A. M. Abaturova

Direct simulation of plastocyanin and cytochrome f interactions in solution

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.

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.

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.

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.

Brownian-dynamics simulations of protein–protein interactions in the photosynthetic electron transport chain

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 c6, and ferredoxin) with their reaction partners (cytochrome b6f complex, photosystem I, ferredoxin:NADP reductase, and hydrogenase) are considered.

Multiparticle computer simulation of protein interactions in the photosynthetic membrane

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.

The identification of intermediate states of the electron-transfer proteins plastocyanin and cytochrome f diffusional encounters

The Brownian dynamics method was used for qualitative analysis of the events that lead to the formation of a functionally active plastocyanin–cytochrome f complex. The intermediate states of this process were identified by density-based hierarchical clustering. Diffusive entrapment of plastocyanin by cytochrome f is the key point of the suggested putative scenario of protein–protein encounter. The motion of plastocyanin was characterized for different values of protein–protein electrostatic interaction energy.