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

Abstract

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.

Keywords: Electron transport; Fluorescence; Kinetic models; Microalgae; Multiparticle Brownian models; Photosynthesis; Photosynthetic membrane.

Fig. 1

Diagram of the catalytic cycle of the PS II. Each rectangle is the kinetic state of PSII, determined by the redox states of the electron carriers included in the PSII.$⟨\begin{array}{c}\mathit{Chl}\\ P680\end{array}⟩$—all chlorophyll of PSII, including pigments of the antenna and RC P680;$⟨\begin{array}{c}\mathit{Chl}\\ P680\end{array}⟩\begin{array}{c}\ast \end{array}$—singlet excited states of Chl *, delocalized on all pigments of the antenna and reaction center. Phe is the primary electron acceptor of pheophytin; Q_A and Q_B are the primary and secondary quinone acceptors. PQ—plastoquinone; PQH₂—plastoquinol; H_L⁺—protons in the lumen and H_S⁺—protons in the stroma of the thylakoid. Over the rectangles, the variables of the model (x_i, y_i, z_i, g_i, i = 1, …, 7) are denoted. States with shadows are the source of fluorescence. Dashed arrows show fast (less than 1 ms) cycle stages, bold—light stages. The numbers above the arrows correspond to the reaction numbers. Dotted arcs show irreversible reactions of non-radiative recombination of Phe⁻ with P680⁺ (42–45), Q_A⁻ with P680.⁺ (46–49) (re-drown from Belyaeva et al. 2019)

Fig. 2

Transition of Chl * to the ground state: emission of fluorescence (k_F); non-radiative dissipation of singlet-excited chlorophyll molecules by quenching caused by the cation, by the P680 radical and/or triplet states of carotenoids with rate constants kP680 ⁺ and k.³Car, respectively; non-radiative dissipation of excitation into heat (k_HD)

Fig. 3

Simulation of the experimental results of the fluorescence yield using the PSII model presented in Fig. 1. A laser flash (10 ns) induces changes in the yield of fluorescence) in whole leaves of the wild type of plants. The results of measurements are shown by symbols (circles) for different values of the laser flash energy: 7.5·10¹⁶ photon/(cm² impulse)—blue, 6.2·10¹⁵ photon(cm² impulse)—magenta, 3.0·10¹⁵ photon/(cm² impulse)—beige and 5.4·10¹⁴ photon/(cm²-pulse)—light-green. The results of the numerical fitting are represented by curves calculated for the values of the rate constants k_L-Max: 7.2·10⁹ s⁻¹—dark blue, 6.0·10⁸ s⁻¹—red, 2.9·10⁸ s⁻¹—brown, 5.2·10⁷ s⁻¹—green. The dashed lines (magenta) show the time course of the function that determines the rate constant kL (t) of the light reaction, calculated by the equation for the corresponding values of k_L-Max and normalized with a coefficient of 10⁻⁷. Low-intensity measurement light was used to record the value of FL before the beginning of the saturation flash (− 50 μs) and then in the time interval 100 ns–10 s to record the changes in the FL output curves, setting the light constant k_L-Min = 0.2 s.⁻¹ в in the PSII model (Belyaeva et al. 2011)

Fig. 4

The scheme of Thylakoid membrane involving light—induced regulatory factors. The diagram comprises the components of the electron transfer chain (ETC) in leaves or alga: the thylakoid compartments and charge fluxes induced by light. PSII, PSI—the photosystems II and I; PQ(PQH₂)—plastoquinone (quinole) pool; bf—Cyt b₆ f complex; mobile Fd—ferredoxin; Pc—plastocyanin and R-COO—buffer groups. The stromal phase components: NADP(NADPH); FNR—ferredoxin-NADP-oxidoreductase. ATP synthase CF₀-CF₁ complex is responsible for the synthesis of ATP from ADP and inorganic phosphate (P_i). Light—induced oxidation of water by PSII, or PQH₂ by Cyt b₆f, releases protons (H.⁺_L) into the lumen. Pink wavy arrow denotes the way of pH-dependent regulation of thermal dissipation of excitation (brown arrow) in PSII antenna via energy-dependent quenching (qE). Pink curve arrows indicate the regulation of FNR electron transport: low activity (thin dotted line) after dark-adaptation increases upon light—induction to operate with the maximal rate (thick line) (Belyaeva et al. 2019)

Fig. 5

Schemes of the catalytic cycles: cytochrome (Cyt) b₆f (a); photosystem I (PSI) (d); electron transfer chain components are interrelated by the linear electron flow (LEF) and cyclic electron flow (CEF) branches (b); and by coupled electron/proton transfer into lumenal and stromal sites (c). The reactions of NADPH consumption in stroma are shown by one green curved arrow in (b) scheme. The light-induced FNR activation is taken into account for the step ‘65’ reaction with the time-dependent rate constant k_FNR(t) (Belyaeva et al. 2019)

Fig. 6

Experimental induction curves of fluorescence (brown) and absorption in the A810 (green) band and model curves of the fluorescence (red) and redox transformations of P700 (violet) in the time range up to 30 s. The time axis is represented on a logarithmic scale (Belyaeva et al. 2019)

Fig. 7

A Chlorophyll fluorescence rise curve recorded in C. reinhardtii at the beginning of S depletion (t = 0.1 h) and result of its multiexponential analysis (A). Changes of the OJIP transients and their component composition during S deficiency (B). Curves are normalized to the maximum amplitude (OP); absolute values of minimum (O) and maximum (P) fluorescence levels are indicated. Height and color of each band refer to the magnitude and lifetime of the corresponding kinetic phase, respectively (Antal et al. 2019)

Fig. 8

Simulated fluorescence transients under different intensities of actinic light: 120, 1000, 2000, 6000 and 12,000 µmol photons m⁻² s.⁻¹ (curves 1, 2, 3, 4 and 5, respectively). Inset shows the corresponding light-induced redox transitions of P₆₈₀ (Antal et al. 2018)

Fig. 9

Scene in the model of multiparticle Brownian dynamics, a section of the photosynthetic membrane, on which the mobile Pc protein transfers an electron from cyt f, a subunit of the cytochrome complex, to the donor part of PSI. (Kovalenko et al. 2017)

Fig. 10

a1, b1: central structures of the first (a1) and second (b1) clusters of encounter complexes of plastocyanin and cytochrome f from higher plants with electrostatic attraction energy of more than 8 kT. a2, b2: distance between copper and iron atoms of plastocyanin and cytochrome f, obtained from molecular dynamics calculations with the central structure of the first (a2) and second (b2) clusters as initial conformations. a3, b3: structures of the first (a3) and second (b3) final complexes obtained from molecular dynamics calculations (Fedorov et al. 2019)

Fig. 11

Schematic representation of protein–protein complex formation for electron transfer proteins Pc and Cyt f. The proteins from higher plants are shown. The surfaces of the proteins are colored in accordance with their surface potential in the range from − 100 to 100 mV. Negatively charged areas are shown in red, positively charged—in blue (Fedorov et al. 2019)