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Sensitivity Analysis of Discrete Stochastic Systems

Rudiyanto Gunawan ^*, Yang Cao , Linda Petzold  and Francis J. Doyle, III ^*

^* Department of Chemical Engineering, and Department of Computer Science, University of California, Santa Barbara, California

Correspondence: Address reprint requests to Francis J. Doyle III, Tel.: 805-893-8133; Fax: 805-893-4731; E-mail: doyle{at}engineering.ucsb.edu.

Sensitivity analysis quantifies the dependence of system behavior on the parameters that affect the process dynamics. Classical sensitivity analysis, however, does not directly apply to discrete stochastic dynamical systems, which have recently gained popularity because of its relevance in the simulation of biological processes. In this work, sensitivity analysis for discrete stochastic processes is developed based on density function (distribution) sensitivity, using an analog of the classical sensitivity and the Fisher Information Matrix. There exist many circumstances, such as in systems with multistability, in which the stochastic effects become nontrivial and classical sensitivity analysis on the deterministic representation of a system cannot adequately capture the true system behavior. The proposed analysis is applied to a bistable chemical system—the Schlögl model, and to a synthetic genetic toggle-switch model. Comparisons between the stochastic and deterministic analyses show the significance of explicit consideration of the probabilistic nature in the sensitivity analysis for this class of processes.

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