A generalised dynamic model of leaf-level C3 photosynthesis combining light and dark reactions with stomatal behaviour

A mathematical model to simulate the dynamics of photosynthetic light reactions under harmonically oscillating light

Alternating electric current and alternating electromagnetic fields revolutionized physics and engineering and led to many technologies that shape modern life. Despite these undisputable achievements that have been reached using stimulation by harmonic oscillations over centuries, applications in biology remain rare. Photosynthesis research is uniquely suited to unleash this potential because light can be modulated as a harmonic function, here sinus. Understanding the response of photosynthetic organisms to sinusoidal light is hindered by the complexity of dynamics that such light elicits, and by the mathematical apparatus required for understanding the signals in the frequency domain which, although well-established and simple, is outside typical curricula in biology. Here, we approach these challenges by presenting a mathematical model that was designed specifically to simulate the response of photosynthetic light reactions to light which oscillates with periods that often occur in nature. The independent variables of the model are the plastoquinone pool, the photosystem I donors, lumen pH, ATP, and the chlorophyll fluorescence (ChlF) quencher that is responsible for the qE non-photochemical quenching. Dynamics of ChlF emission, rate of oxygen evolution, and non-photochemical quenching are approximated by dependent model variables. The model is used to explain the essentials of the frequency-domain approaches up to the level of presenting Bode plots of frequency-dependence of ChlF. The model simulations were found satisfactory when compared with the Bode plots of ChlF response of the green alga Chlamydomonas reinhardtii to light that was oscillating with a small amplitude and frequencies between 7.8 mHz and 64 Hz.

From leaf to multiscale models of photosynthesis: applications and challenges for crop improvement

To keep up with the growth of human population and to circumvent deleterious effects of global climate change, it is essential to enhance crop yield to achieve higher production. Here we review mathematical models of oxygenic photosynthesis that are extensively used, and discuss in depth a subset that accounts for diverse approaches providing solutions to our objective. These include models (1) to study different ways to enhance photosynthesis, such as fine-tuning antenna size, photoprotection and electron transport; (2) to bioengineer carbon metabolism; and (3) to evaluate the interactions between the process of photosynthesis and the seasonal crop dynamics, or those that have included statistical whole-genome prediction methods to quantify the impact of photosynthesis traits on the improvement of crop yield. We conclude by emphasizing that the results obtained in these studies clearly demonstrate that mathematical modelling is a key tool to examine different approaches to improve photosynthesis for better productivity, while effective multiscale crop models, especially those that also include remote sensing data, are indispensable to verify different strategies to obtain maximized crop yields.

How much could improving photosynthesis increase crop yields? A call for systems-level perspectives to guide engineering strategies

Global yield gaps can be reduced through breeding and improved agronomy. However, signs of yield plateaus from wheat and rice grown in intensively farmed systems indicate a need for new strategies if output is to continue to increase. Approaches to improve photosynthesis are suggested as a solution. Empirical evidence supporting this approach comes from small-scale free-CO2 air enrichment and transgenic studies. However, the likely achievable gains from improving photosynthesis are less understood. Models predict maximum increases in yield of 5.3-19.1% from genetic manipulation depending on crop, environment, and approach, but uncertainty remains in the presence of stress. This review seeks to provide context to the rationale for improving photosynthesis, highlight areas of uncertainty, and identify the steps required to create more accurate projections.

The operation of PEPCK increases light harvesting plasticity in C4 NAD-ME and NADP-ME photosynthetic subtypes: A theoretical study

The repeated emergence of NADP-malic enzyme (ME), NAD-ME and phosphoenolpyruvate carboxykinase (PEPCK) subtypes of C4 photosynthesis are iconic examples of convergent evolution, which suggests that these biochemistries do not randomly assemble, but are instead specific adaptations resulting from unknown evolutionary drivers. Theoretical studies that are based on the classic biochemical understanding have repeatedly proposed light-use efficiency as a possible benefit of the PEPCK subtype. However, quantum yield measurements do not support this idea. We explore this inconsistency here via an analytical model that features explicit descriptions across a seamless gradient between C4 biochemistries to analyse light harvesting and dark photosynthetic metabolism. Our simulations show that the NADP-ME subtype, operated by the most productive crops, is the most efficient. The NAD-ME subtype has lower efficiency, but has greater light harvesting plasticity (the capacity to assimilate CO2 in the broadest combination of light intensity and spectral qualities). In both NADP-ME and NAD-ME backgrounds, increasing PEPCK activity corresponds to greater light harvesting plasticity but likely imposed a reduction in photosynthetic efficiency. We draw the first mechanistic links between light harvesting and C4 subtypes, providing the theoretical basis for future investigation.

Modelling plants across scales of biological organisation for guiding crop improvement

Grain yield improvement in globally important staple crops is critical in the coming decades if production is to keep pace with growing demand; so there is increasing interest in understanding and manipulating plant growth and developmental traits for better crop productivity. However, this is confounded by complex cross-scale feedback regulations and a limited ability to evaluate the consequences of manipulation on crop production. Plant/crop modelling could hold the key to deepening our understanding of dynamic trait-crop-environment interactions and predictive capabilities for supporting genetic manipulation. Using photosynthesis and crop growth as an example, this review summarises past and present experimental and modelling work, bringing about a model-guided crop improvement thrust, encompassing research into: (1) advancing cross-scale plant/crop modelling that connects across biological scales of organisation using a trait dissection-integration modelling principle; (2) improving the reliability of predicted molecular-trait-crop-environment system dynamics with experimental validation; and (3) innovative model application in synergy with cross-scale experimentation to evaluate G×M×E and predict yield outcomes of genetic intervention (or lack of it) for strategising further molecular and breeding efforts. The possible future roles of cross-scale plant/crop modelling in maximising crop improvement are discussed.

Climate change challenges, plant science solutions

Climate change is a defining challenge of the 21st century, and this decade is a critical time for action to mitigate the worst effects on human populations and ecosystems. Plant science can play an important role in developing crops with enhanced resilience to harsh conditions (e.g. heat, drought, salt stress, flooding, disease outbreaks) and engineering efficient carbon-capturing and carbon-sequestering plants. Here, we present examples of research being conducted in these areas and discuss challenges and open questions as a call to action for the plant science community.

A small dynamic leaf-level model predicting photosynthesis in greenhouse tomatoes

The conversion of supplemental greenhouse light energy into biomass is not always optimal. Recent trends in global energy prices and discussions on climate change highlight the need to reduce our energy footprint associated with the use of supplemental light in greenhouse crop production. This can be achieved by implementing "smart" lighting regimens which in turn rely on a good understanding of how fluctuating light influences photosynthetic physiology. Here, a simple fit-for-purpose dynamic model is presented. It accurately predicts net leaf photosynthesis under natural fluctuating light. It comprises two ordinary differential equations predicting: 1) the total stomatal conductance to CO2 diffusion and 2) the CO2 concentration inside a leaf. It contains elements of the Farquhar-von Caemmerer-Berry model and the successful incorporation of this model suggests that for tomato (Solanum lycopersicum L.), it is sufficient to assume that Rubisco remains activated despite rapid fluctuations in irradiance. Furthermore, predictions of the net photosynthetic rate under both 400ppm and enriched 800ppm ambient CO2 concentrations indicate a strong correlation between the dynamic rate of photosynthesis and the rate of electron transport. Finally, we are able to indicate whether dynamic photosynthesis is Rubisco or electron transport rate limited.

Reduction of bundle sheath size boosts cyclic electron flow in C4 Setaria viridis acclimated to low light

When C₄ leaves are exposed to low light, the CO₂ concentration in the bundle sheath (BS) cells decreases, causing an increase in photorespiration relative to assimilation, and a consequent reduction in biochemical efficiency. These effects can be mitigated by complex acclimation syndromes, which are of primary importance for crop productivity but are not well studied. We unveil an acclimation strategy involving the coordination of electron transport processes. First, we characterize the anatomy, gas exchange and electron transport of C₄ Setaria viridis grown under low light. Through a purposely developed biochemical model, we resolve the photon fluxes and reaction rates to explain how the concerted acclimation strategies sustain photosynthetic efficiency. Our results show that a smaller BS in low-light-grown plants limited leakiness (the ratio of CO₂ leak rate out of the BS over the rate of supply via C₄ acid decarboxylation) but sacrificed light harvesting and ATP production. To counter ATP shortage and maintain high assimilation rates, plants facilitated light penetration through the mesophyll and upregulated cyclic electron flow in the BS. This shade tolerance mechanism, based on the optimization of light reactions, is possibly more efficient than the known mechanisms involving the rearrangement of carbon metabolism, and could potentially lead to innovative strategies for crop improvement.

A System Dynamics Approach to Model Photosynthesis at Leaf Level Under Fluctuating Light

Photosynthesis has been mainly studied under steady-state conditions even though this assumption results inadequate for assessing the biochemical responses to rapid variations occurring in natural environments. The combination of mathematical models with available data may enhance the understanding of the dynamic responses of plants to fluctuating environments and can be used to make predictions on how photosynthesis would respond to non-steady-state conditions. In this study, we present a leaf level System Dynamics photosynthesis model based and validated on an experiment performed on two soybean varieties, namely, the wild type Eiko and the chlorophyll-deficient mutant MinnGold, grown in constant and fluctuating light conditions. This mutant is known to have similar steady-state photosynthesis compared to the green wild type, but it is found to have less biomass at harvest. It has been hypothesized that this might be due to an unoptimized response to non-steady-state conditions; therefore, this mutant seems appropriate to investigate dynamic photosynthesis. The model explained well the photosynthetic responses of these two varieties to fluctuating and constant light conditions and allowed to make relevant conclusions on the different dynamic responses of the two varieties. Deviations between data and model simulations are mostly evident in the non-photochemical quenching (NPQ) dynamics due to the oversimplified combination of PsbS- and zeaxanthin-dependent kinetics, failing in finely capturing the NPQ responses at different timescales. Nevertheless, due to its simplicity, the model can provide the basis of an upscaled dynamic model at a plant level.

Potential metabolic mechanisms for inhibited chloroplast nitrogen assimilation under high CO2

Improving photosynthesis is considered a major and feasible option to dramatically increase crop yield potential. Increased atmospheric CO2 concentration often stimulates both photosynthesis and crop yield, but decreases protein content in the main C3 cereal crops. This decreased protein content in crops constrains the benefits of elevated CO2 on crop yield and affects their nutritional value for humans. To support studies of photosynthetic nitrogen assimilation and its complex interaction with photosynthetic carbon metabolism for crop improvement, we developed a dynamic systems model of plant primary metabolism, which includes the Calvin-Benson cycle, the photorespiration pathway, starch synthesis, glycolysis-gluconeogenesis, the tricarboxylic acid cycle, and chloroplastic nitrogen assimilation. This model successfully captures responses of net photosynthetic CO2 uptake rate (A), respiration rate, and nitrogen assimilation rate to different irradiance and CO2 levels. We then used this model to predict inhibition of nitrogen assimilation under elevated CO2. The potential mechanisms underlying inhibited nitrogen assimilation under elevated CO2 were further explored with this model. Simulations suggest that enhancing the supply of α-ketoglutarate is a potential strategy to maintain high rates of nitrogen assimilation under elevated CO2. This model can be used as a heuristic tool to support research on interactions between photosynthesis, respiration, and nitrogen assimilation. It also provides a basic framework to support the design and engineering of C3 plant primary metabolism for enhanced photosynthetic efficiency and nitrogen assimilation in the coming high-CO2 world.

The role of Cytochrome b6f in the control of steady-state photosynthesis: a conceptual and quantitative model

Here, we present a conceptual and quantitative model to describe the role of the Cytochrome [Formula: see text] complex in controlling steady-state electron transport in [Formula: see text] leaves. The model is based on new experimental methods to diagnose the maximum activity of Cyt [Formula: see text] in vivo, and to identify conditions under which photosynthetic control of Cyt [Formula: see text] is active or relaxed. With these approaches, we demonstrate that Cyt [Formula: see text] controls the trade-off between the speed and efficiency of electron transport under limiting light, and functions as a metabolic switch that transfers control to carbon metabolism under saturating light. We also present evidence that the onset of photosynthetic control of Cyt [Formula: see text] occurs within milliseconds of exposure to saturating light, much more quickly than the induction of non-photochemical quenching. We propose that photosynthetic control is the primary means of photoprotection and functions to manage excitation pressure, whereas non-photochemical quenching functions to manage excitation balance. We use these findings to extend the Farquhar et al. (Planta 149:78-90, 1980) model of [Formula: see text] photosynthesis to include a mechanistic description of the electron transport system. This framework relates the light captured by PS I and PS II to the energy and mass fluxes linking the photoacts with Cyt [Formula: see text], the ATP synthase, and Rubisco. It enables quantitative interpretation of pulse-amplitude modulated fluorometry and gas-exchange measurements, providing a new basis for analyzing how the electron transport system coordinates the supply of Fd, NADPH, and ATP with the dynamic demands of carbon metabolism, how efficient use of light is achieved under limiting light, and how photoprotection is achieved under saturating light. The model is designed to support forward as well as inverse applications. It can either be used in a stand-alone mode at the leaf-level or coupled to other models that resolve finer-scale or coarser-scale phenomena.

Photosynthesis: basics, history and modelling

BACKGROUND

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 CO2 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.

SCOPE

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 (ΔA820) 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.

Surfing the Hyperbola Equations of the Steady-State Farquhar-von Caemmerer-Berry C3 Leaf Photosynthesis Model: What Can a Theoretical Analysis of Their Oblique Asymptotes and Transition Points Tell Us?

The asymptotes and transition points of the net CO2 assimilation (A/Ci) rate curves of the steady-state Farquhar-von Caemmerer-Berry (FvCB) model for leaf photosynthesis of C3 plants are examined in a theoretical study, which begins from the exploration of the standard equations of hyperbolae after rotating the coordinate system. The analysis of the A/Ci quadratic equations of the three limitation states of the FvCB model-abbreviated as Ac, Aj and Ap-allows us to conclude that their oblique asymptotes have a common slope that depends only on the mesophyll conductance to CO2 diffusion (gm). The limiting values for the transition points between any two states of the three limitation states c, j and p do not depend on gm, and the results are therefore valid for rectangular and non-rectangular hyperbola equations of the FvCB model. The analysis of the variation of the slopes of the asymptotes with gm casts doubts about the fulfilment of the steady-state conditions, particularly, when the net CO2 assimilation rate is inhibited at high CO2 concentrations. The application of the theoretical analysis to extended steady-state FvCB models, where the hyperbola equations of Ac, Aj and Ap are modified to accommodate nitrogen assimilation and amino acids export via the photorespiratory pathway, is also discussed.

A leaf-level biochemical model simulating the introduction of C2 and C4 photosynthesis in C3 rice: gains, losses and metabolite fluxes

This work aims at developing an adequate theoretical basis for comparing assimilation of the ancestral C₃ pathway with CO₂ concentrating mechanisms (CCM) that have evolved to reduce photorespiratory yield losses. We present a novel model for C₃ , C₂ , C₂  + C₄ and C₄ photosynthesis simulating assimilatory metabolism, energetics and metabolite traffic at the leaf level. It integrates a mechanistic description of light reactions to simulate ATP and NADPH production, and a variable engagement of cyclic electron flow. The analytical solutions are compact and thus suitable for larger scale simulations. Inputs were derived with a comprehensive gas-exchange experiment. We show trade-offs in the operation of C₄ that are in line with ecophysiological data. C₄ has the potential to increase assimilation over C₃ at high temperatures and light intensities, but this benefit is reversed under low temperatures and light. We apply the model to simulate the introduction of progressively complex levels of CCM into C₃ rice, which feeds > 3.5 billion people. Increasing assimilation will require considerable modifications such as expressing the NAD(P)H Dehydrogenase-like complex and upregulating cyclic electron flow, enlarging the bundle sheath, and expressing suitable transporters to allow adequate metabolite traffic. The simpler C₂ rice may be a desirable alternative.