Effects of system size on population behavior

Abstract

There are many factors to influence the population behavior of cells. Except for the ways of cellular communication and the cellular environment, Which have been considered in the previous studies, the number of cells (or system size) that has been little considered before is also an important factor. This article investigates effects of system size on clustering behavior in a synthetic multicellular system, where individual oscillators are an integration of repressilator and hysteresis-based oscillators and are coupled through a quorum-sensing mechanism. By bifurcation analysis and numerical simulation, we find that increasing the cell number not only can change the size of the stability interval of steady state clusters and induce new clustering behaviors, but also benefits the enlargement of the attraction basin of steady state clusters, implying that cell differentiation may be closely related to the system size. In addition, such an increase can greatly extend the kinds and coexisting modes of steady state and oscillatory clusters, which would provide a good basis for the adaptability of organisms to the environment. Our results have extended the connotation of dynamics of coupled systems and also may be the foundation for understanding multicellular phenomena.