Stochastic stability and its application to the analysis of gene regulatory networks

As gene regulatory network design and implementation becomes more common, understanding the stochastic stability properties of these networks is increasingly becoming more of a necessity. A study of such properties would uncover regimes of stable behavior under both cellular intrinsic biochemical noise, and extrinsic uncertainty resulting from fluctuating environments and noisy interconnections between individual networks. In this paper, we revise and specialize common notions of stochastic stability to study two prototypical models of gene regulatory networks that have extensively been used in the biological literature.