Modeling of the Primary Processes in a Photosynthetic Membrane

Molecular, Brownian, kinetic and stochastic models of the processes in photosynthetic membrane of green plants and microalgae

The paper presents the results of recent work at the Department of Biophysics of the Biological Faculty, Lomonosov Moscow State University on the kinetic and multiparticle modeling of processes in the photosynthetic membrane. The detailed kinetic models and the rule-based kinetic Monte Carlo models allow to reproduce the fluorescence induction curves and redox transformations of the photoactive pigment P700 in the time range from 100 ns to dozens of seconds and make it possible to reveal the role of individual carriers in their formation for different types of photosynthetic organisms under different illumination regimes, in the presence of inhibitors, under stress conditions. The fitting of the model curves to the experimental data quantifies the reaction rate constants that cannot be directly measured experimentally, including the non-radiative thermal relaxation reactions. We use the direct multiparticle models to explicitly describe the interactions of mobile photosynthetic carrier proteins with multienzyme complexes both in solution and in the biomembrane interior. An analysis of these models reveals the role of diffusion and electrostatic factors in the regulation of electron transport, the influence of ionic strength and pH of the cellular environment on the rate of electron transport reactions between carrier proteins. To describe the conformational intramolecular processes of formation of the final complex, in which the actual electron transfer occurs, we use the methods of molecular dynamics. The results obtained using kinetic and molecular models supplement our knowledge of the mechanisms of organization of the photosynthetic electron transport processes at the cellular and molecular levels.

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.

Balancing energy supply during photosynthesis - a theoretical perspective

The photosynthetic electron transport chain (PETC) provides energy and redox equivalents for carbon fixation by the Calvin-Benson-Bassham (CBB) cycle. Both of these processes have been thoroughly investigated and the underlying molecular mechanisms are well known. However, it is far from understood by which mechanisms it is ensured that energy and redox supply by photosynthesis matches the demand of the downstream processes. Here, we deliver a theoretical analysis to quantitatively study the supply-demand regulation in photosynthesis. For this, we connect two previously developed models, one describing the PETC, originally developed to study non-photochemical quenching, and one providing a dynamic description of the photosynthetic carbon fixation in C3 plants, the CBB Cycle. The merged model explains how a tight regulation of supply and demand reactions leads to efficient carbon fixation. The model further illustrates that a stand-by mode is necessary in the dark to ensure that the carbon fixation cycle can be restarted after dark-light transitions, and it supports hypotheses, which reactions are responsible to generate such mode in vivo.

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

The dark-to-light transitions enable energization of the thylakoid membrane (TM), which is reflected in fast and slow (OJIPSMT or OABCDE) stages of fluorescence induction (FI) and P700 oxidoreduction changes (ΔA810). A Thylakoid Membrane model (T-M model), in which special emphasis has been placed on ferredoxin-NADP+-oxidoreductase (FNR) activation and energy-dependent qE quenching, was applied for quantifying the kinetics of FI and ΔA810. Pea leaves were kept in darkness for 15 min and then the FI and ΔA810 signals were measured upon actinic illumination, applied either directly or after a 10-s light pulse coupled with a subsequent 10-s dark interval. On the time scale from 40 µs to 30 s, the parallel T-M model fittings to both FI and ΔA810 signals were obtained. The parameters of FNR activation and the buildup of qE quenching were found to differ for dark-adapted and preilluminated leaves. At the onset of actinic light, photosystem II (PSII) acceptors were oxidized (neutral) after dark adaptation, while the redox states with closed and/or semiquinone QA(-)QB(-) forms were supposedly generated after preillumination, and did not relax within the 10 s dark interval. In qE simulations, a pH-dependent Hill relationship was used. The rate constant of heat losses in PSII antenna kD(t) was found to increase from the basic value kDconst, at the onset of illumination, to its maximal level kDvar due to lumenal acidification. In dark-adapted leaves, a low value of kDconst of ∼ 2 × 106 s-1 was found. Simulations on the microsecond to 30 s time scale revealed that the slow P-S-M-T phases of the fluorescence induction were sensitive to light-induced FNR activation and high-energy qE quenching. Thus, the corresponding time-dependent rate constants kD(t) and kFNR(t) change substantially upon the release of electron transport on the acceptor side of PSI and during the NPQ development. The transitions between the cyclic and linear electron transport modes have also been quantified in this paper.

Simulation of chlorophyll fluorescence rise and decay kinetics, and P700-related absorbance changes by using a rule-based kinetic Monte-Carlo method

A model of primary photosynthetic reactions in the thylakoid membrane was developed and its validity was tested by simulating three types of experimental kinetic curves: (1) the light-induced chlorophyll a fluorescence rise (OJIP transients) reflecting the stepwise transition of the photosynthetic electron transport chain from the oxidized to the fully reduced state; (2) the dark relaxation of the flash-induced fluorescence yield attributed to the Q_A^- oxidation kinetics in PSII; and (3) the light-induced absorbance changes near 820 or 705 nm assigned to the redox transitions of P₇₀₀ in PSI. A model was implemented by using a rule-based kinetic Monte-Carlo method and verified by simulating experimental curves under different treatments including photosynthetic inhibitors, heat stress, anaerobic conditions, and very high light intensity.

Thylakoid membrane model of the Chl a fluorescence transient and P700 induction kinetics in plant leaves

A new Thylakoid model is presented, which describes in detail the electron/proton transfer reactions between membrane protein complexes including photosystems II and I (PSII, PSI), cytochrome (Cyt) b 6 f, mobile plastoquinone PQ pool in the thylakoid membrane, plastocyanin in lumen and ferredoxin in stroma, reduction of NADP via FNR and cyclic electron transfer. The Thylakoid model parameters were fitted both to Chl fluorescence induction data (FI) and oxido-reductions of P700 (ΔA 810) measured from 20 μs up to 20 s in pea leaves. The two-wave kinetics of FI and ΔA 810 (O(JI)PSM and OABCDE) were described quantitatively, provided that the values of membrane electrochemical potential components ΔΨ(t), pHL(t)/pHS(t) are in physiologically relevant ranges. The time courses on the time scale from nanoseconds to tens of seconds of oxido-reduction changes of ET components as well as concentrations of proton/ions (K+, Cl-) were calculated. We assume a low constant FNR activity over this period. Charge movements across the thylakoid membrane by passive leakage and active ATPase transport and proton buffer reactions are simulated. The dynamics of charge fluxes during photosynthetic induction under low light (PFD 200 μmol photons m-2 s-1) were analyzed. The initial wave of P700 oxidation within 20 ms during independent operation of PSI and PSII was followed after 50 ms by PSI donor-side reduction from reduced PQ pool via Cyt b 6 f site. The Cyt b 6 f reactions contribute to the stabilization of fluxes in the time range 1 s < t < 10 s. The detailed analysis of Chl a fluorescence at the PSM stage (t > 10 s) would need the investigation of FNR activation effect in order to explain the transitions between cyclic and linear electron transport.

Influence of pH and ionic strength on electrostatic properties of ferredoxin, FNR, and hydrogenase and the rate constants of their interaction

Ferredoxin (Fd) protein transfers electrons from photosystem I (PSI) to ferredoxin:NADP⁺-reductase (FNR) in the photosynthetic electron transport chain, as well as other metabolic pathways. In some photosynthetic organisms including cyanobacteria and green unicellular algae under anaerobic conditions Fd transfers electrons not only to FNR but also to hydrogenase-an enzyme which catalyzes reduction of atomic hydrogen to H₂. One of the questions posed by this competitive relationship between proteins is which characteristics of thylakoid stroma media allow switching of the electron flow between the linear path PSI-Fd-FNR-NADP⁺ and the path PSI-Fd-hydrogenase-H₂. The study was conducted using direct multiparticle simulation approach. In this method protein molecules are considered as individual objects that experience Brownian motion and electrostatic interaction with the surrounding media and each other. Using the model we studied the effects of pH and ionic strength (I) upon complex formation between ferredoxin and FNR and ferredoxin and hydrogenase. We showed that the rate constant of Fd-FNR complex formation is constant in a wide range of physiologically significant pH values. Therefore it can be argued that regulation of FNR activity doesn't involve pH changes in stroma. On the other hand, in the model rate constant of Fd-hydrogenase interaction dramatically depends upon pH: in the range 7-9 it increases threefold. It may seem that because hydrogenase reduces protons it should be more active when pH is acidic. Apparently, regulation of hydrogenase's affinity to both her reaction partners (H⁺ and Fd) is carried out by changes in its electrostatic properties. In the dark, the protein is inactive and in the light it is activated and starts to interact with both Fd and H⁺. Therefore, we can conclude that in chloroplasts the rate of hydrogen production is regulated by pH through the changes in the affinity between hydrogenase and ferredoxin.

Modeling of the redox state dynamics in photosystem II of Chlorella pyrenoidosa Chick cells and leaves of spinach and Arabidopsis thaliana from single flash-induced fluorescence quantum yield changes on the 100 ns-10 s time scale

The time courses of the photosystem II (PSII) redox states were analyzed with a model scheme supposing a fraction of 11-25 % semiquinone (with reduced [Formula: see text]) RCs in the dark. Patterns of single flash-induced transient fluorescence yield (SFITFY) measured for leaves (spinach and Arabidopsis (A.) thaliana) and the thermophilic alga Chlorella (C.) pyrenoidosa Chick (Steffen et al. Biochemistry 44:3123-3132, 2005; Belyaeva et al. Photosynth Res 98:105-119, 2008, Plant Physiol Biochem 77:49-59, 2014) were fitted with the PSII model. The simulations show that at high-light conditions the flash generated triplet carotenoid (3)Car(t) population is the main NPQ regulator decaying in the time interval of 6-8 μs. So the SFITFY increase up to the maximum level [Formula: see text]/F 0 (at ~50 μs) depends mainly on the flash energy. Transient electron redistributions on the RC redox cofactors were displayed to explain the SFITFY measured by weak light pulses during the PSII relaxation by electron transfer (ET) steps and coupled proton transfer on both the donor and the acceptor side of the PSII. The contribution of non-radiative charge recombination was taken into account. Analytical expressions for the laser flash, the (3)Car(t) decay and the work of the water-oxidizing complex (WOC) were used to improve the modeled P680(+) reduction by YZ in the state S 1 of the WOC. All parameter values were compared between spinach, A. thaliana leaves and C. pyrenoidosa alga cells and at different laser flash energies. ET from [Formula: see text] slower in alga as compared to leaf samples was elucidated by the dynamics of [Formula: see text] fractions to fit SFITFY data. Low membrane energization after the 10 ns single turnover flash was modeled: the ∆Ψ(t) amplitude (20 mV) is found to be about 5-fold smaller than under the continuous light induction; the time-independent lumen pHL, stroma pHS are fitted close to dark estimates. Depending on the flash energy used at 1.4, 4, 100 % the pHS in stroma is fitted to 7.3, 7.4, and 7.7, respectively. The biggest ∆pH difference between stroma and lumen was found to be 1.2, thus pH- dependent NPQ was not considered.

Chlorophyll a fluorescence: beyond the limits of the Q(A) model

Chlorophyll a fluorescence is a non-invasive tool widely used in photosynthesis research. According to the dominant interpretation, based on the model proposed by Duysens and Sweers (1963, Special Issue of Plant and Cell Physiology, pp 353-372), the fluorescence changes reflect primarily changes in the redox state of Q(A), the primary quinone electron acceptor of photosystem II (PSII). While it is clearly successful in monitoring the photochemical activity of PSII, a number of important observations cannot be explained within the framework of this simple model. Alternative interpretations have been proposed but were not supported satisfactorily by experimental data. In this review we concentrate on the processes determining the fluorescence rise on a dark-to-light transition and critically analyze the experimental data and the existing models. Recent experiments have provided additional evidence for the involvement of a second process influencing the fluorescence rise once Q(A) is reduced. These observations are best explained by a light-induced conformational change, the focal point of our review. We also want to emphasize that-based on the presently available experimental findings-conclusions on α/ß-centers, PSII connectivity, and the assignment of FV/FM to the maximum PSII quantum yield may require critical re-evaluations. At the same time, it has to be emphasized that for a deeper understanding of the underlying physical mechanism(s) systematic studies on light-induced changes in the structure and reaction kinetics of the PSII reaction center are required.

A model of chlorophyll a fluorescence induction kinetics with explicit description of structural constraints of individual photosystem II units

Chlorophyll a fluorescence induction (FI) kinetics, in the microseconds to the second range, reflects the overall performance of the photosynthetic apparatus. In this paper, we have developed a novel FI model, using a rule-based kinetic Monte Carlo method, which incorporates not only structural and kinetic information on PSII, but also a simplified photosystem I. This model has allowed us to successfully simulate the FI under normal or different treatment conditions, i.e., with different levels of measuring light, under 3-(3',4'-dichlorophenyl)-1,1-dimethylurea treatment, under 2,5-dibromo-3-methyl-6-isopropyl-p-benzoquinone treatment, and under methyl viologen treatment. Further, using this model, we have systematically studied the mechanistic basis and factors influencing the FI kinetics. The results of our simulations suggest that (1) the J step is caused by the two-electron gate at the Q B site; (2) the I step is caused by the rate limitation of the plastoquinol re-oxidation in the plastoquinone pool. This new model provides a framework for exploring impacts of modifying not only kinetic but also structural parameters on the FI kinetics.

New direct dynamic models of protein interactions coupled to photosynthetic electron transport reactions

This review covers the methods of computer simulation of protein interactions taking part in photosynthetic electron transport reactions. A direct multiparticle simulation method that simulates reactions describing interactions of ensembles of molecules in the heterogeneous interior of a cell is developed. In the models, protein molecules move according to the laws of Brownian dynamics, mutually orient themselves in the electrical field, and form complexes in the 3D scene. The method allows us to visualize the processes of molecule interactions and to calculate the rate constants for protein complex formation reactions in the solution and in the photosynthetic membrane. Three-dimensional multiparticle computer models for simulating the complex formation kinetics for plastocyanin with photosystem I and cytochrome bf complex, and ferredoxin with photosystem I and ferredoxin:NADP+-reductase are considered. Effects of ionic strength are featured for wild type and mutant proteins. The computer multiparticle models describe nonmonotonic dependences of complex formation rates on the ionic strength as the result of long-range electrostatic interactions.