Conversion of a stable fixed point into a transient peak by stochastic fluctuation in a gene regulatory network

초록

The deterministic rate equation has been considered as an approximate description of the dynamics of the gene regulatory network, derived in the limit of vanishing stochastic fluctuations. When stochastic fluctuations are introduced, the stable fixed points of the deterministic equation usually turn into local maxima of the stationary distribution. Here, I consider a simple genetic regulatory network with a positive feedback and a cooperative binding, where the stationary distribution does not have a local minimum at a stable fixed point. I show that a transient peak appears at the stable fixed point instead, whose life-time grows exponentially as the stochastic fluctuation decreases. The result shows that the order of the limits is important for retrieving the deterministic dynamics.

키워드