Mathematical modeling of critical phenomena in biomedical systems

Abstract

According to the differential-topological approach, the spaces in which the conditions of stable and unstable phase are fulfilled are determined on the phase diagram of the existence of the CRISPR-systems, and the fulfillment of the conditions of the existence of the second-order critical space is investigated. The methods of mathematical modeling of critical phenomena in multicomponent systems, which have the prospect of use in modern biomedical and gene technologies, are applied. The proposed method involves modeling the states of the CRISPR-systems by systems of equations and inequalities containing potential functions of the system state that depend on several variables. The purpose of the modeling is to determine the stability spaces, bifurcations and spaces of simultaneous coexistence of several phases of the studied system. In the investigated area of the phase diagram of the CRISPR-systems, the existence of a stable and an unstable phase was determined. The position of the spaces of the phase diagram in which the conditions for the existence of a stable and unstable phase, i.e. bifurcation space, are fulfilled are found. It was found that there are no spaces of the phase diagram in which the condition of simultaneous coexistence of two phases is fulfilled. From this, it is concluded that in the studied space of the phase diagram, the system does not tend to disintegrate into two coexisting phases. The simulation results can be used to analyze the stability of the CRISPR-systems under different conditions of synthesis and operation.