### Stochastic travelling waves in bistable biochemical system: Numerical and mathematical analysis

Lipniacki, T *(Polish Academy of Sciences)*

Thursday 30 August 2012, 11:30-12:30

Seminar Room 1, Newton Institute

#### Abstract

I will discuss stochastic transitions in a bistable biochemical system of trans-activating molecules on a hexagonal lattice. Kinetic Monte Carlo simulations demonstrated that the steady state of the system is controlled by the diffusion, and size of the reactor. In considered example, in small reactor the system remains inactive. In larger domain, however, the system activates spontaneously at some place of the reactor and then the activity wave propagates until whole domain becomes active. The expected time to
activation grows exponentially with the diffusion coefficient.

I will interpret these results by analytical considerations of a simpler bistable system, which evolution is equivalent to the one dimensional birth and death process.

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