  We study by mean-field analysis and stochastic simulations chemical models
for genetic toggle switches formed from pairs of genes that mutually repress
each other. In order to determine the stability of the genetic switches, we
make a connection with reactive flux theory and transition state theory. The
switch stability is characterised by a well defined lifetime $\tau$. We find
that $\tau$ grows exponentially with the mean number $\Nmean$ of transcription
factor molecules involved in the switching. In the regime accessible to direct
numerical simulations, the growth law is well characterised by
$\tau\sim\Nmean{}^{\alpha}\exp(b\Nmean)$, where $\alpha$ and $b$ are
parameters. The switch stability is decreased by phenomena that increase the
noise in gene expression, such as the production of multiple copies of a
protein from a single mRNA transcript (shot noise), and fluctuations in the
number of proteins produced per transcript. However, robustness against
biochemical noise can be drastically enhanced by arranging the transcription
factor binding domains on the DNA such that competing transcription factors
mutually exclude each other on the DNA. We also elucidate the origin of the
enhanced stability of the exclusive switch with respect to that of the general
switch: while the kinetic prefactor is roughly the same for both switches, the
`barrier' for flipping the switch is significantly higher for the exclusive
switch than for the general switch.
