Computer method to analyze structural-dynamic properties of Rhodobacter sphaeroides reaction centers based on system of differential equations

Background: Reactions of the natural objects to external influences can be analyzed using balance equations. If such reactions have a multi-exponential character, they can be represented as a sum of exponent components. Such kind of reaction is due both to the influence of hidden parameters, and the influence of the reaction itself on the structure of the object. The problem is that it is often not possible to determine empirically the values of the constants of the velocities of the balance equation, their relation with the parameters of the exponential components of the reaction, the kinetics of the population of the substates of the object. Objectives: The aim of the work is to develop a method of detailed analysis of the reaction of the object to external influence, which allows to determine the kinetics of the population of possible substates of the object by constructing a system of differential equations with constant coefficients. Materials and methods: Isolated reaction centers (RC) of Rhodobacter sphaeroides bacteria, the structure of which is well known, were used as an object. Behavior of the RC under photo-excitation was analyzed by constructing a system of differential equations with constant coefficients. The experimental kinetics of the cyclic electron transfer of the RC was approximated by the sum of three exponential functions. The parameters of these functions were used to determine the balance rate constants solving an optimization problem by a gradient method. The task was to study the RC using the method of constructing the system of differential equations and the method of two expositions. Results: A computer procedure was developed to determine the values of the speed constants of four balance equations, to analyze the kinetics of the population of the bases of the RC using the parameters of three exponential functions of the kinetics of electron transfer. Experimental and calculated kinetics of the donor population after photoexcitation of the RC are in a good agreement. The results of the two methods are correlated. They show that in the process of photo-excitation the maxima of populations of RC states correspond to a range of 3–140 s after the turning on (turning off) the light. Conclusion: RC corresponds to the system of four electron-conformational states. The features of the kinetics of population of the bases of the RC characterize the spatial-temporal characteristics of the RC.