Analysis of differentiation ratio regulation dynamics in a globally coupled cell population model based on its reduced models

The mathematical model of a cell population interacting through a common pool (external environment) is a representative model of spatial-independent cell differentiation. This model shows an interesting phenomenon: the ratio of cell differentiation (differentiation ratio) is restricted to a specific range. However, the number of variables increases as the number of cells increases, making the analysis difficult for large cell populations. Therefore, this study takes “symmetry” of the cell population model into account, introducing two different reduced models to decrease the number of variables. Through simulations and bifurcation analyses, several aspects of the differentiation ratio regulation dynamics in the original model are revealed.