Multiscale and stochastic approaches play a crucial role in faithfully
capturing the dynamical features and making insightful predictions of
cellular reacting systems involving gene expression. A Genetic
Regulatory Networks (GRN), describing all the reacting channels and
species involved in gene expression, consists of a set of genes,
proteins, small molecules and their mutual regulatory
interactions. From the point of view of modeling, Genetic Regulatory
Networks, unlike metabolism networks, involve fewer
species and lower concentrations of molecules in a small volume within a
cell; therefore stochastic effects have a significant
impact on the system. Despite their accuracy, the standard stochastic
simulation algorithms are necessarily inefficient for most of the
realistic problems with a multiscale nature characterized by 1.) Rare
events arising from the metastability
of the system, 2.) Multiple time scales induced by widely disparate
reactions rates, and 3.) Multiple well separated concentration scales of
the reacting species. In this talk, I will discuss some recent progress
on using asymptotic techniques for probability theory, e.g. Random
Homogenization and Large Deviation Theory, to simplify the complex
networks and help to design efficient numerical schemes.