Multiscale modeling of chemical kinetics via the master equation

Multiscale Modeling and Simulation

Volumn 6, Issue 4, 2007, Pages 1146-1168

  Macnamara, Shev ^a   Burrage, Kevin ^a   Sidje, Roger B ^a  

^a UNIVERSITY OF QUEENSLAND   (Australia)

Author keywords

Chemical master equation; Stochastic simulation algorithm; Systems biology

Indexed keywords

APPROXIMATION ALGORITHMS; DIRECT NUMERICAL SIMULATION; MODEL STRUCTURES; NUMERICAL METHODS; OLIGOMERIZATION; STOCHASTIC CONTROL SYSTEMS; SYSTEMS ANALYSIS; TRANSCRIPTION;

BIOLOGICALLY INSPIRED; CHEMICAL KINETICS; CHEMICAL MASTER EQUATION; CHEMICAL MASTER EQUATIONS; DIRECT SOLUTIONS; FINITE STATES; HYBRID METHODS; IMPROVED PERFORMANCES; MASTER EQUATIONS; MULTISCALE MODELING; NEW APPROACHES; PROJECTION ALGORITHMS; REGULATED GENES; STOCHASTIC SIMULATION ALGORITHM; STOCHASTIC SIMULATION ALGORITHMS; SYSTEMS BIOLOGY; TEST SUITES;

STOCHASTIC MODELS;

EID: 49749098924     PISSN: 15403459     EISSN: 15403467     Source Type: Journal    
DOI: 10.1137/060678154     Document Type: Article

References (37)

1. T. ALARCÓN and K. M. PAGE, Stochastic models of receptor oligomerisation by bivalent ligand, J. R. Soc. Lond. Interface, 3 (2006), pp. 545-559.
2. A. ARKIN, J. ROSS, and H. MCADAMS, Stochastic kinetic analysis of developmental pathway bifurcation in phage lambda-infected Escherichia coli cells, Genetics, 149 (1998), pp. 1633-1648.
3. W. J. BLAKE, M. KæRN, C. R. CANTOR, and J. J. COLLINS, Noise in eukaryotic gene expression, Nature, 422 (2003), pp. 633-637.
4. A. BOURAS and V. FRAYSSÉ, Inexact matrix-vector products in Krylov methods for solving linear systems: A relaxation strategy, SIAM J. Matrix Anal. Appl., 26 (2005), pp. 660-678.
5. K. BURRAGE, Parallel and Sequential Methods for Ordinary Differential Equations, Oxford University Press, Oxford, UK, 1995.
6. K. BURRAGE, M. HEGLAND, S. MACNAMARA, and R. B. SIDJE, A Krylov-based finite state projection algorithm for solving the chemical master equation arising in the discrete modelling of biological systems, in 150th Markov Anniversary Meeting (Charleston, SC), A. N. Langville and W. J. Stewart, eds., Boson Books, Raleigh, NC, 2006, pp. 21-38.
7. K. BURRAGE, S. MAC, and T. TIAN, Accelerated leap methods for simulating discrete stochastic chemical kinetics, in Positive Systems, Lecture Notes in Control and Inform. Sci. 341, Springer-Verlag, Berlin, 2006, pp. 359-366.
8. K. BURRAGE, T. TIAN, and P. BURRAGE, A multi-scaled approach for simulating chemical reaction systems, Prog. Biophys. Mol. Biol., 85 (2004), pp. 217-234.
9. H. de JONG, Modeling and simulation of genetic regulatory systems: A literature review, J. Comput. Biol., 9 (2002), pp. 67-103.
10. M. EHRENBER, J. ELF, E. AURELL, R. SANDBERG, and J. TEGNER, Systems biology is taking off, Genome Res., 13 (2003), pp. 2377-2380.
11. M. B. ELOWITZ, M. G. SURETTE, P. E. WOLF, J. B. STOCK, and S. LEIBLER, Protein mobility in the cytoplasm of escherichia coli, J. Bacteriol., 181 (1999), pp. 197-203.
12. S. ENGBLOM, Numerical Methods for the Chemical Master Equation, Ph.D. thesis, Uppsala University, Uppsala, Sweden, 2006.
13. N. FEDEROFF and W. FONTANA, Small numbers of big molecules, Science, 297 (2002), pp. 1129-1131.
14. T. S. GARDNER, C. R. CANTOR, and J. J. COLLINS, Construction of a genetic toggle switch in Escherichia coli, Nature, 403 (2000), pp. 339-342.
15. D. T. GILLESPIE, Exact stochastic simulation of coupled chemical reactions, J. Phys. Chem., 81 (1977), pp. 2340-2361.
16. D. T. GILLESPIE. Markov Processes: An Introduction for Physical Scientists, Academic Press, Boston, MA, 1992.
17. D. T. GILLESPIE, Approximate accelerated stochastic simulation of chemically reacting systems, J. Chem. Phys., 115 (2001), pp. 1716-1733.
18. D. T. GILLESPIE and L. R. PETZOLD, Improved leap-size selection for accelerated stochastic simulation, J. Chem. Phys., 119 (2003), pp. 8229-8234.
19. J. GOUTSIAS, Quasiequilibrium approximation of fast reaction kinetics in stochastic biochemical systems, J. Chem. Phys., 122 (2005), 184102.
20. E. L. HASELTINE and J. B. RAWLINGS, Approximate simulation of coupled fast and slow reactions for stochastic chemical kinetics, J. Chem. Phys., 117 (2002), pp. 6959-6969.
21. T. KATO, Perturbation Theory for Linear Operators, Springer-Verlag, Berlin, New York, 1976.
22. P. LÖTSTEDT and L. FERM, Dimensional reduction of the Fokker-Planck equation for stochastic chemical reactions, Multiscale Model. Simul., 5 (2006), pp. 593-614.
23. S. F. MACNAMARA, R. B. SIDJE, and K. BURRAGE, An improved dynamic finite state projection algorithm for the numerical solution of the chemical master equation with applications, in Computational Techniques and Applications Conference, James Cook University, Townsville, Australia, 2006, submitted.
24. C. MOLER and C. VAN LOAN. Nineteen dubious ways to compute the exponential of a matrix, twenty-five years later, SIAM Rev., 45 (2003), pp. 3-49.
25. B. MUNSKY and M. KHAMMASH, The finite state projection algorithm for the solution of the chemical master equation, J. Chem. Phys., 124 (2006), 044104.
26. J. R. NORRIS, Markov Chains, Cambridge University Press, Cambridge, UK, 1997.
27. 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 (2006), 204104.
28. M. RATHINAM, L. R. PETZOLD, Y. CAO, and D. T. GILLESPIE, Consistency and stability of tau-leaping schemes for chemical reaction systems, Multiscale Model. Simul., 4 (2005), pp. 867-895.
29. 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 (2003), pp. 12784-12794.
30. R. B. SIDJE, Expokit: A software package for computing matrix exponentials, ACM Trans. Math. Software, 24 (1998), pp. 130-156.
31. R. B. SIDJE and W. J. STEWART, A numerical study of large sparse matrix exponentials arising in Markov chains, Comput. Statist. Data Anal., 29 (1999), pp. 345-368.
32. V. SIMONCINI and D. B. SZYLD, Theory of inexact Krylov subspace methods and applications to scientific computing, SIAM J. Sci. Comput., 25 (2003), pp. 454-477.
33. W. J. STEWART, Introduction to the Numerical Solution of Markov Chains, Princeton University Press, Princeton, NJ, 1994.
34. T. TIAN and K. BURRAGE, Binomial leap methods for simulating stochastic chemical kinetics, J. Chem. Phys., 121 (2004), pp. 10356-10364.
35. T. TIAN and K. BURRAGE, Bistability and switching in the lysis/lysogeny genetic regulatory network of bacteriophage lambda, J. Theoret. Biol., 227 (2004), pp. 229-237.
36. T. TIAN and K. BURRAGE, Stochastic models for regulatory networks of the genetic toggle switch, Proc. Natl. Acad. Sci. USA, 103 (2006), pp. 8372-8377.
37. N. G. van KAMPEN, Stochastic Processes in Physics and Chemistry, North-Holland, Amsterdam, 2001.