MATHEMATICAL AND COMPUTER MODELLING REGULATORIKA OF HIERARCHICAL MOLECULAR-GENETIC SYSTEMS

Abstract

The progress achieved in biology during the last century has led to development of mathematical and computer modelling of functioning regulatory mechanisms (regulatorika) in molecular-genetic processes in living systems. In this work we consider one of the possible methods for mathematical and computer mod- elling of molecular-genetic systems regulatorika. The corresponding equations (in the class of delay functional-differential equations) are developed, using the approaches by B.Goodwin, Bl. Sendov, M. Eigen, B.A. Ratner, and taking into account of tempo- rary relations, presence of multifunctional feedback and cooperative nature of processes in cell's regulatory loops. Results on the regulatorika for uniform molecular-genetic systems, as well as the problem of the origin and development of hierarchical molecular- genetic systems are considered. Results of using the considered method for analyzing cell's molecular-genetic systems in the presence of the alien genes (on the example of hepatic cell infections by hepatitis B virus) are given. 1 Introduction The analysis of main protein-ferments participating in the specific func- tioning of cells in a multicellular organism shows, that each cell contains different complex of protein molecules, though all cells have the same set of chromosomes and, consequently, identical genetic information (1, 2, 3). It happens because in eukaryotic cells there is mech- anism of hierarchical organizations of molecular-genetic system, regulating genes activity: which groups of genes at the moment must be active and which genes should be in the inactive condition. Existence of biochemical properties and processes, inherent all cells of the organism (syntheses of energy proteins, amino acid, to maintain and build membrane, etc) shows that there are universal groups of genes functioning in all cells regardless of specialization. Remaining part of genes consists of groups of general genes (its operation depends on activity conditions in universal groups of genes), containing information on general functions characteristic for many, but not all cells and groups of specific genes (its functioning depends on activity conditions of universal and general genes groups), keeping information on strictly specific functions of concrete cells (4). Under such approach, the whole cell genome of multicellular organism works as evolutionary established hierarchical system of universal, general and specific genes groups (Figure 1). Hierarchical organization of molecular-genetic systems is of the utmost importance in regulatorika of intracellular processes and cellular functions. Their account makes it possible to carry out studying mechanisms of origin, existence and development of living systems when quantitatively analyzing activity patterns of molecular-genetic systems. In this work we develop the mathematical modelling of genes activity (section 2), possible equations of molecular-genetic systems regulatorika (sections 3,4) and certain problems concerning the mathematical and computer modelling of hierarchical molecular-genetic systems (sections