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The key to a robust life system is to ensure that each cell population ismaintained in an appropriate state. In this work, a mathematical model was usedto investigate the control of the switching between the migrating andnon-migrating states of the Bacillus subtilis cell population. In this case,the motile cells and matrix producers were the predominant cell types in themigrating cell population and non-migrating state, respectively, and could besuitably controlled according to the environmental conditions and cell densityinformation. A minimal smooth model consisting of four ordinary differentialequations was used as the mathematical model to control the B. subtilis celltypes. Furthermore, the necessary and sufficient conditions for the hysteresis,which pertains to the change in the pheromone concentration, were clarified. Ingeneral, the hysteretic control of the cell state enables stable switchingbetween the migrating and growth states of the B. subtilis cell population,thereby facilitating the biofilm life cycle. The results of correspondingculture experiments were examined, and the obtained corollaries were used todevelop a model to input environmental conditions, especially, the external pH.On this basis, the environmental conditions were incorporated in a simulationmodel for the cell type control. In combination with a mathematical model ofthe cell population dynamics, a prediction model for colony growth involvingmultiple cell states, including concentric circular colonies of B. subtilis,could be established.

Necessary and sufficient condition for hysteresis in the mathematical model of the cell type regulation of Bacillus subtilis