Journal of Chemical Physics
Feedback | Help | Exit
The Journal of Chemical Physics
Search:
   
 
 
 
Previous Article
Interpolating moving least-squares methods for fitting potential energy surfaces: Improving efficiency via local approximants
The local interpolating moving least-squares (IMLS) method for constructing potential energy surfaces is investigated. The method retains the advantageous features of the IMLS approach in that the ab ...
Next Article
Nonlinear scaling schemes for Lennard-Jones interactions in free energy calculations
Alchemical free energy calculations provide a means for the accurate determination of free energies from atomistic simulations and are increasingly used as a tool for computational studies of protein-...

A modified next reaction method for simulating chemical systems with time dependent propensities and delays

J. Chem. Phys. 127, 214107 (2007); doi:10.1063/1.2799998

Published 6 December 2007 | See: Publisher's Note

You are not logged in to this journal. Log in

David F. Anderson
Department of Mathematics, University of Wisconsin-Madison, Madison, Wisconsin 53706, USA
Chemical reaction systems with a low to moderate number of molecules are typically modeled as discrete jump Markov processes. These systems are oftentimes simulated with methods that produce statistically exact sample paths such as the Gillespie algorithm or the next reaction method. In this paper we make explicit use of the fact that the initiation times of the reactions can be represented as the firing times of independent, unit rate Poisson processes with internal times given by integrated propensity functions. Using this representation we derive a modified next reaction method and, in a way that achieves efficiency over existing approaches for exact simulation, extend it to systems with time dependent propensities as well as to systems with delays. ©2007 American Institute of Physics
History: Received 20 June 2007; accepted 26 September 2007; published 6 December 2007; publisher error corrected 28 January 2008
Permalink: http://link.aip.org/link/?JCPSA6/127/214107/1
BUY THIS ARTICLE   (US$24)
Download HTML Download Sectioned HTML Download PDF (200 kB) View Cart

ERRATUM

  1. Publisher's Note: “A modified next reaction method for simulating chemical systems with time dependent propensities and delays” [J. Chem. Phys. 127, 214107 (2007)]
    David F. Anderson
    J. Chem. Phys. 128, 109903 (2008)

KEYWORDS and PACS

Keywords
PACS
  • 82.20.Uv
    Stochastic theories of rate constants in chemical kinetics
  • 82.20.Wt
    Computational modeling and simulation of chemical kinetics
  • YEAR: 2007

RELATED DATABASES


To view database links for this article,
you need to log in.
To view database links for this article,
you need to log in.

PUBLICATION DATA

ISSN:
0021-9606 (print)   1089-7690 (online)
Publisher:
AIP is a member of CrossRef AIP

REFERENCES (20)
View in Separate Window/Tab
For access to fully linked references, you need to log in. For access to fully linked references, you need to Log in.
  1. A. Arkin, J. Ross, and H. H. McAdams, Genetics 149, 1633 (1998).
  2. H. H. McAdams and A. Arkin, Proc. Natl. Acad. Sci. U.S.A. 94, 814 (1997).
  3. E. M. Ozbudak, M. Thattai, I. Kurtser, A. D. Grossman, and A. van Oudenaarden, Nat. Genet. 31, 69 (2002).
  4. H. E. Samad, M. Khammash, L. Petzold, and D. Gillespie, Int. J. Robust Nonlinear Control 15, 691 (2005).
  5. D. T. Gillespie, J. Comput. Phys. 22, 403 (1976).
  6. D. T. Gillespie, J. Phys. Chem. 81, 2340 (1977).
  7. M. Gibson and J. Bruck, J. Phys. Chem. A 105, 1876 (2000).
  8. T. G. Kurtz, Ann. Probab. 8, 682 (1980).
  9. S. N. Ethier and T. G. Kurtz, Markov Processes: Characterization and Convergence (Wiley, New York, 1986).
  10. K. Ball, T. G. Kurtz, L. Popovic, and G. Rempala, Ann. Appl. Probab. 16, 1925 (2006).
  11. D. Bratsun, D. Volfson, L. S. Tsimring, and J. Hasty, Proc. Natl. Acad. Sci. U.S.A. 102, 14593 (2005).
  12. M. Barrio, K. Burrage, A. Leier, and T. Tian, PLOS Comput. Biol. 2, 1017 (2006).
  13. X. Cai, J. Chem. Phys. 126, 124108 (2007).
  14. D. Y. Burman, Adv. Appl. Probab. 13, 846 (1981).
  15. R. Schassberger, Adv. Appl. Probab. 10, 836 (1978).
  16. P. W. Glynn, Proc. IEEE 77, 14 (1989).
  17. P. J. Haas, Stochastic Petri Nets: Modelling Stability, Simulation, 1st ed. (Springer, New York, 2002).
  18. D. F. Anderson, “Incorporating postleap checks in tau-leaping,” J. Chem. Phys. (to be published).
  19. T. Lu, D. Volfson, L. Tsimring, and J. Hasty, IEE Syst. Biol. 1, 1 (2004).
  20. G. A. Rempala, K. S. Ramos, and T. Kalbfleisch, J. Theor. Biol. 242, 101 (2006).

CITING ARTICLES
For access to citing articles, you need to log in.
For access to citing articles, you need to Log in.


Copyright © American Institute of Physics