  Bistable biochemical switches are ubiquitous in gene regulatory networks and
signal transduction pathways. Their switching dynamics, however, are difficult
to study directly in experiments or conventional computer simulations, because
switching events are rapid, yet infrequent. We present a simulation technique
that makes it possible to predict the rate and mechanism of flipping of
biochemical switches. The method uses a series of interfaces in phase space
between the two stable steady states of the switch to generate transition
trajectories in a ratchet-like manner. We demonstrate its use by calculating
the spontaneous flipping rate of a symmetric model of a genetic switch
consisting of two mutually repressing genes. The rate constant can be obtained
orders of magnitude more efficiently than using brute-force simulations. For
this model switch, we show that the switching mechanism, and consequently the
switching rate, depends crucially on whether the binding of one regulatory
protein to the DNA excludes the binding of the other one. Our technique could
also be used to study rare events and non-equilibrium processes in soft
condensed matter systems.
