Accelerated Simulation of Hybrid Biological Models with Quasi-Disjoint Deterministic and Stochastic Subnets
Computational biological models are indispensable tools for in silico hypothesis testing. But with the increasing complexity of biological systems, traditional simulators become inefficient to tackle emerging computational challenges. Hybrid simulation, which combines deterministic and stochastic parts, is a promising direction to deal with such challenges. However, currently existing algorithms of hybrid simulation are impractical for implementing real and complex biological systems. One reason for such limitation is that the performance of hybrid simulation not only relies on the number of stochastic events, but also on the type as well as the efficiency of the deterministic solver. In this paper, a new method is proposed for improving the performance of hybrid simulators by reducing the frequent reinitialisation of the deterministic solver. The proposed approach works well with models that contain a substantial number of stochastic events and higher numbers of continuous variables with limited connections between the deterministic and stochastic regimes. We tested these improvements on a number of case studies and it turns out that, for certain examples, the amended algorithm is ten times faster than the exact method.
KeywordsAccelerated hybrid simulation Deterministic and stochastic simulation Dependency graph Computational modelling
This work has been partially funded by the GE-SEED grant (7934) which is administrated by STDF(Science and Technology Development Fund, Egypt) and DAAD (German Academic Exchange Service). We also acknowledge the helpful comments of the anonymous reviewers for improving a previous version of the paper.
- 2.Barik, D., Baumann, W.T., Paul, M.R., Novak, B., Tyson, J.J.: A model of yeast cell-cycle regulation based on multisite phosphorylation. Molecular Syst. Biol. 6(1), 405 (2010)Google Scholar
- 3.Blätke, M., Heiner, M., Marwan, W.: BioModel engineering with Petri nets, chap. 7, pp. 141–193. Elsevier Inc. (2015). http://store.elsevier.com/product.jsp?isbn=9780128012130
- 15.Herajy, M., Heiner, M.: A steering server for collaborative simulation of quantitative Petri nets. In: Ciardo, G., Kindler, E. (eds.) PETRI NETS 2014. LNCS, vol. 8489, pp. 374–384. Springer, Heidelberg (2014)Google Scholar
- 16.Herajy, M., Liu, F., Rohr, C.: Coloured hybrid Petri nets for systems biology. In: Proceedings of the 5th International Workshop on Biological Processes & Petri Nets (BioPPN), Satellite Event of PETRI NETS 2014, CEUR Workshop Proceedings, vol. 1159, pp. 60–76 (2014)Google Scholar
- 17.Herajy, M., Schwarick, M.: A hybrid Petri net model of the eukaryotic cell cycle. In: Proceedings of the 3rd International Workshop on Biological Processes and Petri Nets (BioPPN), Satellite Event of PETRI NETS 2012, CEUR Workshop Proceedings, vol. 852, pp. 29–43 (2012). CEUR-WS.org. http://ceur-ws.org/Vol-852/
- 18.Herajy, M., Heiner, M.: Modeling and simulation of multi-scale environmental systems with generalized hybrid Petri nets. Front. Environ. Sci. 3(53) (2015)Google Scholar
- 31.Tyson, J.J., Novk, B.: Irreversible transitions, bistability and checkpoint controls in the eukaryotic cell cycle: a systems-level understanding, Chapt. 14. In: Walhout, A.M., Vidal, M., Dekker, J. (eds.) Handbook of Systems Biology, pp. 265–285. Academic Press, San Diego (2013)CrossRefGoogle Scholar