The evolutionary dynamics of cell-to-cell communication in bacterial populations (living in biofilms or growing in nutrient media) can be examined using mathematical modelling and computer simulations. A significant trend in recent decades has been the development of hybrid models for describing complex, difficult to formalize microbial systems to predict and control their states. The current project aims at the more in-depth development of hybrid approaches for in silico studies of the cell-to-cell bacterial communication processes in microbial populations embedded within different lifestyles.

The first mathematical model is proposed to describe the pattern formation of bacteria grown on a nutrition medium and the corresponding bacterial communication characteristics of the microbial system. The conceptualization includes the deterministic model of bacterial quorum sensing, and the Allen-Cahn-based model of bacterial colony evolution combined with the model of changes in biomass-dependent nutrient concentration. Various computation experiments were performed to examine different scenarios of the spatio-temporal dynamics of key substances of the biosystem, taking into account the Allee effect. In the second part, we develop the hybrid cellular automation-based model of biofilm evolution with the mechanism of cell-to-cell bacterial communication. We proposed the simulation algorithm for biofilm formation given the mechanism of bacterial cell-to-cell communication. The results of the discrete-dynamic simulations indicate various spatial biofilm structures formed by variations in nutritional regimes, quorum levels, and mechanisms of inoculation processes.