Simulation of genetic networks modelled by piecewise deterministic Markov processes

IET Systems Biology

Volumn 2, Issue 3, 2008, Pages 113-135

  Zeiser, S ^a   Franz, U ^b   Wittich, O ^c   Liebscher, V ^d  

^a INSTITUTE OF EPIDEMIOLOGY   (Germany)

^b UNIVERSITÉ DE FRANCHE COMTÉ   (France)

^c EINDHOVEN UNIVERSITY OF TECHNOLOGY   (Netherlands)

^d UNIVERSITY OF GREIFSWALD   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; MARKOV PROCESSES; NUMERICAL ANALYSIS; PIECEWISE LINEAR TECHNIQUES;

GENE REGULATORY NETWORKS; MESOSCOPIC NATURE;

GENES;

MESSENGER RNA;

ALGORITHM; ARTICLE; CONTROLLED STUDY; GENE EXPRESSION; GENE NUMBER; GENE REGULATORY NETWORK; GENE REPRESSION; GENETIC TRANSCRIPTION; HYBRID; MATHEMATICAL ANALYSIS; NONHUMAN; POSITIVE FEEDBACK; PROBABILITY; PROMOTER REGION; SENSITIVITY ANALYSIS; SIGNAL NOISE RATIO; SIMULATION; STOCHASTIC MODEL; SYSTEMS BIOLOGY;

ALGORITHMS; ANIMALS; CATALYSIS; COMPUTER SIMULATION; FEEDBACK, BIOCHEMICAL; GENE EXPRESSION REGULATION; GENE REGULATORY NETWORKS; GENES, SWITCH; HUMANS; MARKOV CHAINS; MODELS, BIOLOGICAL; NONLINEAR DYNAMICS; PROMOTER REGIONS (GENETICS); SYSTEMS BIOLOGY;

EID: 44949139699     PISSN: 17518849     EISSN: None     Source Type: Journal    
DOI: 10.1049/iet-syb:20070045     Document Type: Article

References (35)

1. McAdams, H.H., and Arkin, A.: 'Stochastic mechanisms in gene expression', Proc. Natl. Acad. Sci. USA, 1997, 94, p. 814-819 0027-8424
2. Arkin, A., Ross, J., and McAdams, H.H.: 'Stochastic kinetic analysis of developmental pathway bifurcation in phage-lambda infected Escherichia coli cells', Genetics, 1998, 149, p. 1633-1648
3. Elowitz, M.B., Levine, A.J., Siggia, E.D., and Swain, P.S.: 'Stochastic gene expression in a single cell', Science, 2002, 297, p. 1183-1186 0036-8075
4. Hume, D.A.: 'Probability in transcriptional regulation and its implications for leukocyte differentiation and inducible gene expression', Blood, 2000, 96, p. 2323-2328
5. Blake, W.J., Kærn, M., Cantor, C.R., and Collins, J.J.: 'Noise in eukaryotic gene expression', Nature, 2003, 422, p. 633637 0028-0836
6. Raj, A., Peskin, C.S., Tranchina, D., Vargas, D.Y., and Tyagi, S.: 'Stochastic mRNA synthesis in mammalian cells', PLoS Biol., 2006, 4, p. 1707-1719
7. Gillespie, D.T.: 'A general method for numerically simulating the stochastic time evolution of coupled chemical reactions', J. Comput. Phys., 1976, 22, p. 403-434 0021-9991
8. Gillespie, D.T.: 'Exact stochastic simulation of coupled chemical reactions', J. Phys. Chem., 1977, 81, p. 2340-2361 0022-3654
9. Gibson, M.A., and Bruck, J.: 'Efficient exact stochastic simulation of chemical systems with many species and many channels', J. Phys. Chem. A, 2000, 104, p. 1876-1889 1089-5639
10. Gillespie, D.T., and Petzold, L.R.: 'Improved leap-size selection for accelerated stochastic simulation', J. Chem. Phys., 2003, 119, p. 8229-8234 0021-9606
11. Griffith, M., Courtney, T., Peccoud, J., and Sanders, W.H.: 'Dynamic partitioning for hybrid simulation of the bistable HIV-1 transactivation network', Bioinformatics, 2006, 22, p. 2782-2789
12. Haseltine, E.L., and Rawlings, J.B.: 'Approximate simulation of coupled fast and slow reactions for stochastic chemical kinetics', J. Chem. Phys., 2002, 117, p. 6959-6969 0021-9606
13. Kiehl, T.R., Mattheyses, R.M., and Simmons, M.K.: 'Hybrid simulation of cellular behavior', Bioinformatics, 2004, 20, p. 316-322
14. Davis, M.H.A.: 'Piecewise-deterministAc Markov processes: a general class of non-diffusion stochastic models', J. R. Statist. Soc. B, 1984, 46, p. 353-388
15. Gillespie, D.T.: 'Approximate accelerated stochastic simulation of chemically reacting systems', J. Chem. Phys., 2001, 115, p. 1716-1733 0021-9606
16. Puchalka, J., and Kierzek, A.M.: 'Bridging the gap between stochastic and deterministic regimes in the kinetic simulations of the biochemical reaction networks', Biophys. J., 2004, 86, p. 1357-1372 0006-3495
17. Salis, H., and Kaznessis, Y.: 'Accurate hybrid stochastic simulation of a system of coupled chemical or biochemical reactions', J. Chem. Phys., 2005, 122, p. 054103 0021-9606
18. Rao, C., and Arkin, A.: 'Stochastic chemical kinetics and the quasi-steadystate assumption: Applications to the Gillespie algorithm', J. Chem. Phys., 2003, 118, p. 4999-5010 0021-9606
19. Weinberger, L.S., Burnett, J.C., Toettcher, J.E., Arkin, A.P., and Schaffer, D.V.: 'Stochastic gene expression in a lentiviral positive-feedback loop: HIV-1 Tat fluctuations drive phenotypic diversity', Cell, 2005, 121, p. 169-182
20. Samoilov, M.S., and Arkin, A.P.: 'Deviant effects in molecular reaction pathways', Nat. Biotechnol., 2006, 24, p. 1235-1240
21. Lipniacki, T., Paszek, P., Marciniak-Czochra, A., Brasier, A.R., and Kimmel, M.: 'Transcriptional stochasticity in gene expression', J. Theor. Biol., 2006, 238, p. 348-367
22. Peccoud, J., and Ycart, B.: 'Markovian modelling of gene products synthesis', Theor. Pop. Biol., 1995, 48, p. 222-234
23. Blake, W.J., Balázsi, G., and Kohanski, M.A.: Et al. 'Phenotypic consequences of promoter-mediated transcriptional noise', Mol. Cell, 2006, 24, p. 853-865
24. Becskei, A., and Serrano, L.: 'Engineering stability in gene networks by autoregulation', Nature, 2000, 405, p. 590-593 0028-0836
25. Hardin, P.E., Hall, J.C., and Rosbash, M.: 'Feedback of the Drosophila period gene product on circadian cycling of its messenger RNA levels', Nature, 1990, 343, p. 536-540 0028-0836
26. Becskei, A., Séraphin, B., and Serrano, L.: 'Positive feedback in eukaryotic gene networks: Cell differentiation by graded to binary response conversion', EMBO J., 2001, 20, p. 2528-35
27. Isaacs, F.J., Hasty, J., Cantor, C.R., and Collins, J.J.: 'Prediction and measurement of an autoregulatory genetic module', Proc. Natl. Acad. Sci. USA, 2003, 100, p. 7714-7719 0027-8424
28. Bundschuh, R., Hayot, F., and Jayaprakash, C.: 'The role of dimerization in noise reduction of simple genetic networks', J. Theor. Biol., 2003, 220, p. 261-269
29. Maamar, H., and Dubnau, D.: 'Bistability in the Bacillus subtilis k-state (competence) system requires a positive feedback loop', Mol. Microbiol., 2005, 56, p. 615-624
30. Ajo-Franklin, C.M., Drubin, D.A., and Eskin, J.A.: Et al. 'Rational design of memory in eukaryotic cells', Genes Dev., 2007, 21, p. 2271-2276
31. Andrecut, M., and Kauffman, S.A.: 'Noise in genetic toggle switch models', J. Int. Bioinform., 2006, 3, (1), p. 0023
32. Tian, T., and Burrage, K.: 'Stochastic models for regulatory networks of the genetic toggle switch', Proc. Natl. Acad. Sci. USA, 2006, 103, p. 8372-8377 0027-8424
33. Gardner, T.S., Cantor, C.R., and Collins, J.J.: 'Construction of a genetic toggle switch in Escherichia coli', Nature, 2000, 403, p. 339-42 0028-0836
34. Kramer, B.P., Viretta, A.U., Daoud-El-Baba, M., Aubel, D., Weber, W., and Fussenegger, M.: 'An engineered epigenetic transgene switch in mammalian cells', Nat. Biotechnol., 2004, 22, p. 867-870
35. Elowitz, M.B., and Leibler, S.: 'A synthetic oscillatory network of transcriptional regulators', Nature, 2000, 403, p. 335-338 0028-0836