Perfect sampling of the master equation for gene regulatory networks

Biophysical Journal

Volumn 93, Issue 2, 2007, Pages 401-410

  Hemberg, Martin ^a   Barahona, Mauricio ^a  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHM; ARTICLE; DOMINATED COUPLING FROM THE PAST ALGORITHM; GENE CONTROL; STOCHASTIC MODEL;

EID: 34447336982     PISSN: 00063495     EISSN: None     Source Type: Journal    
DOI: 10.1529/biophysj.106.099390     Document Type: Article

References (56)

1. Acar, M., A. Becskei, and A. van Oudenaarden. 2005. Enhancement of cellular memory by reducing stochastic transitions. Nature. 435:228-232.
2. Austin, D., M. Allen, J. McCollum, R. Dar, J. Wilgus, G. Sayler, N. Samatova, C. Cox, and M. Simpson. 2006. Gene network shaping of inherent noise spectra. Nature. 439:608-611.
3. Beckskei, A., B. Séraphin, and L. Serrano. 2001. Positive feedback in eukaryotic gene networks: cell differentiation by graded to binary response conversion. EMBO J. 20:2528-2535.
4. Blake, W. J., M. Kaern, C. R. Cantor, and J. Collins. 2003. Noise in eukaryotic gene expression. Nature. 422:633-637.
5. Cai, L., N. Friedman, and X. S. Xie. 2006. Stochastic protein expression in individual cells at the single molecule level. Nature. 440:358-362.
6. Elowitz, M. B., and S. Leibler. 2000. A synthetic oscillatory network of transcriptional regulators. Nature. 403:335-339.
7. Fung, E., W. W. Wong, J. K. Suen, T. Butler, S. G. Lee, and J. C. Liao. 2005. A synthetic gene-metabolic oscillator. Nature. 435:118-122.
8. Gardner, T. S., C. R. Cantor, and J. J. Collins. 2000. Construction of a genetic toggle switch in Escherichia coli. Nature. 403:339-343.
9. Pedraza, J. M., and A. van Oudenaarden. 2005. Noise propagation in gene networks. Science. 307:1965-1969.
10. Volfson, D., J. Marciniak, W. J. Blake, N. Ostroff, L. S. Tsimring, and J. Hasty. 2006. Origins of extrinsic variability in eukaryotic gene expression. Nature. 439:861-864.
11. McAdams, H. H., and A. Arkin. 1997. Stochastic mechanisms in gene expression. Proc. Natl. Acad. Sci. USA. 94:814-819.
12. Elf, J., J. Paulsson, O. G. Berg, and M. Ehrenberg. 2003. Near-critical phenomena in intracellular metabolite pools. Biophys. J. 84:154-170.
13. van Kampen, N. G. 1992. Stochastic Processes in Physics and Chemistry, 2nd Ed. Elsevier, Dordrecht.
14. Bratsun, D., D. Volfson, L. S. Tsimring, and J. Hasty. 2005. Delay-induced stochastic oscillations in gene regulation. Proc. Natl. Acad. Sci. USA. 102:14593-14598.
15. Erban, R., I. G. Kevrekidis, D. Adalsteinsson, and T. C. Elston. 2006. Gene regulatory networks: a coarse-grained, equation-free approach to multiscale computation. J. Chem. Phys. 124:084106.
16. Hasty, J., J. Pradines, M. Dolnik, and J. J. Collins. 2000. Noise based switches and amplifiers for gene expression. Proc. Natl. Acad. Sci. USA. 97:2075-2080.
17. Kaern, M., T. C. Elston, W. J. Blake, and J. J. Collins. 2005. Stochasticity in gene expression: from theories to phenotypes. Nature Rev. 6:451-464.
18. Kepler, T. B., and T. C. Elston. 2001. Stochasticity in transcriptional regulation: origins, consequences and mathematical representations. Biophys. J. 81:3116-3136.
19. Paulsson, J. 2004. Summing up the noise in gene networks. Nature. 427:415-419.
20. Swain, P. S., and M. B. Elowitz. 2002. Intrinsic and extrinsic contributions to stochasticity in gene expression. Proc. Natl. Acad. Sci. USA. 99:12795-12800.
21. Thattai, M., and A. van Oudenaarden. 2001. Intrinsic noise in gene regulatory networks. Proc. Natl. Acad. Sci. USA. 98:8614-8619.
22. Elf, J., and M. Ehrenberg. 2003. Fast evaluation of fluctuations in biochemical networks with the linear noise approximation. Genome Res. 13:2475-2484.
23. Lai, K., M. J. Robertson, and D. Schaffer. 2004. The sonic hedgehog signaling system as a bistable genetic switch. Biophys. J. 86:2748-2757.
24. Samoilov, M., S. Plyasunov, and A. P. Arkin. 2005. Stochastic ampli-fication and signaling in enzymatic futile cycles through noise-induced bistability with oscillations. Proc. Natl. Acad. Sci. USA. 102:2310-2315.
25. Delbrück, M. 1940. Statistical fluctuations in autocatalytic reactions. J. Chem. Phys. 8:120-124.
26. McQuarrie, D. 1967. Stochastic approach to chemical kinetics. J. Appl. Probab. 4:413-478.
27. Paulsson, J. 2005. Models of stochastic gene expression. Phys. Life Rev. 2:157-175.
28. Gillespie, D. T. 1976. A general method for numerically simulating the stochastic time evolution of coupled chemical reactions. J. Comput. Phys. 22:403-434.
29. Doob, J. L. 1945. Markoff chains - denumerable case. Trans. Am. Math. Soc. 58:455-473.
30. Gillespie, D. T. 1992. A rigorous derivation of the chemical master equation. Physica A. 188:404-425.
31. Elf, J., and M. Ehrenberg. 2004. Spontaneous separation of bi-stable biochemical systems into spatial domains of opposite phases. IEE Sys. Biol. 1:230-236.
32. Stundzia, A. B., and C. J. Lumsden. 1996. Stochastic simulation of coupled reaction-diffusion processes. J. Comput. Phys. 127:196-207.
33. Cao, Y., D. T. Gillespie, and L. R. Petzold. 2006. Efficient step size selection for the τ-leaping simulation method. J. Chem. Phys. 124:044109.
34. Gibson, M. A., and J. Bruck. 2000. Efficient exact stochastic simulation of chemical systems with many species and many channels. J. Phys. Chem. A. 104:1876-1899.
35. Kummer, U., B. Krajnc, J. Pahle, A. K. Green, C. J. Dixon, and M. Marhl. 2005. Transition from stochastic to deterministic behavior in calcium oscillations. Biophys. J. 89:1603-1611.
36. Tomioka, R., H. Kimura, T. J. Kobayashi, and K. Aihara. 2004. Multivariate analysis of noise in genetic regulatory networks. J. Theor. Biol. 229:501-521.
37. Norris, J. R. 1999. Markov Chains. Cambridge University Press, Cambridge.
38. Propp, J. G., and D. B. Wilson. 1996. Exact sampling with coupled Markov chains and applications to statistical mechanics. Random Structures Algorithms. 9:223-252.
39. Kendall, W. S. 1997. Perfect simulation for spatial point processes. In Bulletin ISI, 51st Session Proceedings, Vol. 3. Istanbul.
40. Thönnes, E. 2000. A primer on perfect simulation. In Springer Lecture Notes in Physics, Vol. 554. K. R. Mecke and D. Stoyan, editors. Springer-Verlag, Berlin.
41. Häggström, O., and K. Nelander. 1998. Exact sampling from anti-monotone systems. Stat. Neerl. 52:360-380.
42. Gadgil, C., C.-H. Lee, and H. G. Othmer. 2005. A stochastic analysis of first-order reaction networks. Bull. Math. Biol. 67:901-946.
43. Shreider, Y. A. 1966. The Monte Carlo Method. Pergamon Press, New York.
44. Scott, M., B. Ingalls, and M. Kaern. 2006. Estimation of intrinsic and extrinsic noise in models of nonlinear genetic networks. Chaos. 16:026107.
45. Cornish-Bowden, A. 2004. Fundamentals of Enzyme Kinetics, 3rd Ed. Portland Press, London.
46. Xiong, W., and J. E. Ferrell, Jr. 2003. A positive-feedback-based bistable "memory module" that governs a cell fate decision. Nature. 426:460-465.
47. Chung, F. R. K. 1997. Spectral Graph Theory. CBMS Regional Conference Series in Mathematics, No. 92. American Mathematical Society, Providence, RI.
48. Craciun, G., Y. Tang, and M. Feinberg. 2006. Understanding bistability in complex enzyme-driven reaction networks. Proc. Natl. Acad. Sci. USA. 103:8697-8702.
49. Tomshine, J., and Y. N. Kaznessis. 2006. Optimization of a stochastically simulated gene network model via simulated annealing. Biophys. J. 91:3196-3205.
50. Fill, J. A., M. Machida, D. J. Murdoch, and J. S. Rosenthal. 2000. Extension of Fill's perfect rejection sampling algorithm to general chains. Random Struct. Algorithms. 9:223-252.
51. Widder, S., J. Schicho, and P. Schuster. 2005. Dynamic patterns of gene regulation I: simple two-gene systems. Http://www.santafe.edu/research/ publications/wpabstract/200603007.
52. Karlin, S., and J. McGregor. 1955. Representation of a class of stochastic processes. Proc. Natl. Acad. Sci. USA. 41:387-391.
53. Nikiforov, A. F., S. K. Suslov, and V. B. Uvarov. 1991. Classical Orthogonal Polynomials of a Discrete Variable. Springer-Verlag, Berlin.
54. Meixner, J. 1939. Erzeugende funktionen der Charlierschen polynome. Math. Z. 44:531-535.
55. Lee, P.-A. 1997. Markov processes and a multiple generating function of product of generalized Laguerre polynomials. J. Phys. A. 30:373-377.
56. Rosenfeld, N., M. B. Elowitz, and U. Alon. 2002. Negative autoregulation speeds up the response times of transcription networks. J. Mol. Biol. 323:785-793.