Hybrid Stochastic Simulation of Rule-Based Polymerization Models

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9957)

Abstract

Modeling and simulation of polymer formation is an important field of research not only in the material sciences but also in the life sciences due to the prominent role of processes such as actin filament formation and multivalent ligand-receptor interactions. While the advantages of a rule-based description of polymerizations has been successfully demonstrated, no efficient simulation of these mostly stiff processes is currently available, in particular for large system sizes.

We present a hybrid stochastic simulation approach, in which the average changes of highly abundant species due to fast reactions are deterministically simulated while for the remaining species with small counts a rule-based simulation is performed. We propose a nesting of rejection steps to arrive at an approach that is efficient and accurate. We test our method on two case studies of polymerization.

Keywords

Polymerization Rule-based modeling Hybrid simulation 

References

  1. 1.
    Ali Parsa, M., Kozhan, I., Wulkow, M., Hutchinson, R.A.: Modeling of functional group distribution in copolymerization: a comparison of deterministic and stochastic approaches. Macromol. Theory Simul. 23(3), 207–217 (2014)CrossRefGoogle Scholar
  2. 2.
    Anderson, D.F.: A modified next reaction method for simulating chemical systems with time dependent propensities and delays. J. Chem. Phys. 127(21), 214107 (2007)CrossRefGoogle Scholar
  3. 3.
    Bortolussi, L., Krüger, T., Lehr, T., Wolf, V.: Rule-based modelling and simulation of drug-administration policies. In: Proceedings of the Symposium on Modeling and Simulation in Medicine, pp. 53–60. Society for Computer Simulation International (2015)Google Scholar
  4. 4.
    Cao, Y., Gillespie, D.T., Petzold, L.R.: Accelerated stochastic simulation of the stiff enzyme-substrate reaction. J. Chem. Phys. 123(14), 144917 (2005)CrossRefGoogle Scholar
  5. 5.
    Cao, Y., Gillespie, D.T., Petzold, L.R.: The slow-scale stochastic simulation algorithm. J. Chem. Phys. 122(1), 014116 (2005)CrossRefGoogle Scholar
  6. 6.
    Craft, D.L., Wein, L.M., Selkoe, D.J.: A mathematical model of the impact of novel treatments on the a\(\beta \) burden in the Alzheimers brain, CSF and plasma. Bull. Math. Biol. 64(5), 1011–1031 (2002)CrossRefMATHGoogle Scholar
  7. 7.
    Crudu, A., Debussche, A., Radulescu, O.: Hybrid stochastic simplifications for multiscale gene networks. BMC Syst. Biol. 3(1), 1 (2009)CrossRefGoogle Scholar
  8. 8.
    Danos, V., Feret, J., Fontana, W., Harmer, R., Krivine, J.: Rule-based modelling of cellular signalling. In: Caires, L., Vasconcelos, V.T. (eds.) CONCUR 2007. LNCS, vol. 4703, pp. 17–41. Springer, Heidelberg (2007). doi:10.1007/978-3-540-74407-8_3 CrossRefGoogle Scholar
  9. 9.
    Danos, V., Feret, J., Fontana, W., Krivine, J.: Scalable simulation of cellular signaling networks. In: Shao, Z. (ed.) APLAS 2007. LNCS, vol. 4807, pp. 139–157. Springer, Heidelberg (2007). doi:10.1007/978-3-540-76637-7_10 CrossRefGoogle Scholar
  10. 10.
    Danos, V., Laneve, C.: Core formal molecular biology. In: Degano, P. (ed.) ESOP 2003. LNCS, vol. 2618, pp. 302–318. Springer, Heidelberg (2003). doi:10.1007/3-540-36575-3_21 CrossRefGoogle Scholar
  11. 11.
    Faeder, J.R., Blinov, M.L., Goldstein, B., Hlavacek, W.S.: Rule-based modeling of biochemical networks. Complexity 10(4), 22–41 (2005)CrossRefGoogle Scholar
  12. 12.
    Fehlberg, E.: Low-order classical runge-kutta formulas with stepsize control and their application to some heat transfer problems. Technical report, NASA TR R-315, National Aeronautics and Space Administration, Washington, D.C., July 1969Google Scholar
  13. 13.
    Gillespie, D.T.: Exact stochastic simulation of coupled chemical reactions. J. Phys. Chem. 81(25), 2340–2361 (1977)CrossRefGoogle Scholar
  14. 14.
    Gillespie, D.T.: Stochastic simulation of chemical kinetics. Annu. Rev. Phys. Chem. 58, 35–55 (2007)CrossRefGoogle Scholar
  15. 15.
    Goldstein, B., Perelson, A.S.: Equilibrium theory for the clustering of bivalent cell surface receptors by trivalent ligands. Biophys. J. 45(6), 1109 (1984)CrossRefGoogle Scholar
  16. 16.
    Helal, M., Hingant, E., Pujo-Menjouet, L., Webb, G.F.: Alzheimer’s disease: analysis of a mathematical model incorporating the role of prions. J. Math. Biol. 69(5), 1207–1235 (2014)MathSciNetCrossRefMATHGoogle Scholar
  17. 17.
    Herajy, M., Heiner, M.: Hybrid representation and simulation of stiff biochemical networks. Nonlinear Anal. Hybrid Syst. 6(4), 942–959 (2012)MathSciNetCrossRefMATHGoogle Scholar
  18. 18.
    Hogg, J.S., Harris, L.A., Stover, L.J., Nair, N.S., Faeder, J.R.: Exact hybrid particle/population simulation of rule-based models of biochemical systems. PLoS Comput. Biol. 10(4), e1003544 (2014)CrossRefGoogle Scholar
  19. 19.
    Kiparissides, C.: Polymerization reactor modeling: a review of recent developments and future directions. Chem. Eng. Sci. 51(10), 1637–1659 (1996)CrossRefGoogle Scholar
  20. 20.
    Lewis, P.A., Shedler, G.S.: Simulation of nonhomogeneous poisson processes by thinning. Naval Res. Logistics Q. 26(3), 403–413 (1979)MathSciNetCrossRefMATHGoogle Scholar
  21. 21.
    Mastan, E., Zhu, S.: Method of moments: a versatile tool for deterministic modeling of polymerization kinetics. Eur. Polym. J. 68, 139–160 (2015)CrossRefGoogle Scholar
  22. 22.
    Monine, M.I., Posner, R.G., Savage, P.B., Faeder, J.R., Hlavacek, W.S.: Modeling multivalent ligand-receptor interactions with steric constraints on configurations of cell-surface receptor aggregates. Biophys. J. 98(1), 48–56 (2010)CrossRefGoogle Scholar
  23. 23.
    Puchałka, J., Kierzek, A.M.: Bridging the gap between stochastic and deterministic regimes in the kinetic simulations of the biochemical reaction networks. Biophys. J. 86(3), 1357–1372 (2004)CrossRefGoogle Scholar
  24. 24.
    Roland, J., Berro, J., Michelot, A., Blanchoin, L., Martiel, J.L.: Stochastic severing of actin filaments by actin depolymerizing factor/cofilin controls the emergence of a steady dynamical regime. Biophys. J. 94(6), 2082–2094 (2008)CrossRefGoogle Scholar
  25. 25.
    Sneddon, M.W., Faeder, J.R., Emonet, T.: Efficient modeling, simulation and coarse-graining of biological complexity with NFsim. Nat. Methods 8(2), 177–183 (2011)CrossRefGoogle Scholar
  26. 26.
    Thanh, V.H., Priami, C.: Simulation of biochemical reactions with time-dependent rates by the rejection-based algorithm. J. Chem. Phys. 143(5), 054104 (2015)CrossRefGoogle Scholar
  27. 27.
    Van Steenberge, P., Dhooge, D., Reyniers, M.F., Marin, G.: Improved kinetic Monte Carlo simulation of chemical composition-chain length distributions in polymerization processes. Chem. Eng. Sci. 110, 185–199 (2014)CrossRefGoogle Scholar
  28. 28.
    Wolkenhauer, O., Ullah, M., Kolch, W., Cho, K.H.: Modeling and simulation of intracellular dynamics: choosing an appropriate framework. IEEE Trans. Nanobiosci. 3(3), 200–207 (2004)CrossRefGoogle Scholar
  29. 29.
    Wulkow, M.: Numerical treatment of countable systems of ordinary differential equations. Konrad-Zuse-Zentrum für Informationstechnik (1990)Google Scholar
  30. 30.
    Wulkow, M.: Computer aided modeling of polymer reaction engineeringthe status of predici, I-simulation. Macromol. React. Eng. 2(6), 461–494 (2008)MathSciNetCrossRefGoogle Scholar
  31. 31.
    Yang, J., Monine, M.I., Faeder, J.R., Hlavacek, W.S.: Kinetic Monte Carlo method for rule-based modeling of biochemical networks. Phys. Rev. E 78(3), 031910 (2008)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  1. 1.Modeling and Simulation GroupSaarland UniversitySaarbrückenGermany

Personalised recommendations