The Brownian dynamics method is used for qualitative analysis of events leading to formation of a functionally active plastocyanin-cytochrome f complex. Intermediate states of this process are identified by density-based hierarchical clustering. Diffusive entrapment of plastocyanin by cytochrome f is a key point of the suggested putative scenario of protein-protein approaching. Mobility of plastocyanin is characterized for different values of protein-protein electrostatic interaction energy.

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.

Protein-protein interactions are of central importance for virtually every process in living matter. Modeling the dynamics of protein association is crucial for understanding their functionality. This paper proposes novel simulation software ProKSim (Protein Kinetics Simulator) for modeling of protein interactions by means of the multi-particle Brownian Dynamics. Effect of long-range electrostatic interactions on the process of transient encounter complex formation is numerically estimated. Investigation of transient encounter complex formation was performed for three pairs of proteins: ferredoxin and ferredoxin:NADP+-redustase, plastocyanin and cytochrome f, barnase and barstar.

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.

A multiparticle computer model of plastocyanin-cytochrome f complex formation in the thylakoid lumen has been designed, which takes into account the electrostatic interactions of proteins and membrane. The Poisson-Boltzmann formalism was used to determine the electrostatic potentials of the electron carrier proteins and the thylakoid membrane at different ionic strengths. The membrane electrostatic field was shown to influence plastocyanin diffusion and interaction with cytochrome f. The rate constants for plastocyanin-cytochrome f complex formation were calculated as a function of ionic strength and membrane surface charge.

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.

Kinetics of complex formation between components of the photosynthetic electron transport chain - flavodoxin and membrane complex photosystem I has been studied using computer model based on methods of multiparticle simulation and Brownian dynamics. We simulated Brownian motion of several hundreds of flavodoxin molecules, taking into account electrostatic interactions and complex shape of the molecules. Our model could describe experimental nonmonotonic dependence of the association rate constant for flavodoxin and photosystem I. This lets us conclude that electrostatic interactions are sufficient to form such kind of nonmonotonic dependence.

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.

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.