No data available.

Please log in to see this content.

You have no subscription access to this content.

No metrics data to plot.

The attempt to load metrics for this article has failed.

The attempt to plot a graph for these metrics has failed.

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

Rent:

Rent this article for

USD

10.1063/1.3677230

### Abstract

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 perturbationanalysis) 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.

© 2012 American Institute of Physics

Received 15 July 2011
Accepted 27 December 2011
Published online 20 January 2012

Acknowledgments: The authors wish to acknowledge financial support from the National Science Foundation under Grant Nos. NSF-ECCS-0835847 and NSF-ECCS-0802008 and from the National Institute of Health under Grant No. R01-GM04983.

Article outline:

I. INTRODUCTION

II. INFINITESIMAL SENSITIVITY ANALYSIS IN STOCHASTIC CHEMICAL KINETICS

III. THE REGULARIZED PATHWISE DERIVATIVE METHOD

A. Algorithm

IV. NUMERICAL EXAMPLES

A. Monomolecular birth-death system

B. Reversible isomerization system

C. Genetic oscillator

D. Toggle switch

V. ON THE SELECTION OF THE PARAMETER *w*

VI. CONCLUSIONS

/content/aip/journal/jcp/136/3/10.1063/1.3677230

http://aip.metastore.ingenta.com/content/aip/journal/jcp/136/3/10.1063/1.3677230

Article metrics loading...

/content/aip/journal/jcp/136/3/10.1063/1.3677230

2012-01-20

2014-04-23

Full text loading...

### Most read this month

Article

content/aip/journal/jcp

Journal

5

3

Commenting has been disabled for this content