Studying growth kinetics of microbial populations using information technology. Solving the Cauchy problem

Abstract

The possibilities of information technologies in the study of growth dynamics and development of microbial populations have been shown. In the R programming language in the Jupyter Notebooks environment, a direct kinetic problem has been solved. Kinetic regularities of growth of microbial populations under periodic cultivation have been considered within the framework of an approximation based on numerical integration of velocity equations. The one-step Runge-Kutta method of the fourth order of accuracy has been used as a method for solving a differential equation with initial conditions (Cauchy problem). Initial conditions of the problem were: the number of time steps n=10,000; initial substrate concentration S0=1; the initial concentration of microorganisms has been considered in four variants: M0=0.01, M0=0.05, M0=0.1, M0=0.2, which correspond to 1%, 5%, 10%, 20% of the inoculum density accordingly; affinity ration of the substrate to microorganisms Ks=0.5. The use of modern information technologies in the analysis of microbial growth patterns is mainly determined by the capabilities of personal computers, software environments and shells. The potential of modern software in the implementation of applied engineering and research problems in solving ordinary differential equations describing the development and course of the microbial process over time has been presented.