanted feature in industrial cultivation, where one aims atutilising the applied light energy for photochemistry with thehighest possible efficiency. Clearly, a thorough understandingof the molecular signalling mechanisms guiding acclimationresponses is required to optimise biotechnological exploitationof photosynthetic organisms, for example for the productionof high-value commodities. Such an understanding, which canonly be obtained by combining several scientific approaches,will allow to assess, quantify and eventually minimise therate of energy loss. In the long term, this knowledge has thepotential to support increasing plant productivity, and thuscontribute to solving the grand challenge of the 21st centuryimposed by the increasing food and energy demand [3, 4].

    Theoretical approaches are powerful to discover organisa-tional principles governing the design of biological systems.Properly constructed mathematical models verify and comple-ment experimentally obtained results, reflect the current stateof knowledge and set theoretical frameworks to derive novelhypotheses and perform investigations which are often experi-mentally challenging, if not impossible. Mathematical modelscan take many forms, depending on the research question theyaim to answer [5]. By definition, models are a simplified rep-resentation of reality and can focus on different timescales anddifferent levels of complexity (Figure 1). System-level modelsof metabolism found a number of applications but, becauseof the intrinsic assumption of a stationary state, they face thechallenge of including the dynamics of photosynthesis [6]when applied to phototrophic organisms.

    In this review, we aim to provide arguments for the appli-cation of reductionist approaches in photosynthetic researchto study self regulation in plants. For that we discuss math-ematical models published on the topic in the past decadeand discuss challenges and future prospects associated withdynamic, differential equation-based models.

    Self regulation

    In natural conditions, plants are exposed to rapid fluctuationsin their environment [11] including changes in light intensityand quality. When a chlorophyll absorbs a photon it is ex-

    cited to a higher energy state from which it can relax eitherby fuelling the photochemical reactions or by dissipating theexcess energy in the form of fluorescence or heat [1]. In highlight, excitation of chlorophyll may be faster than relaxationand chlorophyll singlet excited states accumulate [12]. Thisleads to the formation of chlorophyll triplets that, by reactingwith molecular oxygen, result in highly reactive and dan-gerous singlet oxygen [13]. Through processes collectivelynamed as non-photochemical quenching (NPQ) almost alleukaryotic autotrophs [14] avoid and minimise such photoox-idative stress. Photosynthesis is driven by energy collectedby complexes associated with two photosystems, which arepreferentially excited by different wavelengths. Acclimationto fluctuating environments by balancing excitation of thesetwo photosystems is achieved by an additional mechanism, inwhich light-harvesting complexes are relocated [15].

    Although a number of genes and proteins involved in theseacclimation pathways have been identified, in many cases themolecular basis for their dynamics remains unknown. Thus,a number of mathematical models have been developed withthe goal to understand the regulatory principles and to supportthe identification of the underlying molecular mechanisms.

    ModelsMuch of todays knowledge about the dynamics of photosyn-thesis was brought by reductionist models, dating back to theextremely simplified, but illustrative pioneering model of leafphotosynthesis by Thornley [16]. The question is whetherthis approach is still justified in the era of quantitative biology.The recent rapid advance in experimental techniques, such asmass-spectrometry and high-throughput sequencing, allowsobtaining global snapshots of the status of a cell with unprece-dented precision [17]. This wealth of information allows forexample the reconstruction of genome-scale metabolic net-works encompassing the entirety of all known biochemicalreactions [18]. One would expect that with this richness ofavailable data, a fundamental biochemical process like pho-tosynthesis would be already well understood. In fact, a fewattempts have been made to apply genome-scale metabolicmodels to photosynthetic organisms including plants [19],green algae [20] and cyanobacteria [21] (recently reviewedin [6]) and these approaches were successful in providing valu-able insight into the dependence of stationary flux distributionsto external conditions. However, the inherent steady-state as-sumptions in the mathematical analysis techniques [22] makesthem unsuitable to explore the regulatory mechanisms un-derlying the dynamic responses, which are so essential fororganisms that need to cope with changing environmentalconditions [23].

    In contrast, small-scale kinetic models are designed foran in-depth investigation of individual biological componentsand can provide information on the dynamics of the system,far away from the steady state, and predict temporal responsesto different perturbations. Here, reduced model complexityand low numbers of model parameters support the process of

    .CC-BY-NC 4.0 International licensepeer-reviewed) is the author/funder. It is made available under aThe copyright holder for this preprint (which was not. http://dx.doi.org/10.1101/033894doi: bioRxiv preprint first posted online Dec. 7, 2015;

    http://dx.doi.org/10.1101/033894http://creativecommons.org/licenses/by-nc/4.0/

  • A reductionist approach to model photosynthetic self-regulation in eukaryotes in response to light 3/9

    Figure 1. The three dimensions of model reduction. Existing photosynthetic models cover different levels of complexityand details depending on the research questions they aim to answer, ranging from the detailed models of processes occurringwithin PSII on the timescale of picoseconds to nanoseconds, reviewed in [7], over the biochemically structured models ofculture growth in bioreactors [8, 9] to models of photosynthethic evolution [10]. All of them reduce the commplexity byfocussing on selected temporal and spatial scales.

    creating a general theoretical platform to study mechanismsconserved over a wide range of species, including the plantkingdom, but also other photosynthetic microalgae. In thepast decade a handful of new kinetic models have been pub-lished with the aim to help understand underlying principlesgoverning short term acclimation mechanisms. Due the factthat the effect of regulatory acclimation mechanisms can beeasily monitored in a minimally invasive way by chlorophyllfluores