Mechanisms of the complex formation between plastocyanin and cytochrome f in higher plants (Spinacia oleracea and Brassica rapa), green microalgae Chlamydomonas reinhardtii and two species of cyanobacteria (Phormidium laminosum and Nostoc sp.) were investigated using combined Brownian and molecular dynamics simulations and hierarchical cluster analysis. In higher plants and green algae, electrostatic interactions force plastocyanin molecule close to the heme of cytochrome f. In the subsequent rotation of plastocyanin molecule around the point of electrostatic contact in the vicinity of cytochrome f, copper (Cu) atom approaches cytochrome heme forming a stable configuration where cytochrome f molecule behaves as a rather rigid body without conformational changes. In Nostoc plastocyanin molecule approaches cytochrome f in a different orientation (head‐on) where the stabilization of the plastocyanin–cytochrome f complex is accompanied by the conformational changes of the G188E189D190 loop that stabilizes the whole complex. In cyanobacterium P. laminosum, electrostatic preorientation of the approaching molecules was not detected, thus indicating that random motions rather than long‐range electrostatic interactions are responsible for the proper mutual orientation. We demonstrated that despite the structural similarity of the investigated electron transport proteins in different photosynthetic organisms, the complexity of molecular mechanisms of the complex formation increases in the following sequence: non‐heterocystous cyanobacteria – heterocystous cyanobacteria – green algae – flowering plants.

The application of Brownian dynamics for simulation of transient protein–protein interactions is reviewed. The review focuses on the theoretical basics of the Brownian-dynamics method, its particular implementations, and the advantages and drawbacks of this method. The outlook for future development of Brownian dynamics-based simulation techniques is discussed. Special attention is given to analysis of Brownian dynamics trajectories. The second part of the review is dedicated to the role of Brownian-dynamics simulations in studying photosynthetic electron transport. Interactions of mobile electron carriers (plastocyanin, cytochrome c 6, and ferredoxin) with their reaction partners (cytochrome b 6 f complex, photosystem I, ferredoxin:NADP reductase, and hydrogenase) are considered.

The paper is devoted to the method of computer simulation of protein interactions taking part in photosynthetic electron transport reactions. Using this method we have studied kinetic characteristics of protein-protein complex formation for four pairs of proteins involved in photosynthesis at a variety of ionic strength values. Computer simulations describe non-monotonic dependences of complex formation rates on the ionic strength as the result of long-range electrostatic interactions. Calculations confirm that the decrease in the association second order rate constant at low values of the ionic strength is caused by the protein pairs spending more time in "wrong" orientations which do not satisfy the docking conditions and so do not form the final complex capable of the electron transfer.

The basic principles of the design of direct multiparticle models and the results of multiparticle computer simulation of electron transfer by mobile protein carriers in the photosynthetic membrane of a chloroplast thylakoid are presented. The reactions of complex formation of the plastocyanin with cytochrome f and the pigment-protein complex of photosystem I, as well as of ferredoxin with FNR and photosystem I are considered. The regulatory role of diffusion and electrostatic interactions as well as the effect of the shape of the reaction volume and ionic strength on the rate of electron transport are discussed.

Methods for estimating the input signal of a measuring device are considered. Information about the device is contained in the measurement results of a set of known test signals and the measurements were obtained in natural or in computational experiments. A method is proposed for the approximation of the measurement model by means of a piecewise linear model that is consistent with the results of measurements and the method of evaluation of the input signal and its accuracy. An example is given of the solution of a problem of the interpretation of measurements based on the approximation of a model of the photosynthetic system, in which the measured parameters are the values of saturation ΔpH and the rate of ATP synthesis and the estimated parameters are the concentration of photosystem-2 and light intensity.

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.

Plastocyanin diffusion in the thylakoid lumen and its binding to cytochrome f (a subunit of the membrane b 6 f 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.

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. DOI: 10.1134/S0006350907050053

The diffusion of the protein plastocyanine and complex formation between plastocyanine and cytochrome f (a subunit of a cytochrome b6/f complex) in the chloroplast thylakoid lumen has been studied. A 3D computer simulation model of diffusion and binding of plastocyanine and cytochrome f has been constructed, which considers their electrostatic interaction. Based on the experimental data, the parameters of the model for complex formation between plastocyanine and cytochrome f in solution have been estimated. The dependence of the rate of plastocyanine-cytochrome f reaction on the size of the luminal space has been studied. It was shown that the contraction of the luminal space leads to a decrease in the reaction rate, which is in agreement with the experimental data on the inhibition of the reaction under hyperosmotic stress.

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.

Most biological functions, including photosynthetic activity, are mediated by protein interactions. The proteins plastocyanin and cytochrome f are reaction partners in a photosynthetic electron transport chain. We designed a 3D computer simulation model of diffusion and interaction of spinach plastocyanin and turnip cytochrome f in solution. It is the first step in simulating the electron transfer from cytochrome f to photosystem 1 in the lumen of thylakoid. The model is multiparticle and it can describe the interaction of several hundreds of proteins. In our model the interacting proteins are represented as rigid bodies with spatial fixed charges. Translational and rotational motion of proteins is the result of the effect of stochastic Brownian force and electrostatic force. The Poisson-Boltzmann formalism is used to determine the electrostatic potential field generated around the proteins. Using this model we studied the kinetic characteristics of plastocyanin-cytochrome f complex formation for plastocyanin mutants at pH 7 and a variety of ionic strength values.