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Journal of Chemical Physics / Volume 135 / Issue 23 / ARTICLES / Theoretical Methods and Algorithms

J. Chem. Phys. 135, 234108 (2011); http://dx.doi.org/10.1063/1.3668100 (11 pages)

State-dependent doubly weighted stochastic simulation algorithm for automatic characterization of stochastic biochemical rare events

Min K. Roh1, Bernie J. Daigle, Jr.1, Dan T. Gillespie2, and Linda R. Petzold1

1Department of Computer Science, University of California Santa Barbara, Santa Barbara, California 93106, USA
2Dan T Gillespie Consulting, 30504 Cordoba Place, Castaic, California 91384, USA

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(Received 9 September 2011; accepted 21 November 2011; published online 20 December 2011)

In recent years there has been substantial growth in the development of algorithms for characterizing rare events in stochastic biochemical systems. Two such algorithms, the state-dependent weighted stochastic simulation algorithm (swSSA) and the doubly weighted SSA (dwSSA) are extensions of the weighted SSA (wSSA) by H. Kuwahara and I. Mura [J. Chem. Phys. 129, 165101 (2008)]10.1063/1.2987701. The swSSA substantially reduces estimator variance by implementing system state-dependent importance sampling (IS) parameters, but lacks an automatic parameter identification strategy. In contrast, the dwSSA provides for the automatic determination of state-independent IS parameters, thus it is inefficient for systems whose states vary widely in time. We present a novel modification of the dwSSA—the state-dependent doubly weighted SSA (sdwSSA)—that combines the strengths of the swSSA and the dwSSA without inheriting their weaknesses. The sdwSSA automatically computes state-dependent IS parameters via the multilevel cross-entropy method. We apply the method to three examples: a reversible isomerization process, a yeast polarization model, and a lac operon model. Our results demonstrate that the sdwSSA offers substantial improvements over previous methods in terms of both accuracy and efficiency.

© 2011 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. BACKGROUND
    1. Rare event probabilities and the SSA
    2. Doubly weighted SSA
  3. SDWSSA FORMULATION AND THE MULTILEVEL CROSS-ENTROPY METHOD
    1. State-dependent doubly weighted SSA
    2. The sdwSSA and the cross-entropy method
  4. EXAMPLES
    1. Reversible isomerization
    2. Yeast polarization
    3. Lac operon
  5. CONCLUSION

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KEYWORDS and PACS

Keywords

biochemistry, entropy, importance sampling, isomerisation, parameter estimation, stochastic processes

PACS

  • 82.39.-k

    Chemical kinetics in biological systems

  • 87.15.R-

    Reactions and kinetics

  • 82.30.Qt

    Isomerization and rearrangement

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.3668100

PUBLICATION DATA

ISSN

0021-9606 (print)  
1089-7690 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

For access to fully linked references, you need to log in.
    H. Kuwahara and I. Mura, J. Chem. Phys. 129, 165101 (2008)JCPSA6000129000016165101000001.

    B. J. Daigle Jr., M. K. Roh, D. T. Gillespie, and L. R. Petzold, J. Chem. Phys. 134, 044110 (2011)JCPSA6000134000004044110000001.

    M. K. Roh, D. T. Gillespie, and L. R. Petzold, J. Chem. Phys. 133, 174106 (2010)JCPSA6000133000017174106000001.


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