Efficient computation of parameter sensitivities of discrete stochasticchemical reaction networks

摘要

Parametric sensitivity of biochemical networks is an indispensable tool for studying systemrobustness properties, estimating network parameters, and identifying targets for drug therapy. Fordiscrete stochastic representations of biochemical networks where Monte Carlo methods arecommonly used, sensitivity analysis can be particularly challenging, as accurate finite differencecomputations of sensitivity require a large number of simulations for both nominal and perturbedvalues of the parameters. In this paper we introduce the common random number (CRN) method inconjunction with Gillespie's stochastic simulation algorithm, which exploits positive correlationsobtained by using CRNs for nominal and perturbed parameters. We also propose a new methodcalled the common reaction path (CRP) method, which uses CRNs together with the random timechange representation of discrete state Markov processes due to Kurtz to estimate the sensitivity viaa finite difference approximation applied to coupled reaction paths that emerge naturally in thisrepresentation. While both methods reduce the variance of the estimator significantly compared toindependent random number finite difference implementations, numerical evidence suggests that theCRP method achieves a greater variance reduction. We also provide some theoretical basis for thesuperior performance of CRP. The improved accuracy of these methods allows for much moreefficient sensitivity estimation. In two example systems reported in this work, speedup factorsgreater than 300 and 10 000 are demonstrated.