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Abstract <p>Mathematical models and simulation of the growth kinetics of microorganisms under certain external conditions provide the basis for diagnostics, as well as for the control and prediction of chemical substances characterizing the state of systems of various natures. This paper studies an approach to develop and numerically specify the structural and dynamic characteristics of patterning during the surface cultivation of bacteria on nutrient media. The mathematical model is formalized as an initial-boundary problem for a system of reaction-diffusion equations that determine the concentrations of the bacterial biomass and nutrient substrate. For the model description of naturalistic patterns, the stochastic procedure is introduced to provide the evolutionary deformation of the bacterial population with colonization potential and the formation of colonies with different incubation periods. An algorithm for the numerical solution of a nonlinear differential problem is constructed using the Yanenko finite-difference scheme, supplemented by an iterative procedure. The technique for assessing the geometric characteristics of bacterial patterns is based on the calculation of the fractal dimension of the boundaries of cluster structures. The software implementation of the algorithms is performed using the Matlab software. The results of a series of computational experiments are presented to visualize the spatiotemporal distributions of the bacterial biomass and nutrient substrate with variation of the control parameters of the hybrid model. The bacterial pattern formation of a branching morphological type is specified depending on changes in the level of the initial nutrient concentration, diffusion parameter, and stochastic growth parameter. The simulation results indicate that an increase in the initial concentration of the nutrient leads to a geometric phase transition, i.e., the transformation of the structure from a dendrite, through an irregular structure with a floral pattern, to a homogeneous cluster with a fairly smooth boundary.</p>

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Hybrid Approach to Modeling and Evaluating the Structural Features for Patterns of Cultured Bacteria

  • 期刊论文

  • 发表日期：

    2025年4月25日

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  • I. A. Shevkun,
  • A. G. Maslovskaya

摘要

Abstract

Mathematical models and simulation of the growth kinetics of microorganisms under certain external conditions provide the basis for diagnostics, as well as for the control and prediction of chemical substances characterizing the state of systems of various natures. This paper studies an approach to develop and numerically specify the structural and dynamic characteristics of patterning during the surface cultivation of bacteria on nutrient media. The mathematical model is formalized as an initial-boundary problem for a system of reaction-diffusion equations that determine the concentrations of the bacterial biomass and nutrient substrate. For the model description of naturalistic patterns, the stochastic procedure is introduced to provide the evolutionary deformation of the bacterial population with colonization potential and the formation of colonies with different incubation periods. An algorithm for the numerical solution of a nonlinear differential problem is constructed using the Yanenko finite-difference scheme, supplemented by an iterative procedure. The technique for assessing the geometric characteristics of bacterial patterns is based on the calculation of the fractal dimension of the boundaries of cluster structures. The software implementation of the algorithms is performed using the Matlab software. The results of a series of computational experiments are presented to visualize the spatiotemporal distributions of the bacterial biomass and nutrient substrate with variation of the control parameters of the hybrid model. The bacterial pattern formation of a branching morphological type is specified depending on changes in the level of the initial nutrient concentration, diffusion parameter, and stochastic growth parameter. The simulation results indicate that an increase in the initial concentration of the nutrient leads to a geometric phase transition, i.e., the transformation of the structure from a dendrite, through an irregular structure with a floral pattern, to a homogeneous cluster with a fairly smooth boundary.