Deterministic and Stochastic Models of Genetic Regulatory Networks

Methods in Enzymology

Volumn 467, Issue C, 2009, Pages 335-356

  Shmulevich, Ilya ^a   Aitchison, John D ^a  

^a INSTITUTE FOR SYSTEMS BIOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ACCURACY; CELL CYCLE; CELL DIVISION; CELL FUNCTION; CELL GROWTH; CELL TYPE; ENGINEERING; GENETIC REGULATION; HUMAN; INFORMATION SCIENCE; MATHEMATICAL COMPUTING; NOISE; NONHUMAN; PHENOTYPE; PREDICTION; PRIORITY JOURNAL; PROBABILITY; REVIEW; STEADY STATE; STOCHASTIC MODEL;

ALGORITHMS; COMPUTATIONAL BIOLOGY; COMPUTER SIMULATION; GENE REGULATORY NETWORKS; MATHEMATICS; MODELS, GENETIC; NONLINEAR DYNAMICS; PHENOTYPE; SACCHAROMYCES; STOCHASTIC PROCESSES;

EID: 71549141289     PISSN: 00766879     EISSN: None     Source Type: Book Series    
DOI: 10.1016/S0076-6879(09)67013-0     Document Type: Review

References (58)

1. Aldana M., Coppersmith S., and Kadanoff L.P. Boolean dynamics with random couplings. In: Kaplan E., Marsden J.E., and Sreenivasan K.R. (Eds). Perspectives and Problems in Nonlinear Science (2002), Springer, New York 23-89
2. Alvarez-Buylla E.R., Chaos A., Aldana M., Benítez M., Cortes-Poza Y., Espinosa-Soto C., Hartasánchez D.A., Lotto R.B., Malkin D., Escalera Santos G.J., and Padilla-Longoria P. Floral morphogenesis: Stochastic explorations of a gene network epigenetic landscape. PLoS ONE 3 11 (2008) e3626
3. Bornholdt S. Boolean network models of cellular regulation: Prospects and limitations. J. R. Soc. Interface 5 Suppl. 1 (2008) S85-S94
4. Braunewell S., and Bornholdt S. Superstability of the yeast cell-cycle dynamics: Ensuring causality in the presence of biochemical stochasticity. J. Theor. Biol. 245 4 (2006) 638-643
5. Brun M., Dougherty E.R., and Shmulevich I. Steady-state probabilities for attractors in probabilistic Boolean networks. Signal Process. 85 4 (2005) 1993-2013
6. Cao Y., and Samuels D.C. Discrete stochastic simulation methods for chemically reacting systems. Methods Enzymol. 454 (2009) 115-140
7. Chang H.H., Hemberg M., Barahona M., Ingber D.E., and Huang S. Transcriptome-wide noise controls lineage choice in mammalian progenitor cells. Nature 453 7194 (2008) 544-547
8. Chaves M., Albert R., and Sontag D. Robustness and fragility of Boolean models for genetic regulatory networks. J. Theor. Biol. 235 (2005) 431-449
9. Chen K.C., Calzone L., Csikasz-Nagy A., Cross F.R., Novak B., and Tyson J.J. Integrative analysis of cell cycle control in budding yeast. Mol. Biol. Cell 15 (2004) 3841-3862
10. Davidich M., and Bornholdt S. The transition from differential equations to Boolean networks: A case study in simplifying a regulatory network model. J. Theor. Biol. 255 3 (2008) 269-277
11. Davidich M.I., and Bornholdt S. Boolean network model predicts cell cycle sequence of fission yeast. PLoS ONE 3 2 (2008) e1672
12. Drossel B. Random Boolean networks. In: Schuster H.G. (Ed). Annual Review of Nonlinear Dynamics and Complexity, Vol. 1 (2007), Wiley
13. Fauré A., Naldi A., Chaouiya C., and Thieffry D. Dynamical analysis of a generic Boolean model for the control of the mammalian cell cycle. Bioinformatics 22 14 (2006) e124-e131
14. Glass L. Classification of biological networks by their qualitative dynamics. J. Theor. Biol. 54 (1975) 85-107
15. Glass L., and Kauffman S.A. The logical analysis of continuous, nonlinear biochemical control networks. J. Theor. Biol. 39 (1973) 103-129
16. Goryanin I., Hodgman T.C., and Selkov E. Mathematical simulation and analysis of cellular metabolism and regulation. Bioinformatics 15 9 (1999) 749-758
17. Huang S. Gene expression profiling, genetic networks, and cellular states: An integrating concept for tumorigenesis and drug discovery. J. Mol. Med. 77 6 (1999) 469-480
18. Huang S., and Ingber D.E. Shape-dependent control of cell growth, differentiation, and apoptosis: Switching between attractors in cell regulatory networks. Exp. Cell Res. 261 1 (2000) 91-103
19. Huang S., Eichler G., Bar-Yam Y., and Ingber D.E. Cell fates as high-dimensional attractor states of a complex gene regulatory network. Phys. Rev. Lett. 94 12 (2005) 128701-128704
20. Irons D.J. Logical analysis of the budding yeast cell cycle. J. Theor. Biol. 257 4 (2009) 543-559
21. Jacob F., and Monod J. On the regulation of gene activity. Cold Spring Harb. Symp. Quant. Biol. 26 (1961) 193-211
22. Kauffman S.A. Metabolic stability and epigenesis in randomly constructed genetic nets. J. Theor. Biol. 22 (1969) 437-467
23. Kauffman S.A. Homeostasis and differentiation in random genetic control networks. Nature 224 (1969) 177-178
24. Kauffman S.A. The large scale structure and dynamics of genetic control circuits: An ensemble approach. J. Theor. Biol. 44 (1974) 167-190
25. Kauffman S.A. The Origins of Order: Self-Organization and Selection in Evolution (1993), Oxford University Press, New York
26. Kauffman S. A proposal for using the ensemble approach to understand genetic regulatory networks. J. Theor. Biol. 230 4 (2004) 581-590
27. Kim S., Li H., Dougherty E.R., Cao N., Chen Y., Bittner M.L., and Suh E.B. Can Markov chain models mimic biological regulation?. J. Biol. Syst. 10 4 (2002) 431-445
28. Lähdesmäki H., Hautaniemi S., Shmulevich I., and Yli-Harja O. Relationships between probabilistic Boolean networks and dynamic Bayesian networks as models of gene regulatory networks. Signal Process. 86 4 (2006) 814-834
29. Lambert J.D. Numerical Methods for Ordinary Differential Equations (1991), Wiley, Chichester
30. Li F., Long T., Lu Y., Quyang Q., and Tang C. The yeast cell-cycle network is robustly designed. Proc. Natl. Acad. Sci. USA 101 14 (2004) 4781-4786
31. MacLeod M.C. A possible role in chemical carcinogenesis for epigenetic, heritable changes in gene expression. Mol. Carcinog. 15 4 (1996) 241-250
32. Manninen T., Linne M.L., and Ruohonen K. Developing Itô stochastic differential equation models for neuronal signal transduction pathways. Comput. Biol. Chem. 30 4 (2006) 280-291
33. Mendes P. GEPASI: A software package for modelling the dynamics, steady states and control of biochemical and other systems. Comput. Appl. Biosci. 9 5 (1993) 563-571
34. Muroga S. Threshold Logic and its Applications (1971), Wiley-Interscience
35. Murphy K., and Mian S. Modelling Gene Expression Data using Dynamic Bayesian Networks (1999), Technical Report, University of California, Berkeley
36. Novak B., Pataki Z., Ciliberto A., and Tyson J.J. Mathematical model of the cell division cycle of fission yeast. Chaos 11 1 (2001) 277-286
37. Ozbudak E.M., Thattai M., Kurtser I., Grossman A.D., and van Oudenaarden A. Regulation of noise in the expression of a single gene. Nat. Genet. 31 1 (2002) 69-73
38. Ramsey S., Orrell D., and Bolouri H. Dizzy: Stochastic simulations of large-scale genetic regulatory networks. J. Bioinform. Comput. Biol. 3 2 (2005) 1-21
39. Rao C.V., Wolf D.M., and Arkin A.P. Control, exploitation and tolerance of intracellular noise. Nature 420 6912 (2002) 231-237
40. Raser J.M., and O'Shea E.K. Noise in gene expression: Origins, consequences, and control. Science 309 5743 (2005) 2010-2013
41. Richmond C.S., Glasner J.D., Mau R., Jin H., and Blattner F.R. Genome-wide expression profiling in Escherichia coli K-12. Nucleic Acids Res. 27 (1999) 3821-3835
42. Rissanen J. Information and Complexity in Statistical Modeling (2007), Springer
43. Schmidt H., and Jirstrand M. Systems biology toolbox for MATLAB: A computational platform for research in systems biology. Bioinformatics 22 4 (2006) 514-515
44. Shmulevich I., and Zhang W. Binary analysis and optimization-based normalization of gene expression data. Bioinformatics 18 4 (2002) 555-565
45. Shmulevich I., Dougherty E.R., Kim S., and Zhang W. Probabilistic Boolean networks: A rule-based uncertainty model for gene regulatory networks. Bioinformatics 18 2 (2002) 261-274
46. Shmulevich I., Dougherty E.R., and Zhang W. Gene perturbation and intervention in probabilistic Boolean networks. Bioinformatics 18 10 (2002) 1319-1331
47. Shmulevich I., Dougherty E.R., and Zhang W. From Boolean to probabilistic Boolean networks as models of genetic regulatory networks. Proc. IEEE 90 11 (2002) 1778-1792
48. Shmulevich I., Gluhovsky I., Hashimoto R., Dougherty E.R., and Zhang W. Steady-state analysis of probabilistic Boolean networks. Comp. Funct. Genom. 4 6 (2003) 601-608
49. Sible J.C., and Tyson J.J. Mathematical modeling as a tool for investigating cell cycle control networks. Methods 41 2 (2007) 238-247
50. SimBiology 3.0 Toolbox. http://www.mathworks.com/products/simbiology
51. Steuer R. Effects of stochasticity in models of the cell cycle: From quantized cycle times to noise-induced oscillations. J. Theor. Biol. 228 3 (2004) 293-301
52. Swain P.S., Elowitz M.B., and Siggia E.D. Intrinsic and extrinsic contributions to stochasticity in gene expression. Proc. Natl. Acad. Sci. USA 99 20 (2002) 12795-12800
53. Thomas R. Boolean formalization of genetic control circuits. J. Theor. Biol. 42 (1973) 563-585
54. Weaver D.C., Workman C.T., and Stormo G.D. Modeling regulatory networks with weight matrices. Pac. Symp. Biocomput. 4 (1999) 112-123
55. Wolf D.M., and Eeckman F.H. On the relationship between genomic regulatory element organization and gene regulatory dynamics. J. Theor. Biol. 195 2 (1998) 167-186
56. Yu J., Smith V.A., Wang P.P., Hartemink A.J., and Jarvis E.D. Advances to Bayesian network inference for generating causal networks from observational biological data. Bioinformatics 20 18 (2004) 3594-3603
57. Zhang Y., Qian M., Ouyang Q., Deng M., Li F., and Tang C. Stochastic model of yeast cell-cycle network. Physica D 219 1 (2006) 35-39
58. Zou M., and Conzen S.D. A new dynamic Bayesian network (DBN) approach for identifying gene regulatory networks from time course microarray data. Bioinformatics 21 1 (2005) 71-79