  Stochasticity in gene expression can result in fluctuations in gene product
levels. Recent experiments indicated that feedback regulation plays an
important role in controlling the noise in gene expression. A quantitative
understanding of the feedback effect on gene expression requires analysis of
the corresponding stochastic model. However, for stochastic models of gene
expression with general regulation functions, exact analytical results for gene
product distributions have not been given so far. Here, we propose a technique
to solve a generalized ON-OFF model of stochastic gene expression with
arbitrary (positive or negative, linear or nonlinear) feedbacks including
posttranscriptional or posttranslational regulation. The obtained results,
which generalize results obtained previously, provide new insights into the
role of feedback in regulating gene expression. The proposed analytical
framework can easily be extended to analysis of more complex models of
stochastic gene expression.
