Leaf C3 Photosynthesis in silico: Integrated Carbon/Nitrogen Metabolism

Assessing key parameters in simultaneous simulation of rapid kinetics of chlorophyll a fluorescence and trans-thylakoid electric potential difference

Our study attempts to address the following questions: among numerous photosynthetic modules, which parameters notably influence the rapid chlorophyll fluorescence (ChlF) rise, the so-called O-J-I-P transient, in conjunction with the P515 signal, as these two records are easily obtained and widely used in photosynthesis research, and how are these parameters ranked in terms of their importance? These questions might be difficult to answer solely through experimental assays. Therefore, we employed an established photosynthesis model. Firstly, we utilized the model to simulate the measured rapid ChlF rise and P515 kinetics simultaneously. Secondly, we employed the sensitivity analysis (SA) tool by randomly altering model parameters to observe their effects on model output variables. Thirdly, we systematically identified significant parameters for both or one of the kinetics across various scenarios. A novel aspect of our study is the application of the Morris method, a global SA tool, to simultaneously assess the significance of model parameters in shaping both or one of the kinetics. The Morris SA technique enables the quantification of how much a specific parameter affects O-J-I-P transient during particular time intervals (e.g., J, I, and P steps). This allowed us to theoretically analyze which step is more significantly influenced by the parameter. In summary, our study contributes to the field by providing a comprehensive analysis of photosynthesis kinetics and emphasizing the importance of parameter selection in modelling this process. These findings can inform future research efforts aimed at improving photosynthesis models and advancing our understanding of photosynthetic processes.

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.

Into the Shadows and Back into Sunlight: Photosynthesis in Fluctuating Light

Photosynthesis is an important remaining opportunity for further improvement in the genetic yield potential of our major crops. Measurement, analysis, and improvement of leaf CO₂ assimilation (A) have focused largely on photosynthetic rates under light-saturated steady-state conditions. However, in modern crop canopies of several leaf layers, light is rarely constant, and the majority of leaves experience marked light fluctuations throughout the day. It takes several minutes for photosynthesis to regain efficiency in both sun-shade and shade-sun transitions, costing a calculated 10-40% of potential crop CO₂ assimilation. Transgenic manipulations to accelerate the adjustment in sun-shade transitions have already shown a substantial productivity increase in field trials. Here, we explore means to further accelerate these adjustments and minimize these losses through transgenic manipulation, gene editing, and exploitation of natural variation. Measurement andanalysis of photosynthesis in sun-shade and shade-sun transitions are explained. Factors limiting speeds of adjustment and how they could be modified to effect improved efficiency are reviewed, specifically nonphotochemical quenching (NPQ), Rubisco activation, and stomatal responses.

The limiting factors and regulatory processes that control the environmental responses of C3, C3-C4 intermediate, and C4 photosynthesis

Here, we describe a model of C3, C3-C4 intermediate, and C4 photosynthesis that is designed to facilitate quantitative analysis of physiological measurements. The model relates the factors limiting electron transport and carbon metabolism, the regulatory processes that coordinate these metabolic domains, and the responses to light, carbon dioxide, and temperature. It has three unique features. First, mechanistic expressions describe how the cytochrome b6f complex controls electron transport in mesophyll and bundle sheath chloroplasts. Second, the coupling between the mesophyll and bundle sheath expressions represents how feedback regulation of Cyt b6f coordinates electron transport and carbon metabolism. Third, the temperature sensitivity of Cyt b6f is differentiated from that of the coupling between NADPH, Fd, and ATP production. Using this model, we present simulations demonstrating that the light dependence of the carbon dioxide compensation point in C3-C4 leaves can be explained by co-occurrence of light saturation in the mesophyll and light limitation in the bundle sheath. We also present inversions demonstrating that population-level variation in the carbon dioxide compensation point in a Type I C3-C4 plant, Flaveria chloraefolia, can be explained by variable allocation of photosynthetic capacity to the bundle sheath. These results suggest that Type I C3-C4 intermediate plants adjust pigment and protein distributions to optimize the glycine shuttle under different light and temperature regimes, and that the malate and aspartate shuttles may have originally functioned to smooth out the energy supply and demand associated with the glycine shuttle. This model has a wide range of potential applications to physiological, ecological, and evolutionary questions.

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.

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

Global food demand is rising, impelling us to develop strategies for improving the efficiency of photosynthesis. Classical photosynthesis models based on steady-state assumptions are inherently unsuitable for assessing biochemical and stomatal responses to rapid variations in environmental drivers. To identify strategies to increase photosynthetic efficiency, we need models that account for the timing of CO₂ assimilation responses to dynamic environmental stimuli. Herein, I present a dynamic process-based photosynthetic model for C₃ leaves. The model incorporates both light and dark reactions, coupled with a hydro-mechanical model of stomatal behaviour. The model achieved a stable and realistic rate of light-saturated CO₂ assimilation and stomatal conductance. Additionally, it replicated complete typical assimilatory response curves (stepwise change in CO₂ and light intensity at different oxygen levels) featuring both short lag times and full photosynthetic acclimation. The model also successfully replicated transient responses to changes in light intensity (light flecks), CO₂ concentration, and atmospheric oxygen concentration. This dynamic model is suitable for detailed ecophysiological studies and has potential for superseding the long-dominant steady-state approach to photosynthesis modelling. The model runs as a stand-alone workbook in Microsoft® Excel® and is freely available to download along with a video tutorial.

Dynamic modelling of limitations on improving leaf CO2 assimilation under fluctuating irradiance

A dynamic model of leaf CO₂ assimilation was developed as an extension of the canonical steady-state model, by adding the effects of energy-dependent non-photochemical quenching (qE), chloroplast movement, photoinhibition, regulation of enzyme activity in the Calvin cycle, metabolite concentrations, and dynamic CO₂ diffusion. The model was calibrated and tested successfully using published measurements of gas exchange and chlorophyll fluorescence on Arabidopsis thaliana ecotype Col-0 and several photosynthetic mutants and transformants affecting the regulation of Rubisco activity (rca-2 and rwt43), non-photochemical quenching (npq4-1 and npq1-2), and sucrose synthesis (spsa1). The potential improvements on CO₂ assimilation under fluctuating irradiance that can be achieved by removing the kinetic limitations on the regulation of enzyme activities, electron transport, and stomatal conductance were calculated in silico for different scenarios. The model predicted that the rates of activation of enzymes in the Calvin cycle and stomatal opening were the most limiting (up to 17% improvement) and that effects varied with the frequency of fluctuations. On the other hand, relaxation of qE and chloroplast movement had a strong effect on average low-irradiance CO₂ assimilation (up to 10% improvement). Strong synergies among processes were found, such that removing all kinetic limitations simultaneously resulted in improvements of up to 32%.

A generalized stoichiometric model of C3, C2, C2+C4, and C4 photosynthetic metabolism

The goal of suppressing photorespiration in crops to maximize assimilation and yield is stimulating considerable interest among researchers looking to bioengineer carbon-concentrating mechanisms into C₃ plants. However, detailed quantification of the biochemical activities in the bundle sheath is lacking. This work presents a general stoichiometric model for C₃, C₂, C₂+C₄, and C₄ assimilation (SMA) in which energetics, metabolite traffic, and the different decarboxylating enzymes (NAD-dependent malic enzyme, NADP-dependent malic enzyme, or phosphoenolpyruvate carboxykinase) are explicitly included. The SMA can be used to refine experimental data analysis or formulate hypothetical scenarios, and is coded in a freely available Microsoft Excel workbook. The theoretical underpinnings and general model behaviour are analysed with a range of simulations, including (i) an analysis of C₃, C₂, C₂+C₄, and C₄ in operational conditions; (ii) manipulating photorespiration in a C₃ plant; (iii) progressively upregulating a C₂ shuttle in C₃ photosynthesis; (iv) progressively upregulating a C₄ cycle in C₂ photosynthesis; and (v) manipulating processes that are hypothesized to respond to transient environmental inputs. Results quantify the functional trade-offs, such as the electron transport needed to meet ATP/NADPH demand, as well as metabolite traffic, inherent to different subtypes. The SMA refines our understanding of the stoichiometry of photosynthesis, which is of paramount importance for basic and applied research.

Control of Rubisco function via homeostatic equilibration of CO2 supply

Rubisco is the most abundant protein on Earth that serves as the primary engine of carbon assimilation. It is characterized by a slow rate and low specificity for CO2 leading to photorespiration. We analyze here the challenges of operation of this enzyme as the main carbon fixation engine. The high concentration of Rubisco exceeds that of its substrate CO2 by 2-3 orders of magnitude; however, the total pool of available carbon in chloroplast, i.e., mainly bicarbonate, is comparable to the concentration of Rubisco active sites. This makes the reactant stationary assumption (RSA), which is essential as a condition of satisfying the Michaelis-Menten (MM) kinetics, valid if we assume that the delivery of CO2 from this pool is not limiting. The RSA is supported by active carbonic anhydrases (CA) that quickly equilibrate bicarbonate and CO2 pools and supply CO2 to Rubisco. While the operation of stromal CA is independent of light reactions, the thylakoidal CA associated with PSII and pumping CO2 from the thylakoid lumen is coordinated with the rate of electron transport, water splitting and proton gradient across the thylakoid membrane. At high CO2 concentrations, CA becomes less efficient (the equilibrium becomes unfavorable), so a deviation from the MM kinetics is observed, consistent with Rubisco reaching its Vmax at approximately 50% lower level than expected from the classical MM curve. Previously, this deviation was controversially explained by the limitation of RuBP regeneration. At low ambient CO2 and correspondingly limited capacity of the bicarbonate pool, its depletion at Rubisco sites is relieved in that the enzyme utilizes O2 instead of CO2, i.e., by photorespiration. In this process, CO2 is supplied back to Rubisco, and the chloroplastic redox state and energy level are maintained. It is concluded that the optimal performance of photosynthesis is achieved via the provision of continuous CO2 supply to Rubisco by carbonic anhydrases and photorespiration.

Hierarchical modularization of biochemical pathways using fuzzy-c means clustering

Biological systems that are representative of regulatory, metabolic, or signaling pathways can be highly complex. Mathematical models that describe such systems inherit this complexity. As a result, these models can often fail to provide a path toward the intuitive comprehension of these systems. More coarse information that allows a perceptive insight of the system is sometimes needed in combination with the model to understand control hierarchies or lower level functional relationships. In this paper, we present a method to identify relationships between components of dynamic models of biochemical pathways that reside in different functional groups. We find primary relationships and secondary relationships. The secondary relationships reveal connections that are present in the system, which current techniques that only identify primary relationships are unable to show. We also identify how relationships between components dynamically change over time. This results in a method that provides the hierarchy of the relationships among components, which can help us to understand the low level functional structure of the system and to elucidate potential hierarchical control. As a proof of concept, we apply the algorithm to the epidermal growth factor signal transduction pathway, and to the C3 photosynthesis pathway. We identify primary relationships among components that are in agreement with previous computational decomposition studies, and identify secondary relationships that uncover connections among components that current computational approaches were unable to reveal.

Chlorophyll a fluorescence induction: a personal perspective of the thermal phase, the J-I-P rise

The fast (up to 1 s) chlorophyll (Chl) a fluorescence induction (FI) curve, measured under saturating continuous light, has a photochemical phase, the O-J rise, related mainly to the reduction of Q(A), the primary electron acceptor plastoquinone of Photosystem II (PSII); here, the fluorescence rise depends strongly on the number of photons absorbed. This is followed by a thermal phase, the J-I-P rise, which disappears at subfreezing temperatures. According to the mainstream interpretation of the fast FI, the variable fluorescence originates from PSII antenna, and the oxidized Q(A) is the most important quencher influencing the O-J-I-P curve. As the reaction centers of PSII are gradually closed by the photochemical reduction of Q(A), Chl fluorescence, F, rises from the O level (the minimal level) to the P level (the peak); yet, the relationship between F and [Q(A) (-)] is not linear, due to the presence of other quenchers and modifiers. Several alternative theories have been proposed, which give different interpretations of the O-J-I-P transient. The main idea in these alternative theories is that in saturating light, Q(A) is almost completely reduced already at the end of the photochemical phase O-J, but the fluorescence yield is lower than its maximum value due to the presence of either a second quencher besides Q(A), or there is an another process quenching the fluorescence; in the second quencher hypothesis, this quencher is consumed (or the process of quenching the fluorescence is reversed) during the thermal phase J-I-P. In this review, we discuss these theories. Based on our critical examination, that includes pros and cons of each theory, as well mathematical modeling, we conclude that the mainstream interpretation of the O-J-I-P transient is the most credible one, as none of the alternative ideas provide adequate explanation or experimental proof for the almost complete reduction of Q(A) at the end of the O-J phase, and for the origin of the fluorescence rise during the thermal phase. However, we suggest that some of the factors influencing the fluorescence yield that have been proposed in these newer theories, as e.g., the membrane potential ΔΨ, as suggested by Vredenberg and his associates, can potentially contribute to modulate the O-J-I-P transient in parallel with the reduction of Q(A), through changes at the PSII antenna and/or at the reaction center, or, possibly, through the control of the oxidation-reduction of the PQ-pool, including proton transfer into the lumen, as suggested by Rubin and his associates. We present in this review our personal perspective mainly on our understanding of the thermal phase, the J-I-P rise during Chl a FI in plants and algae.

The rate of nitrite reduction in leaves as indicated by O₂ and CO₂ exchange during photosynthesis

Light response (at 300 ppm CO(2) and 10-50 ppm O(2) in N(2)) and CO(2) response curves [at absorbed photon fluence rate (PAD) of 550 μmol m(-2) s(-1)] of O(2) evolution and CO(2) uptake were measured in tobacco (Nicotiana tabacum L.) leaves grown on either NO(3)(-) or NH(4)(+) as N source and in potato (Solanum tuberosum L.), sorghum (Sorghum bicolor L. Moench), and amaranth (Amaranthus cruentus L.) leaves grown on NH(4)NO(3). Photosynthetic O(2) evolution in excess of CO(2) uptake was measured with a stabilized zirconia O(2) electrode and an infrared CO(2) analyser, respectively, and the difference assumed to represent the rate of electron flow to acceptors alternative to CO(2), mainly NO(2)(-), SO(4)(2-), and oxaloacetate. In NO(3)(-)-grown tobacco, as well as in sorghum, amaranth, and young potato, the photosynthetic O(2)-CO(2) flux difference rapidly increased to about 1 μmol m(-2) s(-1) at very low PADs and the process was saturated at 50 μmol quanta m(-2) s(-1). At higher PADs the O(2)-CO(2) flux difference continued to increase proportionally with the photosynthetic rate to a maximum of about 2 μmol m(-2) s(-1). In NH(4)(+)-grown tobacco, as well as in potato during tuber filling, the low-PAD component of surplus O(2) evolution was virtually absent. The low-PAD phase was ascribed to photoreduction of NO(2)(-) which successfully competes with CO(2) reduction and saturates at a rate of about 1 μmol O(2) m(-2) s(-1) (9% of the maximum O(2) evolution rate). The high-PAD component of about 1 μmol O(2) m(-2) s(-1), superimposed on NO(2)(-) reduction, may represent oxaloacetate reduction. The roles of NO(2)(-), oxaloacetate, and O(2) reduction in the regulation of ATP/NADPH balance are discussed.

Modelling the crop: from system dynamics to systems biology

There is strong interplant competition in a crop stand for various limiting resources, resulting in complex compensation and regulation mechanisms along the developmental cascade of the whole crop. Despite decades-long use of principles in system dynamics (e.g. feedback control), current crop models often contain many empirical elements, and model parameters may have little biological meaning. Building on the experience in designing the relatively new model GECROS, we believe models can be made less empirical by employing existing physiological understanding and mathematical tools. In view of the potential added value of robust crop modelling to classical quantitative genetics, model input parameters are increasingly considered to represent 'genetic coefficients'. The advent of functional genomics and systems biology enables the elucidation of the molecular genetic basis of these coefficients. A number of case studies, in which the effects of quantitative trait loci or genes have been incorporated into existing ecophysiological models, have shown the promise of using models in analysing genotype-phenotype relationships of some crop traits. For further progress, crop models must be upgraded based on understanding at lower organizational levels for complicated phenomena such as sink formation in response to environmental cues, sink feedback on source activity, and photosynthetic acclimation to the prevailing environment. Within this context, the recently proposed 'crop systems biology', which combines modern genomics, traditional physiology and biochemistry, and advanced modelling, is believed ultimately to realize the expected roles of in silico modelling in narrowing genotype-phenotype gaps. This review summarizes recent findings and our opinions on perspectives for modelling genotype x environment interactions at crop level.