Quorum sensing model for nutrient-dependent evolution of cultured bacteria: theoretical framework and in silico study

The evolutionary dynamics of cell-to-cell communication in bacterial populations can be examined using mathematical modeling and computer simulations. In the present study, the model of bacterial quorum sensing in colonies cultivated on nutrient media is explored from theoretical and computational points of view. The proposed approach is based on combining the deterministic model for bacterial nutrient-dependent biomass growth and the reaction-diffusion model describing spatial-temporal characteristics of bacterial quorum sensing. The unique solvability of the initial-boundary value problem for the mathematical model of bacterial quorum sensing is proved. The existence of a stationary state is proven and the conditions for its stability are presented. The theoretical results are based on the derivation of new a priori estimates for the solution of the system of semilinear parabolic and elliptic equations. The nonlinear differential problem is solved numerically and the software implementation is executed in combination with the procedure of fractal dimension measure for bacterial pattern boundaries. A series of computational experiments is conducted to analyze the behavior of key chemical substances associated with quorum sensing attributed to Pseudomonas bacteria during the formation of dendrites as well as floral patterns in nutrient media.