  The intrinsic stochasticity of gene expression can give rise to large
fluctuations and rare events that drive phenotypic variation in a population of
genetically identical cells. Characterizing the fluctuations that give rise to
such rare events motivates the analysis of large deviations in stochastic
models of gene expression. Recent developments in non-equilibrium statistical
mechanics have led to a framework for analyzing Markovian processes conditioned
on rare events and for representing such processes by conditioning-free driven
Markovian processes. We use this framework, in combination with approaches
based on queueing theory, to analyze a general class of stochastic models of
gene expression. Modeling gene expression as a Batch Markovian Arrival Process
(BMAP), we derive exact analytical results quantifying large deviations of
time-integrated random variables such as promoter activity fluctuations. We
find that the conditioning-free driven process can also be represented by a
BMAP that has the same form as the original process, but with renormalized
parameters. The results obtained can be used to quantify the likelihood of
large deviations, to characterize system fluctuations conditional on rare
events and to identify combinations of model parameters that can give rise to
dynamical phase transitions in system dynamics.
