A pathwise derivative approach to the computation of parameter sensitivities in discrete stochastic chemical systems

Characterizing the sensitivity to infinitesimally small perturbations in parameters is a powerful tool for the analysis, modeling, and design of chemical reaction networks. Sensitivity analysis of networks modeled using stochastic chemical kinetics, in which a probabilistic description is used to characterize the inherent randomness of the system, is commonly performed using Monte Carlo methods. Monte Carlo methods require large numbers of stochastic simulations in order to generate accurate statistics, which is usually computationally demanding or in some cases altogether impractical due to the overwhelming computational cost. In this work, we address this problem by presenting the regularized pathwise derivative method for efficient sensitivity analysis. By considering a regularized sensitivity problem and using the random time change description for Markov processes, we are able to construct a sensitivity estimator based on pathwise differentiation (also known as infinitesimal perturbation analysis) that is valid for many problems in stochastic chemical kinetics. The theoretical justification for the method is discussed, and a numerical algorithm is provided to permit straightforward implementation of the method. We show using numerical examples that the new regularized pathwise derivative method (1) is able to accurately estimate the sensitivities for many realistic problems and path functionals, and (2) in many cases outperforms alternative sensitivity methods, including the Girsanov likelihood ratio estimator and common reaction path finite difference method. In fact, we observe that the variance reduction using the regularized pathwise derivative method can be as large as ten orders of magnitude in certain cases, permitting much more efficient sensitivity analysis than is possible using other methods.