Cell divisions as a mechanism for selection in stable steady states of multi-stationary gene circuits

We study the properties of attractors and their basins of attraction in gene circuits whose dynamics is accompanied by cell divisions (mitosis). The dynamical equations for such circuits are formulated as hybrid systems with a phase space of variable dimension. As an example, we consider a two-gene circuit which mimics cross-repressing gap genes in the segmentation system of the early Drosophila embryo. We show that the circuit exhibits multi-stationarity and that cell divisions in the circuit substantially reduce the number of steady states reachable by the system, playing, in this way, the specific dynamical role. We clarify two factors underlying the mechanism of selection in steady states and quantify their effects. Because multi-stationarity is a general property underlying such biological phenomena as differentiation and memory, we believe the dynamical role of cell divisions which we report on may be an important element in the correct description of these processes.