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AN ERROR ESTIMATION FOR MOMENT CLOSURE APPROXIMATION OF CHEMICAL REACTION SYSTEMS

  • KIM, KYEONG-HUN (DEPARTMENT OF MATHEMATICS, KOREA UNIVERSITY) ;
  • LEE, CHANG HYEONG (DEPARTMENT OF MATHEMATICAL SCIENCES, ULSAN NATIONAL INSTITUTE OF SCIENCE AND TECHNOLOGY(UNIST))
  • Received : 2017.11.21
  • Accepted : 2017.12.07
  • Published : 2017.12.25

Abstract

The moment closure method is an approximation method to compute the moments for stochastic models of chemical reaction systems. In this paper, we develop an analytic estimation of errors generated from the approximation of an infinite system of differential equations into a finite system truncated by the moment closure method. As an example, we apply the result to an essential bimolecular reaction system, the dimerization model.

Keywords

References

  1. C. V. Rao, D. M. Wolf and A. P. Arkin, Control, exploitation and tolerance of intracellular noise, Nature, 420(6912) (2002), 231. https://doi.org/10.1038/nature01258
  2. M. Thattai and A. Van Oudenaarden, Intrinsic noise in gene regulatory networks, Proceedings of the National Academy of Sciences, 98(15) (2001), 8614-8619. https://doi.org/10.1073/pnas.151588598
  3. D. J. Higham, Modeling and simulating chemical reactions, SIAM review, 50(2) (2008), 347-368. https://doi.org/10.1137/060666457
  4. D. T. Gillespie, A rigorous derivation of the chemical master equation, Physica A: Statistical Mechanics and its Applications, 188 (1992), 404-425. https://doi.org/10.1016/0378-4371(92)90283-V
  5. C. H. Lee and P. Kim, An analytical approach to solutions of master equations for stochastic nonlinear reactions, Journal of Mathematical Chemistry, 50(6) (2012), 1550-1569. https://doi.org/10.1007/s10910-012-9988-7
  6. D. T. Gillespie, Exact stochastic simulation of coupled chemical reactions, The Journal of Physical Chemistry, 81(25) (1977), 2340-2361. https://doi.org/10.1021/j100540a008
  7. D. T. Gillespie, Approximate accelerated stochastic simulation of chemically reacting systems, The Journal of Chemical Physics, 115(4) (2001), 1716-1733. https://doi.org/10.1063/1.1378322
  8. P. Kim and C. H. Lee, A probability generating function method for stochastic reaction networks, The Journal of Chemical Physics, 136(23) (2012), 234108. https://doi.org/10.1063/1.4729374
  9. P. Kim and C. H. Lee, Fast probability generating function method for stochastic chemical reaction networks, MATCH Communications in Mathematical and in Computer Chemistry, 71 (2014), 57-69.
  10. Y. Cao, D. T. Gillespie, and L. R. Petzold, The slow-scale stochastic simulation algorithm, The Journal of Chemical Physics, 122 (2005), 014116. https://doi.org/10.1063/1.1824902
  11. B. Munsky and M. Khammash, The finite state projection algorithm for the solution of the chemical master equation, The Journal of Chemical Physics, 124 (2006), 044104. https://doi.org/10.1063/1.2145882
  12. C. H. Lee and R. Lui, A reduction method for multiple time scale stochastic reaction networks with non-unique equilibrium probability, Journal of Mathematical Chemistry, 47(2) (2010), 750-770. https://doi.org/10.1007/s10910-009-9598-1
  13. C. H. Lee, K-H. Kim and P. Kim, A moment closure method for stochastic reaction networks, The Journal of Chemical Physics, 130(13) (2009), 134107. https://doi.org/10.1063/1.3103264
  14. Ingemar Nasell, Moment closure and the stochastic logistic model, Theoretical Population Biology, 63(2) (2003) 159-168. https://doi.org/10.1016/S0040-5809(02)00060-6
  15. J. P. Hespanha and A. Singh, Stochastic models for chemically reacting systems using polynomial stochastic hybrid systems, International Journal of Robust and nonlinear control, 15 (2005), 669-689. https://doi.org/10.1002/rnc.1017
  16. C. H. Lee, A moment closure method for stochastic chemical reaction networks with general kinetics, MATCH Communications in Mathematical and in Computer Chemistry, 70 (2013), 785-800.
  17. P. Smadbeck and Y. N. Kaznessis, A closure scheme for chemical master equations, Proceedings of the National Academy of Sciences, 110(35) (2013), 14261-14265. https://doi.org/10.1073/pnas.1306481110