  We study a mechanism for reliable switching in biomolecular
signal-transduction cascades. Steady bistable states are created by system-size
cooperative effects in populations of proteins, in spite of the fact that the
phosphorylation-state transitions of any molecule, by means of which the switch
is implemented, are highly stochastic. The emergence of switching is a
nonequilibrium phase transition in an energetically driven, dissipative system
described by a master equation. We use operator and functional integral methods
from reaction-diffusion theory to solve for the phase structure, noise
spectrum, and escape trajectories and first-passage times of a class of minimal
models of switches, showing how all critical properties for switch behavior can
be computed within a unified framework.
