An efficient and exact stochastic simulation method to analyze rare events in biochemical systems

Parameter sensitivity analysis is a powerful tool in the building and analysis of biochemical network models. For stochastic simulations, parameter sensitivity analysis can be computationally expensive, requiring multiple simulations for perturbed values of the parameters. Here, we use trajectory reweighting to derive a method for computing sensitivity coefficients in stochastic simulations without explicitly perturbing the parameter values, avoiding the need for repeated simulations. The method allows the simultaneous computation of multiple sensitivity coefficients. Our approach recovers results originally obtained by application of the Girsanov measure transform in the general theory of stochastic processes [A. Plyasunov and A. P. Arkin, J. Comp. Phys. 221, 724 (2007)]. We build on these results to show how the method can be used to compute steady-state sensitivity coefficients from a single simulation run, and we present various efficiency improvements. For models of biochemical signaling networks the method has a particularly simple implementation. We demonstrate its application to a signaling network showing stochastic focussing and to a bistable genetic switch, and present exact results for models with linear propensity functions.

Section: Computation Of Parameter Sensitivity Coefficientsmentioning

confidence: 99%

Section: Trajectory Reweighting For Kinetic Monte-carlo Simulationsmentioning

confidence: 99%

Section: Trajectory Reweightingmentioning

confidence: 99%

See 1 more Smart Citation

Steady-state parameter sensitivity in stochastic modeling via trajectory reweighting

Warren

Allen

2012

“…As we will see, the new biasing method increases the computational speed not only relative to the SSA but also relative to the scheme used in the original wSSA papers. 1,2 The measure used to calculate gain in computational efficiency is the same as in Ref. 2, given by…”

Section: Numerical Examplesmentioning

confidence: 99%

State-dependent biasing method for importance sampling in the weighted stochastic simulation algorithm

Roh

Petzold

2010

The weighted stochastic simulation algorithm ͑wSSA͒ was developed by Kuwahara and Mura ͓J. Chem. Phys. 129, 165101 ͑2008͔͒ to efficiently estimate the probabilities of rare events in discrete stochastic systems. The wSSA uses importance sampling to enhance the statistical accuracy in the estimation of the probability of the rare event. The original algorithm biases the reaction selection step with a fixed importance sampling parameter. In this paper, we introduce a novel method where the biasing parameter is state-dependent. The new method features improved accuracy, efficiency, and robustness.

“…In Srivastava et al, 23 we obtained a significantly better estimate of the rare state probability using stochastic quasi-steady-steady perturbation analysis (sQSPA), compared to both the full model and importance sampling based methods. 24,25 Figure 7 shows the schematic of the pap operon regulation.…”

Section: Sensitivity Of a Rare State Probabilitymentioning

confidence: 99%

Comparison of finite difference based methods to obtain sensitivities of stochastic chemical kinetic models

Srivastava

Anderson

Rawlings

2013

Sensitivity analysis is a powerful tool in determining parameters to which the system output is most responsive, in assessing robustness of the system to extreme circumstances or unusual environmental conditions, in identifying rate limiting pathways as a candidate for drug delivery, and in parameter estimation for calculating the Hessian of the objective function. Anderson [SIAM J. Numer. Anal. 50, 2237 (2012)] shows the advantages of the newly developed coupled finite difference (CFD) estimator over the common reaction path (CRP) [M. Rathinam, P. W. Sheppard, and M. Khammash, J. Chem. Phys. 132, 034103 (2010)] estimator. In this paper, we demonstrate the superiority of the CFD estimator over the common random number (CRN) estimator in a number of scenarios not considered previously in the literature, including the sensitivity of a negative log likelihood function for parameter estimation, the sensitivity of being in a rare state, and a sensitivity with fast fluctuating species. In all examples considered, the superiority of CFD over CRN is demonstrated. We also provide an example in which the CRN method is superior to the CRP method, something not previously observed in the literature. These examples, along with Anderson's results, lead to the conclusion that CFD is currently the best estimator in the class of finite difference estimators of stochastic chemical kinetic models.