Oberseminar Mathematische Modelle

Mathematical modeling and computer simulation have become indispensable components of research in microbial evolutionary dynamics. Bacteria being the most important types of microbiological communities live within biofilms, which provide a structured and protective environment for microbial growth, survival, and adaptation. Another common form of evolution of bacterial communities is presented by the bacterial culture grown in laboratory conditions using special nutrient substrates. Due to the importance of controlling bacterial biofilms, they have become the objects of interdisciplinary research such as mathematical biology and in silico studies. The current study is aimed at the development of hybrid mathematical models, computational algorithms and programming software to predict and control characteristics of cell-to-cell bacterial communication in microbial populations embedded within different lifestyles. The first direction deals with the mathematical model of communication dynamics in bacterial colonies grown on a nutrition medium. The hybrid approach is based on combining the deterministic models for bacterial nutrient-dependent biomass growth and bacterial quorum sensing. To visualize naturalistic patterns, the model is supplemented with a stochastic procedure for the evolutionary deformation of the bacterial population with colonization potential. The computational algorithm was implemented numerically using the Matlab programming. The behavior of key chemical substances characterizing the quorum sensing was examined during the dynamics of the growth of dendritic bacterial patterns on a nutrient medium. The second part is represented by the development of the advanced cellular automaton model for evolution in biofilm-forming bacterial populations. The designed algorithm computes the space-time distribution of biomass under limited nutrient conditions, taking into account the mechanism formalizing the process of bacterial cell-to-cell communication. The simulation system was developed using C# on the Unity platform. Based on realistic scenario modeling, quantitative dependencies of the geometrical complexity of the formed self-similar biofilm bacterial structures on the consumed nutrients and quorum sensing level were specified.