Algorithms and software for stochastic simulation of biochemical reacting systems

Biotechnology Progress

Volumn 24, Issue 1, 2008, Pages 56-61

  Li, Hong ^a   Cao, Yang ^b   Petzold, Linda R ^a   Gillespie, Daniel T ^c  

^a University of California   (United States)

^b State University   (United States)

^c Dan T Gillespie Consulting   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTER SIMULATION; COMPUTER SOFTWARE; RANDOM PROCESSES;

BIOCHEMICAL PROCESSES; BIOCHEMICAL REACTING SYSTEMS;

BIOTECHNOLOGY;

ALGORITHM; CHEMICAL MODEL; COMPUTER PROGRAM; COMPUTER SIMULATION; CONFERENCE PAPER;

ALGORITHMS; COMPUTER SIMULATION; MODELS, CHEMICAL; SOFTWARE;

EID: 38949164415     PISSN: 87567938     EISSN: None     Source Type: Journal    
DOI: 10.1021/bp070255h     Document Type: Conference Paper

References (56)

1. Gillespie, D. T. A general method for numerically simulating the stochastic time evolution of coupled chemical reactions. J. Comp. Phys. 1976, 22, 403-434.
2. Gillespie, D. T. Exact stochastic simulation of coupled chemical reactions. J. Phys. Chem. 1977, 81, 2340-2361.
3. McAdams, H. H.; Arkin, A. Stochastic mechanisms in gene expression. Proc. Natl. Acad. Sci. U.S.A. 1997, 94, 814-819.
4. Arkin, A.; Ross, J.; McAdams, H. H. Stochastic kinetic analysis of developmental pathway bifurcation in phage λ-infected E. Coli cells. Genetics 1998, 149, 1633-1648.
5. Gibson, M.; Bruck, J. Efficient exact stochastic simulation of chemical systems with many species and many channels. J. Phys. Chem. 2000, 105, 1876-1889.
6. Cao, Y.; Li, H.; Petzold, L. Efficient formulation of the stochastic simulation algorithm for chemically reacting systems. J. Phys. Chem. 2004, 121(9), 4059-4067.
7. McColluma, J. M.; Peterson, G. D.; Cox, C. D.; Simpson, M. L.; Samatova, N. F. The sorting direct method for stochastic simulation of biochemical systems with varying reaction execution behavior. J. Comput. Biol. Chem. 2005, 30, 39-49.
8. Blue, J.; Beichl, I.; Sullivan, F. Faster Monte Carlo simulations. Phys. Rev. E 1995, 51, 867-868.
9. Li, H.; Petzold, L. Logarithmic direct method for discrete stochastic simulation of chemically reacting systems. Technical report; Department of Computer Science, University of California: Santa Barbara, 2006. http://www.engr.ucsb.edu/_cse.
10. StochKit Team. User's Guide for StochKit. http://www.engr.ucsb. edu/_cse.
11. Li, H.; Petzold, L. Efficient parallelization of stochastic simulation algorithm for chemically reacting systems on the graphics processing unit. In preparation.
12. Yoshimi, M.; Osana, Y.; Iwaoka, Y.; Funahashi, A.; Hiroi, N.; Shibata, Y.; lwanaga, N.; Kitano, H.; Amano, H. The design of a scalable stochastic biochemical simulator on FPGA. Proc. I. C. Field Programmable Technol. 2005, 139-140.
13. Gillespie, D. T. Approximate accelerated stochastic simulation of chemically reacting systems. J. Chem. Phys. 2001, 115(4), 1716-1733.
14. Gillespie, D. T. The chemical Langevin equation. J. Chem. Phys. 2000, 113, 297-306.
15. Cao, Y.; Gillespie, D.; Petzold, L. Efficient stepsize selection for the tau-leaping method. J. Chem. Phys. 2006, 124, 044109.
16. Cao, Y.; Gillespie, D.; Petzold, L. Avoiding negative populations in explicit tau leaping. J. Chem. Phys. 2005, 123, 054104-054112.
17. Rathinam, M.; Cao, Y.; Petzold, L. R.; Gillespie, D. T. Stiffness in stochastic chemically reacting systems: The implicit tau-leaping method. J. Chem. Phys. 2003.
18. Cao, Y.; Petzold, L. Trapezoidal tau-leaping formula for the stochastic simulation of biochemical systems. Proc. Found. Syst. Biol. Eng. 2005, 149-152.
19. Cao, Y.; Gillespie, D.; Petzold, L. The adaptive explicit-implicit tau-leaping method with automatic tau selection. J. Chem. Phys. 2007, 126(22), 224101-224109.
20. Haseltine, E. L.; Rawlings, J. B. Approximate simulation of coupled fast and slow reactions for stochastic chemical kinetics. J. Chem. Phys. 2002, 117(15), 6959-6969.
21. Salis, H.; Kaznessis, Y. Accurate hybrid stochastic simulation of a system of coupled chemical or biochemical reactions. J. Chem. Phys. 2005, 122(5), 54103.
22. Adalsteinsson, D.; Erban, R.; Kevrekidis, I.; Elston, T. Gene regulatory networks: a coarse-grained, equation-free approach to multiscale computation. J. Chem. Phys. 2006, 124(17), 084106.
23. Chatterjee, A.; Vlachos, D. G. Multiscale spatial Monte Carlo simulations: Multigridding, computational singular perturbation, and hierarchical stochastic closures. J. Chem. Phys. 2006, 124(6), 64110.
24. Kaznessis, Y. Multi-scale models for gene networks. Chem. Eng. Sci. 2006, 61(3), 940.
25. Rao, C.; Arkin, A. Stochastic chemical kinetics and the quasi steady-state assumption: application to the Gillespie algorithm. J. Chem. Phys. 2003, 118, 4999-5010.
26. Cao, Y.; Gillespie, D.; Petzold, L. The slow-scale stochastic simulation algorithm. J. Chem. Phys. 2005, 122, 014116.
27. Goutsias, J. Quasiequilibrium approximation of fast reaction kinetics in stochastic biochemical systems. J. Chem. Phys. 2005, 122(18), 184102.
28. Cao, Y.; Gillespie, D.; Petzold, L. Multiscale stochastic simulation algorithm with stochastic partial equilibrium assumption for chemically reacting systems. J. Comp. Phys. 2005, 206(2), 395-411.
29. Samant, A.; Vlachos, D. G. Overcoming stiffness in stochastic simulation stemming from partial equilibrium: A multiscale Monte Carlo algorithm. J. Chem. Phys. 2005, 123.
30. Cao, Y.; Gillespie, D. T.; Petzold, L. R. Accelerated stochastic simulation of the stiff enzyme-substrate reaction. J. Chem. Phys. 2005, 123.
31. Haseltine, E. L.; Rawlings, J. B. On the origins of approximations for stochastic chemical kinetics. J. Chem. Phys. 2005, 123.
32. Liu, D. W. E.; Vanden-Eijnden, E. Nested stochastic simulation algorithm for chemical kinetic systems with disparate rates. J. Chem. Phys. 2005, 123.
33. Salis, H.; Kaznessis, Y. An equation-free probabilistic steady-state approximation: dynamic application to the stochastic simulation of biochemical reaction networks. J. Chem. Phys. 2005, 123(21), 214106.
34. Gillespie, D.; Petzold, L.; Cao, Y. Comment on nested stochastic simulation algorithm for chemical kinetic systems with disparate rates [J. Chem. Phys. 2005, 123, 194107]. J. Chem. Phys. 2007, 126, 137101.
35. Ribeiro, A.; Lloyd-Price, J. SGN Sim, a Stochastic Genetic Networks Simulator. Bioinformatics 2007, 23, 777-779.
36. Ramsey, S.; Orrell, D. H. Bolouri. Dizzy: Stochastic simulation of large-scale genetic regulatory networks. J. Bioinformatics Comput. Biol. 2005, 3, 415-436.
37. Salis, H.; Sotiropoulos, V.; Kaznessis, Y. Multiscale Hy3S: Hybrid stochastic simulation for supercomputers. BMC Bioinformatics 2006, 7, 93.
38. Adalsteinsson, D.; McMillen, D.; Elston, T. Biochemical Network Stochastic Simulator (BioNetS): software for stochastic modeling of biochemical networks. BMC Bioinformatics 2004, 5, 24.
39. Message Passing Interface (MPI) Tutorial (http://www.llnl.gov/ computing/tutorials/mpi/).
40. Mascagni, M. SPRNG: A scalable library for pseudorandom number generation. In Proceedings of the Ninth SIAM Conference on Parallel Processing for Scientific Computing, San Antonio, Texas, 1999.
41. Mascagni, M.; Srinivasan, A. SPRNG: A scalable library for pseudorandom number generation. ACM Trans. Math. Software 2000, 26, 436-461.
42. Brown, B.; Lovato, W. J.; Russell, K. RANLIB.C Library of C Routines for Random Number Generation. M.D. Anderson Cancer Center, The University of Texas: Houston, 1991.
43. Hucka, M.; Finney, A.; Sauro, H. M.; Bolouri, H.; Doyle, J. C.; Kitano, H. The Systems Biology markup Language (SBML): a medium for representation and exchange of biochemical network models. Bioinformatics 2003, 19(4), 524-531.
44. Cao, Y.; Petzold, L. Accuracy limitations and the measurement of errors in the stochastic simulation of chemically reacting systems. J. Comput. Phys. 2006, 212, 6-24.
45. Schlögl, F. On thermodynamics near a steady state. Zeitschirft Phys. 1971, 248, 446-458.
46. Gillespie, D. Markov Processes: An Introduction for Physical Scientists; Academic Press: New York, 1992.
47. Rathinam, M.; Petzold, L.; Cao, Y.; Gillespie, D. Consistency and stability of tau leaping schemes for chemical reaction systems. SIAM Multiscale Model. 2005, 4, 867-895.
48. Cao, Y.; Petzold, L.; Rathinam, M.; Gillespie, D. The numerical stability of leaping methods for stochastic simulation of chemically reacting systems. J. Chem. Phys. 2004, 121(24), 12169-12178.
49. Gunawan, R.; Cao, Y.; Petzold, L.; Doyle, F. J., III. Sensitivity analysis of discrete stochastic systems. J. Biophys. 2005, 88, 2530-2540.
50. Kim, D.; Debusschere, B. J.; Najm, H. N. Spectral methods for parametric sensitivity in stochastic dynamical systems. J. Biophys. 2007, 92, 379-393.
51. Kurata, H.; El-Samad, H.; Yi, T.; Khammash, M.; Doyle, J. Feedback regulation of the heat shock response in E. Coli. Proceedings of the 40th IEEE conference on Decision and Control, 2001, 1, 837-842.
52. Kurata, H.; Khammash, M.; Doyle, J. Stochastic analysis of the heat shock response in E. Coli. In 3rd International Conference on Systems Biology; Stockholm, Sweden, 2002.
53. Tyson, J. J.; Novak, B. Regulation of the eukaryotic cell cycle: Molecular antagonism, hysteresis, and irreversible transitions. J. Theor. Biol. 2001.
54. Vass, M.; Allen, N.; Shaffer, C. A.; Ramakrishnan, N.; Watson, L. T.; Tyson, J. J. The Jigcell model builder and run manager. Bioinformatics 2004, 18, 3680-3681.
55. Tyson, J. J. Personal communication.
56. Cao, Y.; Petzold, L. Slow scale tau-leaping method. Submitted.