Extinction and resurrection in gene networks.

When gene regulatory networks operate in regimes where the number of protein molecules is so small that the molecular species are on the verge of extinction, the death and resurrection of the species greatly modifies the attractor landscape. Deterministic models and the diffusion approximation to the master equation break down at the limits of protein populations in a way very analogous to the breakdown of geometrical optics that occurs at distances <1 wavelength of light from edges. Stable stochastic attractors arise from extinction and resurrection events that are not predicted by the deterministic description. With this view, we explore the attractors of the regular toggle switch and the exclusive switch, focusing on the effects of cooperative binding and the production of protein in bursts. Our arguments suggest that the stability of lysogeny in the lambda-phage may be influenced by such extinction phenomena.