  Genetic switch systems with mutual repression of two transcription factors
are studied using deterministic methods (rate equations) and stochastic methods
(the master equation and Monte Carlo simulations). These systems exhibit
bistability, namely two stable states such that spontaneous transitions between
them are rare. Induced transitions may take place as a result of an external
stimulus. We study several variants of the genetic switch and examine the
effects of cooperative binding, exclusive binding, protein-protein interactions
and degradation of bound repressors. We identify the range of parameters in
which bistability takes place, enabling the system to function as a switch.
Numerous studies have concluded that cooperative binding is a necessary
condition for the emergence of bistability in these systems. We show that a
suitable combination of network structure and stochastic effects gives rise to
bistability even without cooperative binding. The average time between
spontaneous transitions is evaluated as a function of the biological
parameters.
