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Large-Scale Design Space Exploration of SSA

  • Matthias Jeschke
  • Roland Ewald
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5307)

Abstract

Stochastic simulation algorithms (SSA) are popular methods for the simulation of chemical reaction networks, so that various enhancements have been introduced and evaluated over the years. However, neither theoretical analysis nor empirical comparisons of single implementations suffice to capture the general performance of a method. This makes choosing an appropriate algorithm very hard for anyone who is not an expert in the field, especially if the system provides many alternative implementations. We argue that this problem can only be solved by thoroughly exploring the design spaces of such algorithms. This paper presents the results of an empirical study, which subsumes several thousand simulation runs. It aims at exploring the performance of different SSA implementations and comparing them to an approximation via τ-Leaping, while using different event queues and random number generators.

Keywords

Stochastic Simulation Algorithms Performance Evaluation 

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References

  1. 1.
    Srivastava, R., You, L., Summers, J., Yin, J.: Stochastic vs. deterministic modeling of intracellular viral kinetics. Journal of Theoretical Biology 218, 309–321 (2002)CrossRefPubMedGoogle Scholar
  2. 2.
    Gillespie, D.: A rigorous derivation of the chemical master equation. Physica A Statistical Mechanics and its Applications 188, 404–425 (1992)CrossRefGoogle Scholar
  3. 3.
    Macnamara, S., Burrage, K., Sidje, R.B.: Multiscale modeling of chemical kinetics via the master equation. Multiscale Modeling & Simulation 6(4), 1146–1168 (2008)CrossRefGoogle Scholar
  4. 4.
    Gillespie, D.: Exact Stochastic Simulation of Coupled Chemical Reactions. Journal of Physical Chemistry 81(25) (1977)Google Scholar
  5. 5.
    Sandmann, W.: Simultaneous stochastic simulation of multiple perturbations in biological network models (2007)Google Scholar
  6. 6.
    Gillespie, D.: Approximate accelerated stochastic simulation of chemically reacting systems. The Journal of Chemical Physics 115(4), 1716–1733 (2001)CrossRefGoogle Scholar
  7. 7.
    Cao, Y., Gillespie, D.T., Petzold, L.R.: The slow-scale stochastic simulation algorithm. J. Chem. Phys. 122(1) (January 2005)Google Scholar
  8. 8.
    Weinan, E., Di, L., Vanden-Eijnden, E.: Nested stochastic simulation algorithms for chemical kinetic systems with multiple time scales. J. Comput. Phys. 221(1), 158–180 (2007)CrossRefGoogle Scholar
  9. 9.
    McGeoch, C.: Experimental algorithmics. Communications of the ACM 50(11), 27–31 (2007)CrossRefGoogle Scholar
  10. 10.
    LaMarca, A., Ladner, R.: The influence of caches on the performance of sorting. In: SODA 1997: Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms, Philadelphia, PA, USA. Society for Industrial and Applied Mathematics, pp. 370–379 (1997)Google Scholar
  11. 11.
    Uhrmacher, A., Himmelspach, J., Jeschke, M., John, M., Leye, S., Maus, C., Röhl, M., Ewald, R.: One modeling formalism & simulator is not enough! - a perspective for computational biology based on james ii. In: Proceedings of the 1st FSMB Workshop, London. LNCS. Springer, Heidelberg (to appear, 2008)Google Scholar
  12. 12.
    Himmelspach, J., Uhrmacher, A.: Plug’n simulate. In: Proceedings of the 40th Annual Simulation Symposium, pp. 137–143. IEEE Computer Society, Los Alamitos (to appear, 2007)Google Scholar
  13. 13.
    Ewald, R., Himmelspach, J., Uhrmacher, A.: An algorithm selection approach for simulation systems. In: Proceedings of the 22nd ACM/IEEE/SCS Workshop on Principles of Advanced and Distributed Simulation (PADS 2008) (to appear, 2008)Google Scholar
  14. 14.
    Gibson, M., Bruck, J.: Efficient Exact Stochastic Simulation of Chemical Systems with Many Species and Many Channels. J. Chem. Physics 104, 1876–1889 (2000)CrossRefGoogle Scholar
  15. 15.
    Himmelspach, J., Uhrmacher, A.: The event queue problem and pdevs. In: Proceedings of the SpringSim 2007, DEVS Integrative M&S Symposium, SCS, pp. 257–264 (2007)Google Scholar
  16. 16.
    Rice, J.: The algorithm selection problem. Advances in Computers 15, 65–118 (1976)CrossRefGoogle Scholar
  17. 17.
    Gomes, C., Selman, B.: Algorithm portfolio design: Theory vs. practice. In: Proc. of the 13th Conf. on Uncertainty in Artificial Intelligence (UAI 1997), pp. 190–197. Morgan Kaufmann, San Francisco (1997)Google Scholar
  18. 18.
    Leyton-Brown, K., Nudelman, E., Andrew, G., Mcfadden, J., Shoham, Y.: Boosting as a metaphor for algorithm design. In: Rossi, F. (ed.) CP 2003. LNCS, vol. 2833, pp. 899–903. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  19. 19.
    Houstis, E.N., Catlin, A., Rice, J., Verykios, V., Ramakrishnan, N., Houstis, C.: Pythia ii: A knowledge/database system for managing performance data and recommending scientific software. ACM Transactions on Mathematical Software 26(2), 227–253 (2000)CrossRefGoogle Scholar
  20. 20.
    Busch, H., Sandmann, W., Wolf, V.: A Numerical Aggregation Algorithm for the Enzyme-Catalyzed Substrate Conversion (2006)Google Scholar
  21. 21.
    Cai, X., Wang, X.: Stochastic modeling and simulation of gene networks - a review of the state-of-the-art research on stochastic simulations. Signal Processing Magazine, IEEE 24(1), 27–36 (2007)CrossRefGoogle Scholar
  22. 22.
    Cao, Y., Li, H., Petzold, L.: Efficient formulation of the stochastic simulation algorithm forchemically reacting systems. The Journal of Chemical Physics 121(9), 4059–4067 (2004)CrossRefPubMedGoogle Scholar
  23. 23.
    Gillespie, D.: The chemical langevin equation. The Journal of Chemical Physics 113(1), 297–306 (2000)CrossRefGoogle Scholar
  24. 24.
    Tian, T., Burrage, K.: Binomial leap methods for simulating stochastic chemical kinetics. The Journal of Chemical Physics 121(21), 10356–10364 (2004)CrossRefPubMedGoogle Scholar
  25. 25.
    Cao, Y., Gillespie, D., Petzold, L.: Avoiding negative populations in explicit Poisson tau-leaping. J. Chem. Phys. 123, 054104 (2005)CrossRefGoogle Scholar
  26. 26.
    Cao, Y., Gillespie, D.T., Petzold, L.R.: Efficient step size selection for the tau-leaping simulation method. J. Chem. Phys. 124(4) (January 2006)Google Scholar
  27. 27.
    Rathinam, M., Petzold, L.R., Cao, Y., Gillespie, D.T.: Stiffness in stochastic chemically reacting systems: The implicit tau-leaping method. The Journal of Chemical Physics 119, 12784–12794 (2003)CrossRefGoogle Scholar
  28. 28.
    Cai, X., Xu, Z.: K-leap method for accelerating stochastic simulation of coupled chemical reactions. The Journal of Chemical Physics 126, 4102 (2007)Google Scholar
  29. 29.
    EMBL-EBI: Biomodels database, 10 (accessed July 18, 2008), http://www.ebi.ac.uk/biomodels/
  30. 30.
    Matsumoto, M., Nishimura, T.: Mersenne twister: a 623-dimensionally equidistributed uniform pseudo-random number generator. ACM Trans. Model. Comput. Simul. 8(1), 3–30 (1998)CrossRefGoogle Scholar
  31. 31.
    Marsaglia, G.: The Marsaglia random number CDROM including the Diehard battery of tests of randomness (1995), http://www.stat.fsu.edu/pub/diehard/
  32. 32.
    Jenkins, B.: ISAAC, a fast cryptographic random number generator (1996), http://www.burtleburtle.net/bob/rand/isaacafa.html
  33. 33.
    Hellekalek, P.: Good random number generators are (not so) easy to find. Math. Comput. Simul. 46(5-6), 485–505 (1998)CrossRefGoogle Scholar
  34. 34.
    Grassberger, P.: On correlations in “good” random number generators. Physics Letters A 181(1), 43–46 (1993)CrossRefGoogle Scholar
  35. 35.
    Matsumoto, M., Wada, I., Kuramoto, A., Ashihara, H.: Common defects in initialization of pseudorandom number generators. ACM Trans. Model. Comput. Simul. 17(4) (September 2007)Google Scholar
  36. 36.
    Marsaglia, G.: Seeds for random number generators. Commun. ACM 46(5), 90–93 (2003)CrossRefGoogle Scholar
  37. 37.
    Goh, R., Thng, I.: Mlist: An efficient pending event set structure for discrete event simulation. International Journal of Simulation - Systems, Science & Technology 4(5-6), 66–77 (2003)Google Scholar
  38. 38.
    Brown, R.: Calendar queues: a fast 0(1) priority queue implementation for the simulation event set problem. Commun. ACM 31(10), 1220–1227 (1988)CrossRefGoogle Scholar
  39. 39.
    Huberman, B., Lukose, R., Hogg, T.: An economics approach to hard computational problems. Science 275, 51–54 (1997)CrossRefPubMedGoogle Scholar
  40. 40.
    Sheskin, D.J.: Handbook of Parametric and Nonparametric Statistical Procedures, 4th edn. Chapman & Hall/CRC, Boca Raton (January 2007)Google Scholar
  41. 41.
    Pozo, R., Miller, B.: Java scimark, http://math.nist.gov/scimark2/
  42. 42.
    R Development Core Team: R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria (2005)Google Scholar
  43. 43.
    Takahashi, K., Kaizu, K., Hu, B., Tomita, M.: A multi-algorithm, multi-timescale method for cell simulation. Bioinformatics 20 (2004)Google Scholar
  44. 44.
    Phillips, A., Cardelli, L.: A correct abstract machine for the stochastic pi-calculus. Transactions on Computational Systems Biology (2005)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Matthias Jeschke
    • 1
  • Roland Ewald
    • 1
  1. 1.Institute of Computer Science, Modelling and Simulation GroupUniversity of RostockRostockGermany

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