BIOPHYSICAL THEORY AND MODELING |
Spectral Methods for Parametric Sensitivity in Stochastic Dynamical Systems
Dongjin Kim 1, Bert J Debusschere 2* and Habib N Najm 2
1 Georgetown University
2 Sandia National Laboratories
* To whom correspondence should be addressed. E-mail: bjdebus{at}sandia.gov.
Submitted on March 17, 2006
Revised on May 2, 2006
Accepted on 13 September 2006
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Abstract |
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Stochastic dynamical systems governed by the chemical master equation find use in the modeling of biological phenomena in cells, where they provide more accurate representations than their deterministic counterparts, particularly when the levels of molecular population are small. The analysis of parametric sensitivity in such systems requires appropriate methods in order to capture the sensitivity of the system dynamics with respect to variations of the parameters amid the noise from inherent internal stochastic effects. We use spectral polynomial chaos expansions to represent statistics of the system dynamics as polynomial functions of the model parameters. These expansions capture the nonlinear behavior of the system statistics as a result of finite-sized parametric perturbations. We obtain the normalized sensitivity coefficients by taking the derivative of this functional representation with respect to the parameters. We apply this method in two stochastic dynamical systems exhibiting bimodal behavior, including a biologically relevant viral infection model.
Key Words:
bistable, polynomial chaos, sensitivity, stochastic, viral infection
