Modeling and simulation of cell populations interaction

Regenerative medicine and cell therapy provide great hopes for the use of adult and stem cells. The latter are far less present in tissue than the former and must be expanded using cell culture. Stem cells culture requires the conservation of their proliferation and self-renewal capabilities. Still, the complex interaction between cell populations, for example in primary cell cultures, are not well-known and may account for part of the variability of such cultures. In order to represent and understand the evolution of cultured stem cells, we present here a mathematical model of cell proliferation and differentiation. Based on the formalism of cellular automata, this model simulates the evolution of several cell classes (which may represent either different levels of differentiation or different cell types) in an environment modeling the growth medium. We model the cell cycle as on the one hand a quiescence phase during which a cell rests, and on the other hand a division phase during which the cell starts the division process. In order to represent cell–cell interaction, the transition probability between those phases depends on the local composition of the growth medium depending itself on neighboring cells. An interaction between cellular populations is represented by a quantitative parameter which has a direct impact on cellular proliferation. Differentiation results in a change of the cell class and depends on the biological model studied : it may result from an asymmetric division or be a consequence of the local composition of the growth medium. This mathematical model aims at a better understanding of the interactions between cell populations in a culture. By defining constraints on the potential or the type of the cells at the end of a culture, it will then be possible to find optimal experimental conditions for cell production.