Bistable dynamics in a two-gene system with cross-regulation. A. Gene regulatory circuit diagram. Blunt arrows indicate mutual inhibition of genes X and Y. Dashed arrows indicate a basal synthesis (affected by the inhibition) and an independent first-order degradation of the factors. B. Two-dimensional XY phase plane representing the typical dynamics of the circuit. Every point (X, Y) represents a momentary state defined by the values of the pair X, Y. Red arrows are gradient vectors indicating the direction and extent that the system will move to within a unit time at each of the (X, Y) positions. Collectively, the vector field gives rise to a "potential landscape", visualized by the colored contour lines (numerical approximation). In this "epigenetic landscape", the stable states (attractors) are in the lowest points in the valleys: a (X>>Y) and b (Y>>X) (gray dots). C. Schematic representation of the epigenetic landscape as a section through a and b in which every red dot represents a cell. Experimentally, this bistability is manifested as a bimodal distribution in flow cytometry histograms in which the stable states a and b appear as peaks at the respective level of marker expression (e.g., Y).
Chang et al. BMC Cell Biology 2006 7:11 doi:10.1186/1471-2121-7-11