Modeling Environmental Disturbances with the Chemical Master Equation

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Enoch Yeung, James L. Beck, and Richard M. Murray
Submitted, 2013 Conference on Decision and Control (CDC)

In this paper we consider the problem of repre- senting a biological system and its environment using a stochas- tic modeling framework. We first introduce a decomposition of the global chemical reaction system into two systems: a system of interest and its environment. We then present and derive a decomposition of the chemical master equation to achieve a representation describing the dynamics of the system of inter- est, perturbed by an environmental disturbance. We use this decomposition to model examples of two types of environmental disturbances: the disturbance a system experiences through loading effects from limited resources and the disturbance a system experiences when perturbed by an antibiotic that modifies transcription or translation rates.