G. Yu. Riznichenko

Modeling Chlorophyll a Fluorescence Transient: Relation to Photosynthesis

To honor Academician Alexander Abramovitch Krasnovsky, we present here an educational review on the relation of chlorophyll a fluorescence transient to various processes in photosynthesis. The initial event in oxygenic photosynthesis is light absorption by chlorophylls (Chls), carotenoids, and, in some cases, phycobilins; these pigments form the antenna. Most of the energy is transferred to reaction centers where it is used for charge separation. The small part of energy that is not used in photochemistry is dissipated as heat or re-emitted as fluorescence. When a photosynthetic sample is transferred from dark to light, Chl a fluorescence (ChlF) intensity shows characteristic changes in time called fluorescence transient, the OJIPSMT transient, where O (the origin) is for the first measured minimum fluorescence level; J and I for intermediate inflections; P for peak; S for semi-steady state level; M for maximum; and T for terminal steady state level. This transient is a real signature of photosynthesis, since diverse events can be related to it, such as: changes in redox states of components of the linear electron transport flow, involvement of alternative electron routes, the build-up of a transmembrane pH gradient and membrane potential, activation of different nonphotochemical quenching processes, activation of the Calvin-Benson cycle, and other processes. In this review, we present our views on how different segments of the OJIPSMT transient are influenced by various photosynthetic processes, and discuss a number of studies involving mathematical modeling and simulation of the ChlF transient. A special emphasis is given to the slower PSMT phase, for which many studies have been recently published, but they are less known than on the faster OJIP phase.

Application of a Photosystem II Model for Analysis of Fluorescence Induction Curves in the 100 ns to 10 s Time Domain after Excitation with a Saturating Light Pulse

A mathematical model of photosystem II (PSII) events was used to analyze chlorophyll fluorescence transients in the time domain from 100 ns to 10 s after excitation with a saturating 10-ns flash, applied as a part of specialized illumination protocol, using preparations of a thermophilic strain of the unicellular green alga, Chlorella pyrenoidosa Chick (using both intact and diuron-treated cells). Analysis of simulation results has proven that particular attention should be given to flash-induced recombination processes, including nonradiative recombination in PSII, while subsequent charge transfer along the electron transport chain of thylakoid membrane can be adequately described by a single reaction of quinone reoxidation. The PSII model was extended by taking inhibition by diuron of the electron transport in the acceptor side of PSII into account, which allowed simulation of fluorescence induction curves observed in the presence of this inhibitor. The model parameters were determined (stromal pH, rate constants of nonradiative recombination, and the initial reduction state of the quinone pool) which provided adequate simulation of experimentally observed ratios of the maximal and initial fluorescence levels (Fm/F0).

PS II model based analysis of transient fluorescence yield measured on whole leaves of Arabidopsis thaliana after excitation with light flashes of different energies

Our recently presented PS II model (Belyaeva et al., 2008) was improved in order to permit a consistent simulation of Single Flash Induced Transient Fluorescence Yield (SFITFY) traces that were earlier measured by Steffen et al. (2005) on whole leaves of Arabidopsis (A.) thaliana at four different energies of the actinic flash. As the essential modification, the shape of the actinic flash was explicitly taken into account assuming that an exponentially decaying rate simulates the time dependent excitation of PS II by the 10 ns actinic flash. The maximum amplitude of this excitation exceeds that of the measuring light by 9 orders of magnitude. A very good fit of the SFITFY data was achieved in the time domain from 100 ns to 10s for all actinic flash energies (the maximum energy of 7.5 × 10¹⁶ photons/(cm²flash) is set to 100%, the relative energies of weaker actinic flashes were of ∼8%, 4%, ∼1%). Our model allows the calculation and visualization of the transient PS II redox state populations ranging from the dark adapted state, via excitation energy and electron transfer steps induced by pulse excitation, followed by final relaxation into the stationary state eventually attained under the measuring light. It turned out that the rate constants of electron transfer steps are invariant to intensity of the actinic laser flash. In marked contrast, an increase of the actinic flash energy by more than two orders of magnitude from 5.4×10¹⁴ photons/(cm²flash) to 7.5×10¹⁶ photons/(cm²flash), leads to an increase of the extent of fluorescence quenching due to carotenoid triplet (³Car) formation by a factor of 14 and of the recombination reaction between reduced primary pheophytin (Phe(-)) and P680(+) by a factor of 3 while the heat dissipation in the antenna complex remains virtually constant. The modified PS II model offers new opportunities to compare electron transfer and dissipative parameters for different species (e.g. for the green algae and the higher plant) under varying illumination conditions.

Study of the effect of reducing conditions on the initial chlorophyll fluorescence rise in the green microalgae Chlamydomonas reinhardtii

Incubation of Chlamydomonas reinhardtii cells under nutrient deficiency results in the faster initial rise in the light-induced chlorophyll fluorescence kinetic curve. We showed that short-term anaerobic incubation of algal cells altered initial fluorescence in a way similar to nutrient starvation, suggesting an important role of the plastoquinones redox state in the observed effect. Bi-component analysis of highly resolved initial fluorescence rise kinetics in sulfur- or oxygen-depleted C. reinhardtii cells suggested that one of the mechanisms underlying the observed phenomenon involves primary closure (photochemical inactivation via Qa reduction) of β-type PSII as compared to α-PSII. Moreover, results of modeling of the fluorescence curve brought us to the conclusion that accumulation of closed centers in α-PSII supercomplexes may also cause a faster initial fluorescence rise. The observed correlations between nutrient supply rate and initial fluorescence rise pattern in green algae can serve to characterize culture nutritional status in vivo.

Mathematical and computer modeling of primary photosynthetic processes

We review the recent research on kinetic and direct multiparticle modeling of the processes in the photosynthetic membrane conducted at the Chair of Biophysics of the Biological Faculty, Moscow State University. The models take into account the modern experimental data on the heterogeneous structure and the kinetic characteristics of the system. The generalized kinetic model describes the processes in multisubunit complexes (photosystems I and II, the cytochrome complex), the coupled transmembrane ion fluxes and generation of the electrical and electrochemical potentials. Identification of the model parameters allows estimation of the rate constants for reactions that cannot be examined experimentally. Multiparticle models provide a vivid picture of the interaction between the electron transport chain components in the thylakoid lumen and stroma, and explicitly represent Brownian diffusion and electrostatic interactions between electron carriers. Combination of different description methods (differential equations and the Brownian dynamics formalism) makes it possible to model, in the complicated 3D environment of the plant cell, the processes that in the aggregate ensure the high efficacy of energy transduction in photosynthesis.

Computer Simulation of Plastocyanin-Cytochrome f Complex Formation in the Thylakoid Lumen

Plastocyanin diffusion in the thylakoid lumen and its binding to cytochrome f (a subunit of the membrane b6f complex) were studied with a direct multiparticle simulation model that could also take account of their electrostatic interaction. Experimental data were used to estimate the model parameters for plastocyanin-cytochrome f complexing in solution. The model was then employed to assess the dependence of the association rate constant on the dimensions of the lumen. Highest rates were obtained at a lumen span of 8–10 nm; narrowing of the lumen below 7 nm resulted in drastic deceleration of complexing. This corresponded to the experimentally observed effect of hyperosmotic stress on the interaction between plastocyanin and cytochrome f in thylakoids.

Direct computer simulation of ferredoxin and FNR complex formation in solution.

Ferredoxin reduced by Photosystem I in light serves as an electron donor for the reduction of NADP(+) to NADPH, and this reaction is catalyzed by enzyme ferredoxin:NADP(+)-reductase (FNR). Kinetics and mechanisms of this reaction have been extensively studied experimentally by site-specific mutagenesis, laser flash photolysis and stopped-flow methods. We have applied a method of multiparticle computer simulation to study the effects of electrostatic interactions upon the reaction rate of Fd-FNR complex formation. Using the model we calculated rate constants of Fd-FNR complex formation for the wild-type proteins and some mutant forms of FNR at different values of ionic strength. Simulation revealed that electrostatic interactions play an important role in Fd-FNR complex formation and define its specificity.

A model of photosystem II for the analysis of fast fluorescence rise in plant leaves

The polyphasic patterns of fluorescence induction rise in pea leaves in vivo and after the treatment with ionophores have been studied using a Plant Efficiency Analyzer. To analyze in detail photosystem II (PS II) electron transfer processes, an extended PS II model was applied, which included the sums of exponential functions to specify explicitly the light-driven formation of the transmembrane electric potential (ΔΨ(t)) as well as pH in the lumen (pHL(t)) and stroma (pHS(t)). PS II model parameters and numerical coefficients in ΔΨ(t), pHL(t), and pHS(t) were evaluated to fit fluorescence induction data for different experimental conditions: leaf in vivo or after ionophore treatment at low or high light intensity. The model imitated changes in the pattern of fluorescence induction rise due to the elimination of transmembrane potential in the presence of ionophores, when ΔΨ = 0 and pHL(t), pHS(t) changed to small extent relative to control values in vivo, with maximum ΔΨ(t) ∼ 90 mV and ΔΨ(t) ∼ 40 mV for the stationary state at ΔpH ≅ 1.8. As the light intensity was increased from 300 to 1200 μmol m−2 s−1, the heat dissipation rate constants increased threefold for nonradiative recombination of P680+Phe− and by ∼30% for P680+QA−. The parameters ΔΨ, pHS and pHL were analyzed as factors of PS II redox state populations and fluorescence yield. The kinetic mechanism of fluorescence quenching is discussed, which is related with light-induced lumen acidification, when +QA− and P680+ recombination probability increases to regulate the QA reduction.

A novel approach to computer simulation of protein-protein complex formation.

215 The majority of biochemical processes are associated with the functioning of protein molecules and their complexes in the reactions of enzymatic catalysis and cell signaling. Predicting the structure of protein complexes by their simulation is a complex problem that remains largely unsolved. The factors that play the key role in complex formation are as follows: the rate of protein diffusion to the docking site; long-range electrostatic interactions between protein surfaces, geometric and chemical complementarity of binding areas; molecular mobility at the protein–protein interphase, hydrogen bonds, Van der Waals interactions, hydrophobic interactions, and salt bridges. It is known that different factors play different roles at different stages of complex formation [1]. Currently, there is no universal method for simulating protein complex formation that would make it possible to take into account all these factors and accurately predict the structure of protein complex [1, 2]. Molecular diffusion and long-range electrostatic interactions as well as molecule geometry play the decisive role in precomplex formation. The electrostatic interactions significantly accelerate the process of precomplex formation and thereby make it much more effective. If the geometrical correspondence of binding areas is established at the precomplex stage, this ensures the optimal relative position of two molecules prior to subsequent final complex formation. The hydrophobic interaction, hydrogen bonds, and molecular mobility, in turn, play the key role in the conversion of the precompex into the final complex [1]. In this work, we developed a new method for determination of binding areas in proteins and precomplex structure with allowance for the Brownian diffusion and electrostatic interactions of proteins that occur when proteins approach one another. This method significantly simplifies subsequent precise simulation and prediction of the final complex structure. The Brownian dynamics method, which can be used for predicting the structure of protein complexes, considers the interaction of only two molecules in solution [3–5]. A characteristic feature and novelty of our method, as is shown below, is the possibility to use it for studying interaction of several protein molecules simultaneously. This makes it possible to simulate the formation of a large number of complexes, which takes place in solution or cell compartments and to monitor the real-time kinetics of this process. In our method, the process of protein complex formation is conditionally divided into several stages: (1) Brownian diffusion of proteins to the docking site, (2) their approach due to electrostatic attraction forces between molecules, relative spatial position of molecules, and precomplex formation; and (3) final complex formation. As is shown below, relative position of proteins in precomplexes, predicted on the basis of the computer model suggested, in most cases corresponds to their real orientation in final complexes. Method description. The proposed approach is based on direct computer simulation of diffusion and complex formation between mobile electron-transport proteins [6–8]. Simulation is performed in a virtual 3D cubical reaction volume containing randomly distributed protein molecules. Movement is described by the Langevin equation, which describes changes of each coordinate in time caused by random and outer forces:

Miltiparticle computer simulation of photosynthetic electron transport in the thylakoid membrane

Further developing the method for direct multiparticle modeling of electron transport in the thylakoid membrane, here we examine the influence of the shape of the reaction volume on the kinetics of the interaction of the mobile carrier with the membrane complex. Applied to cyclic electron transport around photosystem I, with account of the distribution of complexes in the membrane and restricted diffusion of the reactants, the model demonstrates that the biphasic character of the dark reduction of P700+ is quite naturally explained by the spatial heterogeneity of the system.