Adaptive hybrid simulations for multiscale stochastic reaction networks

Journal of Chemical Physics

Volumn 142, Issue 3, 2015, Pages

  Hepp, Benjamin ^a   Gupta, Ankit ^a   Khammash, Mustafa ^a  

^a ETH ZURICH   (Switzerland)

Author keywords

[No Author keywords available]

Indexed keywords

MONTE CARLO METHODS; RANDOM PROCESSES; STOCHASTIC MODELS; STOCHASTIC SYSTEMS;

CHEMICAL MASTER EQUATION; COMPUTATIONAL TIME; HYBRID SIMULATION; OSCILLATORY DYNAMICS; QUASI-STATIONARY; STOCHASTIC SIMULATION ALGORITHMS; TIME SCALE SEPARATION; USER INTERVENTION;

PROBABILITY DISTRIBUTIONS;

ALGORITHM; AUTOMATED PATTERN RECOGNITION; CHEMICAL MODEL; COMPARATIVE STUDY; COMPUTER SIMULATION; COPY NUMBER VARIATION; DIMERIZATION; PERIODICITY; PROBABILITY; STATISTICS;

ALGORITHMS; COMPUTER SIMULATION; DIMERIZATION; DNA COPY NUMBER VARIATIONS; MODELS, CHEMICAL; PATTERN RECOGNITION, AUTOMATED; PERIODICITY; PROBABILITY; STOCHASTIC PROCESSES;

EID: 84923816631     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.4905196     Document Type: Article

References (46)

1. J. Goutsias, " Classical versus stochastic kinetics modeling of biochemical reaction systems," Biophys. J. 92 (7), 2350-2365 (2007). 10.1529/biophysj.106.093781
2. H. H. McAdams and A. Arkin, " Stochastic mechanisms in gene expression," Proc. Natl. Acad. Sci. U. S. A. 94 (3), 814-819 (1997). 10.1073/pnas.94.3.814
3. B. Munsky, A. Hernday, D. Low, and M. Khammash, " Stochastic modeling of the pap-pili epigenetic switch," in Proc. FOSBE (2005), pp. 145-148.
4. D. Fange and J. Elf, " Noise-induced Min phenotypes in E. coli," PLoS Comput. Biol. 2 (6), e80 (2006). 10.1371/journal.pcbi.0020080
5. T. S. Gardner, C. R. Cantor, and J. J. Collins, " Construction of a genetic toggle switch in Escherichia coli," Nature 403, 339-342 (2000). 10.1038/35002131
6. M. B. Elowitz and S. Leibler, " A synthetic oscillatory network of transcriptional regulators," Nature 403 (6767), 335-338 (2000). 10.1038/35002125
7. J. Goutsias and G. Jenkinson, " Markovian dynamics on complex reaction networks," Phys. Rep. 529, 199 (2013). 10.1016/j.physrep.2013.03.004
8. B. Munsky and M. Khammash, " The finite state projection algorithm for the solution of the chemical master equation," J. Chem. Phys. 124, 044104 (2006). 10.1063/1.2145882
9. V. Kazeev, M. Khammash, M. Nip, and C. Schwab, " Direct solution of the Chemical Master Equation using quantized tensor trains," PLoS Comput. Biol. 10, e1003359 (2014). 10.1371/journal.pcbi.1003359
10. D. T. Gillespie, " Stochastic simulation of chemical kinetics," Annu. Rev. Phys. Chem. 58, 35-55 (2007). 10.1146/annurev.physchem.58.032806.104637
11. W. E, D. Liu, and E. Vanden-Eijnden, " Nested stochastic simulation algorithm for chemical kinetic systems with disparate rates," J. Chem. Phys. 123, 194107 (2005). 10.1063/1.2109987
12. Y. Cao, D. T. Gillespie, and L. R. Petzold, " The slow-scale stochastic simulation algorithm," J. Chem. Phys. 122, 14116 (2005). 10.1063/1.1824902
13. D. T. Gillespie, " Approximate accelerated stochastic simulation of chemically reacting systems," J. Chem. Phys. 115, 1716 (2001). 10.1063/1.1378322
14. Y. Cao, D. T. Gillespie, and L. R. Petzold, " Efficient step size selection for the tau-leaping simulation method," J. Chem. Phys. 124, 044109 (2006). 10.1063/1.2159468
15. Y. Cao, D. T. Gillespie, and L. R. Petzold, " Adaptive explicit-implicit tau-leaping method with automatic tau selection," J. Chem. Phys. 126 (22), 224101 (2007). 10.1063/1.2745299
16. M. Rathinam, L. R. Petzold, Y. Cao, and D. T. Gillespie, " Stiffness in stochastic chemically reacting systems: The implicit tau-leaping method," J. Chem. Phys. 119, 12784 (2003). 10.1063/1.1627296
17. T. G. Kurtz, " Strong approximation theorems for density dependent Markov chains," Stochastic Processes Appl. 6 (3), 223-240 (1978). 10.1016/0304-4149(78)90020-0
18. H.-W. Kang and T. G. Kurtz, " Separation of time-scales and model reduction for stochastic reaction networks," Ann. Appl. Probab. 23 (2), 529-583 (2013). 10.1214/12-AAP841
19. A. Crudu, A. Debussche, and O. Radulescu, " Hybrid stochastic simplifications for multiscale gene networks," BMC Syst. Biol. 3 (1), 89 (2009). 10.1186/1752-0509-3-89
20. M. H. Davis, " Piecewise-deterministic Markov processes: A general class of non-diffusion stochastic models," J. R. Stat. Soc. Ser. B (Methodological), 46, 353-388 (1984).
21. E. L. Haseltine and J. B. Rawlings, " Approximate simulation of coupled fast and slow reactions for stochastic chemical kinetics," J. Chem. Phys. 117 (15), 6959-6969 (2002). 10.1063/1.1505860
22. N. A. Neogi, " Dynamic partitioning of large discrete event biological systems for hybrid simulation and analysis," in Hybrid Systems: Computation and Control (Springer, 2004), pp. 463-476.
23. M. Bentele and R. Eils, " General stochastic hybrid method for the simulation of chemical reaction processes in cells," in Computational Methods in Systems Biology (Springer, 2005), pp. 248-251.
24. H. Salis and Y. Kaznessis, " Accurate hybrid stochastic simulation of a system of coupled chemical or biochemical reactions," J. Chem. Phys. 122, 054103 (2005). 10.1063/1.1835951
25. A. Crudu, A. Debussche, A. Muller, and O. Radulescu, " Convergence of stochastic gene networks to hybrid piecewise deterministic processes," Ann. Appl. Probab. 22 (5), 1822-1859 (2012). 10.1214/11-AAP814
26. A. Alfonsi, E. Cancès, G. Turinici, B. Di Ventura, and W. Huisinga, " Adaptive simulation of hybrid stochastic and deterministic models for biochemical systems," in ESAIM: Proceedings (EDP Sciences, 2005), Vol. 14, pp. 1-13.
27. S. Hoops, R. Gauges, C. Lee, J. Pahle, N. Simus, M. Singhal, L. Xu, P. Mendes, and U. Kummer, " COPASI-A COmplex PAthway SImulator," Bioinformatics 22, 3067-3074 (2006). 10.1093/bioinformatics/btl485
28. M. Griffith, T. Courtney, J. Peccoud, and W. H. Sanders, " Dynamic partitioning for hybrid simulation of the bistable HIV-1 transactivation network," Bioinformatics 22, 2782-2789 (2006). 10.1093/bioinformatics/btl465
29. J. Puchałka and A. M. Kierzek, " Bridging the gap between stochastic and deterministic regimes in the kinetic simulations of the biochemical reaction networks," Biophys. J. 86, 1357-1372 (2004). 10.1016/S0006-3495(04)74207-1
30. K. Burrage, T. Tian, and P. Burrage, " A multi-scaled approach for simulating chemical reaction systems," Prog. Biophys. Mol. Biol. 85 (2-3), 217-234 (2004). 10.1016/j.pbiomolbio.2004.01.014
31. L. A. Harris and P. Clancy, " A "partitioned leaping" approach for multiscale modeling of chemical reaction dynamics," J. Chem. Phys. 125, 144107 (2006). 10.1063/1.2354085
32. J. R. Chubb, T. Trcek, S. M. Shenoy, and R. H. Singer, " Transcriptional pulsing of a developmental gene," Curr. Biol. 16 (10), 1018-1025 (2006). 10.1016/j.cub.2006.03.092
33. J. Pahle, " Biochemical simulations: Stochastic, approximate stochastic and hybrid approaches," Briefings Bioinf. 10, 53-64 (2009). 10.1093/bib/bbn050
34. C. V. Rao and A. P. Arkin, " Stochastic chemical kinetics and the quasi-steady-state assumption: Application to the Gillespie algorithm," J. Chem. Phys. 118 (11), 4999 (2003). 10.1063/1.1545446
35. IUPAC Compendium of Chemical Terminology, (the Gold Book), 2nd ed., edited by A. D. McNaught and A. Wilkinson (Blackwell Scientific Publications, Oxford, 1997), ISBN 0-9678550-9-8; XML on-line corrected version: http://goldbook.iupac.org (2006-), created by M. Nic, J. Jirat, B. Kosata, updates compiled by A. Jenkins. 10.1351/goldbook
36. D. T. Gillespie, " A diffusional bimolecular propensity function," J. Chem. Phys. 131 (16), 164109 (2009). 10.1063/1.3253798
37. S. N. Ethier and T. G. Kurtz, Markov Processes: Characterization and Convergence (Wiley, 2009), Vol. 282.
38. S. Peleš, B. Munsky, and M. Khammash, " Reduction and solution of the chemical master equation using time scale separation and finite state projection," J. Chem. Phys. 125 (20), 204104 (2006). 10.1063/1.2397685
39. O. Radulescu, A. N. Gorban, A. Zinovyev, and A. Lilienbaum, " Robust simplifications of multiscale biochemical networks," BMC Syst. Biol. 2 (1), 86 (2008). 10.1186/1752-0509-2-86
40. See supplementary material at http://dx.doi.org/10.1063/1.4905196 E-JCPSA6-142-030502 for a software implementation of the proposed method.
41. The implementation allows different ODE solvers to be used. However, for the examples we used the Dormand-Prince 5 stepper from the boost odeint library (http://www.boost.org/). The boost odeint library is coupled to our implementation via a Java Native Interface wrapper.
42. J. Elf and M. Ehrenberg, " Spontaneous separation of bi-stable biochemical systems into spatial domains of opposite phases," Syst. Biol. 1 (2), 230-236 (2004). 10.1049/sb:20045021
43. E. Seneta, Non-Negative Matrices and Markov Chains, Springer Series in Statistics (Springer, 2006).
44. D. F. Anderson, G. Craciun, and T. G. Kurtz, " Product-form stationary distributions for deficiency zero chemical reaction networks," Bull. Math. Biol. 72 (8), 1947-1970 (2010). 10.1007/s11538-010-9517-4
45. A. Gupta and M. Khammash, " Determining the long-term behavior of cell populations: A new procedure for detecting ergodicity in large stochastic reaction networks," in Proceedings of the 19th IFAC World Congress, 2014 (IFAC, 2014), Vol. 19, pp. 1711-1716. 10.3182/20140824-6-ZA-1003.00291
46. J. R. Baxter and R. V. Chacon, " Compactness of stopping times," Probab. Theory Relat. Fields 40 (3), 169-181 (1977). 10.1007/bf00736045