Cell population migration cycle and response to environmental pH in Bacillus subtilis

Microbial populations are ubiquitous, many of which form robust, multicellular structures called biofilms that protect cells from environmental damage. Understanding their migration cycles is crucial for controlling target microbial populations. Here we develop a multilevel mathematical model that captures the migration cycle of Bacillus subtilis cell populations and reproduces the periodic expansion of colonies into concentric circles. We construct an input/output model that regulates cell types in response to environmental conditions; based on this, we propose a theoretical model for the generation of cell population migration cycles. We then construct a multilevel system that links the cell-level state regulation model with tissue-level partial differential equations governing cell density, signal, and resource fields. Through this approach, we successfully simulate cyclically expanding colonies as well as their environmental pH dependence. The proposed models provide a robust basis for describing highly self-regulating multicellular systems and predicting broader biofilm-related phenomena.