  A general class of stochastic gene expression models with self regulation is
considered. One or more genes randomly switch between regulatory states, each
having a different mRNA transcription rate. The gene or genes are self
regulating when the proteins they produce affect the rate of switching between
regulatory states. Under weak noise conditions, the deterministic forces are
much stronger than fluctuations from gene switching and protein synthesis.
Metastable transitions, such as bistable switching, can occur under weak noise
conditions, causing dramatic shifts in the expression of a gene. A general tool
used to describe metastability is the quasi stationary analysis (QSA). A large
deviation principle is derived so that the QSA can explicitly account for
random gene switching without using an adiabatic limit or diffusion
approximation, which are unreliable and inaccurate for metastable events.This
allows the existing asymptotic and numerical methods that have been developed
for continuous Markov processes to be used to analyze the full model.
