Dynamic Partitioning of Large Discrete Event Biological Systems for Hybrid Simulation and Analysis

  • Natasha A. Neogi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2993)


Biological systems involving genetic reactions are large discrete event systems, and often contain certain species that occur in small quantities, and others that occur in large quantities, leading to a difficulty in modelling and simulation. Small populations inhibit the usefulness of utilizing differential equations to represent the system, while the large populations cause stochastic discrete event simulation to become computationally intensive. This paper presents an algorithmic approach for the dynamic partitioning and stochastic hybrid simulation of biological systems. The algorithm uses a Poisson approximation for discrete event generation and a Langevin approximation for continuous behaviour. The populations are dynamically partitioned so that some populations are simulated in a discrete stochastic fashion, while others are simulated by continuous differential equations, and this partition between discrete and continuous behaviour is updated at regular intervals. The hybrid model of a simple biological toggle switch yields promising results, and a more complex example is explored.


Poisson Process Master Equation Discrete Event Langevin Equation Continuous Reaction 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    McAdams, H.H., Arkin, A.: Stochastic Mechanisms in Gene Expression. Biochemistry, Proc. Natl. Acad. Sci. 94, 814–819 (1997)CrossRefGoogle Scholar
  2. 2.
    Kastner, J., Solomon, J., Scott, F.: Modeling a Hox Gene Network in Silico Using a Stochastic Simulation Algorithm. Developmental Biology 246, 122–131 (2002)CrossRefGoogle Scholar
  3. 3.
    Kaern, Mads, Blake, William, J., Collins, J.J.: The Engineering of Gene Regulatory Networks. Annu. Rev. Biomed. Eng. 5, 179–206 (2003)CrossRefGoogle Scholar
  4. 4.
    Solari, H.G., Natiello, M.A.: Poisson Approximation to Density Dependent Stochastic Processes: A Numerical Implementation and Test. Physical Review (2003) (in press)Google Scholar
  5. 5.
    Solari, H.G., Natiello, M.A.: Stochastic Population Dynamics: the Poisson Approximation. Physical Review E 67, 031918 (2003)CrossRefGoogle Scholar
  6. 6.
    Aparicio, Juan, P., Solari, H.G.: Population Dynamics: Poisson Approximation and Its Relation to the Langevin Process. Physical Review Letter 86(18) (April 30, 2001)Google Scholar
  7. 7.
    Gibson, M.A., Bruck, J.: Efficient Exact Stochastic Simulation of Chemical Systems with Many Species and Many Channels. J. Phys. Chem. A 104, 1876–1889 (2000)CrossRefGoogle Scholar
  8. 8.
    Haseltine, E.L., Rawlings, J.B.: Approximate Simulation of Coupled Fast and Slow Reactions for Stochastic Chemical Kinetics. Journal of Chemical Physics 117(15), 6959–6969 (2002)CrossRefGoogle Scholar
  9. 9.
    Gardiner, C.W.: Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences, 2nd edn. Springer, Berlin (1990)zbMATHGoogle Scholar
  10. 10.
    Gillespie, D.T.: Markov Processes: An Introduction for Physical Scientists. Academic, New York (1992)zbMATHGoogle Scholar
  11. 11.
    Gard, T.C.: Introduction to Stochastic Differential Equations. Marcel Dekker, New York (1998)Google Scholar
  12. 12.
    Gibson, M.S., Mjolsness, E.: Computational Methods for Modelling. In: Bower, J., Bolouri, H. (eds.) Biochemical Networks, MIT Press, Cambridge (in press)Google Scholar
  13. 13.
    Gillespie, D.T.: Exact Stochastic Simulation of Coupled Chemical Reactions. Journal of Physical Chemistry 81, 2340–2361 (1977)CrossRefGoogle Scholar
  14. 14.
    Kurtz, G.T.: Approximation of Discontinuous Processes by Continuous Processes. In: Arnold, L., Lefever, R. (eds.) Stochastic Nonlinear Systems in Physics, Chemistry and Biology, Springer, Berlin (1981)Google Scholar
  15. 15.
    He, J., Zhang, H., Chen, J., Yang.Y.: Macromolecules, vol. 30, p. 8010 (1997)Google Scholar
  16. 16.
    Rao, C., Arkin, A.: Journal Chem. Phys. (submitted)Google Scholar
  17. 17.
    Janssen, J.A.M.: Journal of Statistical Physics, vol. 57, p. 171 (1989)Google Scholar
  18. 18.
    Vlad, M.O., Pop, A.: Physica A, vol. 155, p. 276 (1989)Google Scholar
  19. 19.
    Gillespie, D.T.: Physica A, vol. 188, p. 404 (1992)Google Scholar
  20. 20.
    Resat, H., Wiley, H.S., Dixon, D.A.: Journal of Physical Chemistry B, vol. 105, p. 11026 (2001)Google Scholar
  21. 21.
    Idaker, T.: Science (2001)Google Scholar
  22. 22.
    Ostergaard, S.: National Biotechnical Journal (2000)Google Scholar
  23. 23.
    Gardner, T.J., Cantor, C.R., Collins, J.J.: Construction of a Genetic Toggle Switch in Escherichia Coli. Nature 403, 339–342 (2000)CrossRefGoogle Scholar
  24. 24.
    Goss & Peccoud, Proc. Nat. Acad. Sci. (1998)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Natasha A. Neogi
    • 1
  1. 1.Department of Aerospace EngineeringUniversity of Illinois, Urbana-ChampaignChampaignUSA

Personalised recommendations