Stochastic cooperativity in non-linear dynamics of genetic regulatory networks

Mathematical Biosciences

Volumn 210, Issue 1, 2007, Pages 121-142

  Rosenfeld, Simon ^a  

^a NATIONAL CANCER INSTITUTE   (United States)

Author keywords

Biochemical networks; Gene expression; Non linear dynamics; S functions; Stochastic processes

Indexed keywords

BIFURCATION (MATHEMATICS); CHAOS THEORY; DIFFERENTIAL EQUATIONS; RANDOM PROCESSES;

BIOCHEMICAL NETWORKS; NON-LINEAR DYNAMICS; S-FUNCTIONS;

GENE EXPRESSION;

MESSENGER RNA;

CONCEPTUAL FRAMEWORK; GENE EXPRESSION; MARKOV CHAIN; NONLINEARITY; NUMERICAL MODEL; STOCHASTICITY;

ARTICLE; GENE EXPRESSION; GENETIC REGULATION; MOLECULAR DYNAMICS; OSCILLATION; STOCHASTIC MODEL; TRANSCRIPTION INITIATION;

BIOCHEMISTRY; GENE EXPRESSION REGULATION; KINETICS; MARKOV CHAINS; MATHEMATICS; MODELS, GENETIC; NONLINEAR DYNAMICS; POISSON DISTRIBUTION; STOCHASTIC PROCESSES; TRANSCRIPTION, GENETIC;

EID: 35348898041     PISSN: 00255564     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mbs.2007.05.006     Document Type: Article

References (70)

1. Alberts B., et al. Molecular Biology of the Cell (2004), Garland Science
2. Lewin B. Genes VIII (2004), Upper Saddle River, NJ
3. Kadonaga J.T. Regulation of RNA polymerase II transcription by sequence-specific DNA binding factors. Cell 116 (2004) 247
4. Golding I., Paulsson J., Zawilski S.M., and Cox E.C. Real-time kinetics of gene activity in individual bacteria. Cell 123 (2005) 1025
5. Golding I., and Cox E.C. RNA dynamics in live Escherichia coli cells. Proc. Natl. Acad. Sci. USA 101 (2004) 11310
6. Guptasarma P. Does replication-induced transcription regulate synthesis of the myriad low copy number proteins of Escherichia coli?. Bioassays 17 (1995) 987
7. Browning D.F., and Busby S.J. The regulation of bacterial transcription initiation. Nat. Rev. Microbiol. 2 (2004) 57
8. Rhodius V.A., Suh W.C., Nonaka G., West J., and Gross C.A. Conserved and variable functions of the sigmaE stress response in related genomes. PLoS Biol. 4 (2006) e2
9. Blake W.J., Kaern M., Cantor C.R., and Collins J.J. Noise in eukaryotic gene expression. Nature 422 (2003) 633
10. Yu J., Xiao J., Ren X., Lao K., and Xie X.S. Probing gene expression in live cells, one protein molecule at a time. Science 311 (2006) 1600
11. M. Scott, Genetic curcuits and noise. Quantitative approach to gene regulatory systems, CTBP Summer School 'Quantitative Methods in Gene Regulation', UCSD, La Jolla, 2006.
12. Geva-Zatorsky N., et al. Oscillations and variability in the p53 system. Mol. Syst. Biol. 2 (2006) 2006
13. Liao J.C., et al. Network component analysis: reconstruction of regulatory signals in biological systems. Proc. Natl. Acad. Sci. USA 100 (2003) 15522
14. Tao Y., Jia Y., and Dewey T.G. Stochastic fluctuations in gene expression far from equilibrium: omega expansion and linear noise approximation. J. Chem. Phys. 122 (2005) 124108
15. McAdams H.H., and Arkin A. Stochastic mechanisms in gene expression. Proc. Natl. Acad. Sci. USA 94 (1997) 814
16. McAdams H.H., and Arkin A. It's a noisy business! Genetic regulation at the nanomolar scale. Trends Genet. 15 (1999) 65
17. Paulsson J. Prime movers of noisy gene expression. Nat. Genet. 37 (2005) 925
18. Scott M., Ingalls B., and Kaern M. Estimations of intrinsic and extrinsic noise in models of nonlinear genetic networks. Chaos 16 (2006) 026107
19. S. Rosenfeld, A nonlinear continuous stochastic model for genetic regulatory networks, Caveats for microarray data analysis, ALIFE-X, 2006, p. 28.
20. Rosenfeld S. Stochastic oscillations in genetic regulatory networks. EURASIP J. Bioinformatics Syst. Biol. (2006) 1
21. S. Rosenfeld, Stochastic oscillations in genetic regulatory networks. Applications to microarray experiment, in: A. Rizzi, M. Vichi (Eds.), COMPSTAT-2006, Physica-Verlag, 2006, p. 1609.
22. deJong H. Modeling and simulation of genetic regulatory systems: a literature review. J. Comput. Biol. 9 (2002) 67
23. Goldbeter A. Computational approaches to cellular rhythms. Nature 420 (2002) 238
24. van Kampen N.G. Stochastic Processes in Physics and Chemistry (2006), North Holland
25. Paulsson J. Summing up the noise in gene networks. Nature 427 (2004) 415
26. Gillespie D.T. Stochastic simulation of chemical kinetics. Annu. Rev. Phys. Chem. (2006)
27. Kaern M., Menzinger M., and Hunding A. A chemical flow system mimics waves of gene expression during segmentation. Biophys. Chem. 87 (2000) 121
28. Zhang D., Gyorgyi L., and Peltier W.R. Deterministic chaos in the Belousov-Zhabotinsky reaction: experiments and simulations. Chaos 3 (1993) 723
29. Nicolis G., and Prigogine I. Self-Organization in Nonequilibrium Systems: From Dissipative Structures to Order through Fluctuations (1977), John Wiley & Sons
30. Glandsdorff P., and Prigogine I. Thermodynamics of Structure, Stability and Fluctuations (1971), Wiley Interscience, NY
31. Simpson M.L., Cox C.D., and Sayler G.S. Frequency domain analysis of noise in autoregulated gene circuits. Proc. Natl. Acad. Sci. USA 100 (2003) 4551
32. Chen T., He H.L., and Church G.M. Modeling gene expression with differential equations. Pac. Symp. Biocomput. (1999) 29
33. Ozbudak E.M., Thattai M., Kurtser I., Grossman A.D., and Van O.A. Regulation of noise in the expression of a single gene. Nat. Genet. 31 (2002) 69
34. Keizer J. Statistical Thermodynamics of Nonequilibrium Processes (1987), Springer, Berlin
35. Gardiner C.W. Handbook of Stochastic Methods: For Physics, Chemistry, and the Natural Sciences (1983), Springer
36. Strogatz S. Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry and Engineering (1994), Springer
37. Lorenz E. Deterministic non-periodic flow. J. Atmos. Sci. 20 (2006) 130
38. Savageau M.A. Biochemical systems analysis. I. Some mathematical properties of the rate law for the component enzymatic reactions. J. Theor. Biol. 25 (1969) 365
39. Savageau M.A. Biochemical systems analysis. II. The steady-state solutions for an n-pool system using a power-law approximation. J. Theor. Biol. 25 (1969) 370
40. Savageau M.A. Biochemical systems analysis. 3. Dynamic solutions using a power-law approximation. J. Theor. Biol. 26 (1970) 215
41. Sorribas A., and Savageau M.A. Strategies for representing metabolic pathways within biochemical systems theory: reversible pathways. Math. Biosci. 94 (1989) 239
42. Voit E.O., and Savageau M.A. Accuracy of alternative representations for integrated biochemical systems. Biochemistry 26 (1987) 6869
43. Voit E.O. Canonical Nonlinear Modeling. S-System Approach to Understanding Complexity (1991), Van Norstand Reinhold, NY
44. Voit E.O. Computational Analysis of Biochemical Systems: A Practical Guide for Biochemists and Molecular Biologists (2000), Cambridge University, Cambridge, UK
45. Savageau M.A., and Voit E.O. Recasting nonlinear differential equations as S-systems. Math. Biosci. 87 (2006) 83
46. Voit E.O., and Radivoyevitch T. Biochemical systems analysis of genome-wide expression data. Bioinformatics 16 (2000) 1023
47. L. Tournier, Approximation of dynamical systems using S-systems theory: application to biological systems, in: International Symposium on Symbolic and Algebraic Computations, 2005, pp. 317-324.
48. Bressan A. Tutorial on the Center Manifold Theory (2003), SISSA, Trieste, Italy
49. Lemon B., and Tjian R. Orchestrated response: a symphony of transcription factors for gene control. Genes Dev. 14 (2000) 2551
50. Gibson M., and Mjolsness E. In: Bower J.M., and Bolouri H. (Eds). Modeling the activity of single genes (2001), MIT Press, Cambridge, MA
51. Perko L. Differential Equations and Dynamical Systems (2001), Springer
52. Zumdahl S. Chemical Principles (2005), Houghton Mifflin, New York
53. I. Prigogine, Time, Structure and Fluctuations, Nobel Lecture, 1977.
54. Ederer M., and Gilles E.D. Thermodynamically feasible kinetic models of reaction networks. Biophys. J. 92 (2007) 1846
55. Qian H., Beard D.A., and Liang S.D. Stoichiometric network theory for nonequilibrium biochemical systems. Eur. J. Biochem. 270 (2003) 415
56. Gantmacher F.R. Applications of the Theory of Matrices (1959), Interscience, NY
57. Heijnen J.J. Approximative kinetic formats used in metabolic network modeling. Biotechnol. Bioeng. 91 (2005) 534
58. Bell S.P., Learned R.M., Jantzen H.M., and Tjian R. Functional cooperativity between transcription factors UBF1 and SL1 mediates human ribosomal RNA synthesis. Science 241 (1988) 1192
59. Ptashne M. Regulated recruitment and cooperativity in the design of biological regulatory systems. Philos. Trans. A Math. Phys. Eng. Sci. 361 (2003) 1223
60. Hoover W.G. Reversible mechanics and time's arrow. Phys. Rev. A 37 (1988) 252
61. Bradley R. Basic properties of strong mixing conditions. A survey and some open questions. Probability Surveys 2 (2005) 107
62. Cramer H., and Leadbetter R. Stationary and Related Stochastic Processes (1967), Wiley, NY
63. Loeve M. Probability theory (The University series in higher mathematics) (1963), Van Nostrand, Holland
64. Johnson N., Kotz S., and Balakrishnan N. Discrete Multivariate Distributions (1997), Wiley & Sons, NY
65. Blake I., and Lindsey W. Level-crossing problems for random processes. IEEE Trans. Inf. Theory 19 (1973) 295
66. Barbe A. A level-crossing-based scaling dimensionality transform applied to stationary Gaussian processes. Part 2. IEEE Trans. Inf. Theory 38 (1992) 814
67. Krauss G. Biochemistry of Signal Transduction and Regulation (1999), Wiley-VCH
68. L. Rocha et al., Simulation and synthesis of living systems, in: Proc. Tenth Int. Conf. ALIFE-X, Bloomington, IN, 2006, Bradford Books, 2006.
69. Gradshtein I., and Ryzhik I. Table of Integrals, Series, and Products (2000), Academic Press, NY
70. Box G.E.P., and Jenkins G.M. Time Series Analysis: Forecasting & Control (1994), Prentice Hall