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

2019 ◽  
Keyword(s):  
Electron Transfer ◽  
Differential Equations ◽  
Rhodobacter Sphaeroides ◽  
Reaction Centers ◽  
System Of Differential Equations ◽  
Balance Equations ◽  
Exponential Functions ◽  
Structural Dynamic ◽  
Constant Coefficients ◽  
Kinetics Of

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.

scholarly journals Analysis of photoinduced reverse changes in bacterial reaction centers

2018 ◽  
Keyword(s):  
Electron Transfer ◽  
Rate Constants ◽  
Logarithmic Derivative ◽  
Reaction Centers ◽  
Main Reaction ◽  
Balance Equations ◽  
Electron Transfer Kinetics ◽  
Cyclic Electron Transfer ◽  
Experimental Kinetics ◽  
Kinetics Of

Background: The membrane protein-pigment complexes of photosynthetic isolated reaction centers (RC) Rhodobacter Sphaeroides are macromolecular systems for studying the physical mechanisms of electron and proton transport in biological structures, the role of molecular dynamics. The experimental kinetics of cyclic electron transfer in molecular complexes has a multiexponential character with negative values of decrements. For their description, a system of balance equations is used. Objective of the work is to determine the features of the kinetics of cyclic electron transfer in the RC using two models of electron transfer and the connection of such features with space-time motions in the RC. Materials and methods: Measurement of the absorption kinetics was performed at 865 nm using a two-channel diode spectrometer. The experimental kinetics of RC absorption (the main reaction of the system) was represented by the fitting method in the form of a sum of three exponential functions. In the first model with time-variable rate constants of the balance equations, the wavelet transform method of the logarithmic derivative of the electron transfer kinetics was used. In the second model, the equation of state and three differential equations with constant coefficients were used as the algebraic sum of the rate constants. To determine the values of the rate constants in the balance equation, an optimization problem was solved. The solution of the system of balance equations by the matrix method made it possible to determine the features of the kinetics of the population of substates of the RC. Results of calculations showed that the features of the wavelet spectrum of the logarithmic derivative of the electron transfer kinetics in the first model coincided with the features of the population kinetics of substates of the RC of the second RC model. These features were in the bands 1 s, 3 s, 60 s from the moment of switching on (off) the light and depend on the photoexcitation parameters. Conclusions: The features of the kinetics of the populations of substates in the RC both at the stage of illumination and at the relaxation stage are determined by changes in the structure of the RC in the form of effects of hidden parameters of the structural self-regulation of the RC (feedback through the RC structure).

Analysis of Kinetics of Electron Transfer in the Reaction Centers of Photosynthetic Bacteria Using the Rips—Jortner Model

2005 ◽  
Vol 405 (1-6) ◽  
pp. 461-464 ◽  
Author(s):  
A. I. Kotel'nikov ◽  
N. S. Goryachev ◽  
A. Yu. Rubtsov ◽  
B. L. Psikha ◽  
J. M. Ortega
Keyword(s):  
Electron Transfer ◽  
Photosynthetic Bacteria ◽  
Reaction Centers ◽  
Kinetics Of

A modified Lorenz system: Definition and solution

2020 ◽  
Vol 13 (08) ◽  
pp. 2050164
Author(s):  
Biljana Zlatanovska ◽  
Donc̆o Dimovski
Keyword(s):  
Differential Equations ◽  
Difference Equations ◽  
Lorenz System ◽  
Local Approximation ◽  
System Of Differential Equations ◽  
Lorentz System ◽  
Constant Coefficients ◽  
Linear Differential ◽  
The Lorenz System ◽  
Fifth Order

Based on the approximations of the Lorenz system of differential equations from the papers [B. Zlatanovska and D. Dimovski, Systems of difference equations approximating the Lorentz system of differential equations, Contributions Sec. Math. Tech. Sci. Manu. XXXIII 1–2 (2012) 75–96, B. Zlatanovska and D. Dimovski, Systems of difference equations as a model for the Lorentz system, in Proc. 5th Int. Scientific Conf. FMNS, Vol. I (Blagoevgrad, Bulgaria, 2013), pp. 102–107, B. Zlatanovska, Approximation for the solutions of Lorenz system with systems of differential equations, Bull. Math. 41(1) (2017) 51–61], we define a Modified Lorenz system, that is a local approximation of the Lorenz system. It is a system of three differential equations, the first two are the same as the first two of the Lorenz system, and the third one is a homogeneous linear differential equation of fifth order with constant coefficients. The solution of this system is based on the results from [D. Dimitrovski and M. Mijatovic, A New Approach to the Theory of Ordinary Differential Equations (Numerus, Skopje, 1995), pp. 23–33].

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