Since the dawn of stochastic chemical reaction network theory over 50 years ago, there have been many general results about (positive) recurrence, especially in the case of mass-action kinetics. One less-explored area is that of mass-action models whose rate constants, rather than being static, are themselves stochastic. Such models have relevance in applications, since biomolecular systems rarely exist in isolation and their rates often depend on time-changing quantities. In this series of two talks, we will study the stability of such models under some linearity assumptions.

This second talk will present conditions for stability and instability which allow for feedback from the CRN to the environment. Specifically, we show that if the underlying model is linear, with "non-borderline" stability, then a certain class of environmental reactions do not disturb instability for any choice of rate constants. These permissible reactions include those where the environment can be viewed as enzymes acting via Michaelis–Menten kinetics, and more besides.