Mathematical modeling of biochemical processes rates in biological systems.

Abstract

Formulation of the scientific problem. The processes that take place in living cells consist of a large number of reactions catalyzed by various enzymes [1]-[3]. For mathematical modeling of these biochemical processes in biological systems, it is necessary to construct systems of a large number of nonlinear differential equations with the same large number of variables [4]-[6]. Even mathematical modeling of individual chains of biochemical processes that consist of a large number of enzymatic reactions is quite complex. Research analysis. To solve these problems, it is necessary to make simplifications taking into account some features of these reactions. In the chain of reactions that take place in a living cell, the slowest reaction is determining. The slowest reaction is determined by the lowest value of the velocities. In the chain of enzymatic reactions, the reaction with the lowest maximum rate will be decisive (see the example of a chain of two consecutive enzymatic reactions given below). When diffusing through several partitions, the determining link will be the partition with the lowest diffusion coefficient. By the reaction rate, we mean the maximum rate of that reaction. Presentation of the main material and the justification of the obtained research results. To find the determining link in the chain of biochemical reactions, it is necessary to find out how the rate of the whole process, i.e. the rate of production of the last link, depends on the rates of individual reactions. Obviously, when changing the maximum rates, any changes in the fast links will not affect the rate of the whole process. The rate of the whole process is affected only by the slowest link. When the rates of individual reactions in the chain of biochemical reactions differ by orders of magnitude, i.e. by 10; 100 or more times, all fast reactions have time to reach equilibrium during the slowest reaction. Since enzymatic reactions have the properties of low inversion and saturation, even when the rates of individual reactions differ little, the rate of the whole process depends only on the rate of the slowest link. Therefore, changes in other faster reactions have almost no effect on the overall rate. Let us prove this using the example of a chain of two consecutive enzymatic reactions: