Origins of stochasticity and burstiness in high-dimensional biochemical networks

Eurasip Journal on Bioinformatics and Systems Biology

Volumn 2009, Issue , 2009, Pages

  Rosenfeld, Simon ^a  

^a EPN 3108   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 47649114879     PISSN: 16874145     EISSN: 16874153     Source Type: Journal    
DOI: 10.1155/2009/362309     Document Type: Article

References (63)

1. Schlitt T.
2. Bork P.
3. Fiehn O., Metabolomicsthe link between genotypes and phenotypes Plant Molecular Biology 2002 48 1-2 155 171
4. Raman R., Raguram S., Venkataraman G., Paulson J. C., Sasisekharan R.
5. Krauss G., Biochemistry of Signal Transduction and Regulation 1999 New York, NY, USA Wiley-VCH
6. May R. M., Will a large complex system be stable? Nature 1972 238 5364 413 414
7. Golding I.
8. Golding I.
9. Krn M., Menzinger M., Hunding A., A chemical flow system mimics waves of gene expression during segmentation Biophysical Chemistry 2000 87 2-3 121 126
10. Yu J., Xiao J., Ren X., Lao K., Xie X. S.
11. Paulsson J.
12. Paulsson J.
13. Goldbeter A., Complex oscillatory phenomena, including multiple oscillations, in regulated biochemical systems Biomedica Biochimica Acta 1985 44 6 881 889
14. Goldbeter A., Computational approaches to cellular rhythms Nature 2002 420 6912 238 245
15. Kepler T. B.
16. Raser J. M., OShea E. K.
17. Arnold L., Arnold L., Lefever R., Qualitative theory of stochastic non-linear systems Stochastic Nonlinear Systems 1981 Berlin, Germany Springer 86 99
18. Kurtz T. G., The relationship between stochastic and deterministic models for chemical reactions The Journal of Chemical Physics 1972 57 7 2976 2978
19. Kurtz T. G., Solutions of ordinary differential equations as limits of pure jump Markov processes Journal of Applied Probability 1972 7 1 49 58
20. Pollett P. K., Vassallo A., Diffusion approximation for some simple chemical reaction schemes Advances in Applied Probability 1992 24 4 875 893
21. Hoffmann A., Levchenko A., Scott M. L., Baltimore D., The I B-NF- B signaling module: temporal control and selective gene activation Science 2002 298 5596 1241 1245
22. de Jong H.
23. Mendes P., GEPASI: a software package for modelling the dynamics, steady states and control of biochemical and other systems Computer Applications in the Biosciences 1993 9 5 563 571
24. Voit E. O., Computational Analysis of Biochemical Systems: A Practical Guide for Biochemists and Molecular Biologists 2000 Cambridge, UK Cambridge University Press
25. Barabsi A.-L.
26. Just W., Kantz H., Rodenbeck C., Helm M., Stochastic modeling: replacing fast degrees of freedom Journal of Physics A 2001 34 15 3199 3213
27. Just W.
28. Mori H., Fujisaka H., Shigematsu H., A new expansion of the master equation Progress in Theoretical Physics 1974 51 1 109 122
29. Zwanzig R., Ensemble method in the theory of Irreversibility The Journal of Chemical Physics 1960 33 5 1338 1341
30. Rosenfeld S.
31. Savageau M. A., Biochemical systems analysis I. Some mathematical properties of the rate law for the component enzymatic reactions Journal of Theoretical Biology 1969 25 3 365 369
32. Savageau M. A., Voit E. O., Recasting nonlinear differential equations as S-systems: a canonical nonlinear form Mathematical Biosciences 1987 87 1 83 115
33. Voit E. O., Canonical Nonlinear Modeling. S-System Approach to Understanding Complexity 1991 New York, NY, USA Van Nostrand Reinhold
34. Savageau M. A., Biochemical systems analysis III. Dynamic solutions using a power-law approximation Journal of Theoretical Biology 1970 26 2 215 226
35. Kimura S.
36. Voit E. O., Radivoyevitch T., Biochemical systems analysis of genome-wide expression data Bioinformatics 2000 16 11 1023 1037
37. Tournier L.
38. Kadonaga J. T.
39. Lemon B., Tjian R.
40. Sorribas A., Savageau M. A., Strategies for representing metabolic pathways within biochemical systems theory: reversible pathways Mathematical Biosciences 1989 94 2 239 269
41. Brenig L., Complete factorisation and analytic solutions of generalized Lotka-Volterra equations Physics Letters A 1988 133 7-8 378 382
42. Brenig L., Goriely A., Universal canonical forms for time-continuous dynamical systems Physical Review A 1989 40 7 4119 4122
43. Rosenfeld S.
44. Zumdahl S., Chemical Principles 2005 New York, NY, USA Houghton Mifflin
45. Gantmacher F. R., Applications of the Theory of Matrices 1959 New York, NY, USA Wiley-Interscience
46. Nikolaev P. I., Sokolov D. P., Selection of an optimal biochemical reactor for microbiological synthesis Chemical and Petroleum Engineering 1980 16 12 707 710
47. Feinberg M., The existence and uniqueness of steady states for a class of chemical reaction networks Archive for Rational Mechanics and Analysis 1995 132 4 311 370
48. Qian H.
49. Ederer M.
50. Colquhoun D.
51. Yang J., Bruno W. J., Hlavacek W. S., Pearson J. E.
52. Bell S. P., Learned R. M., Jantzen H. M., Tjian R., Functional cooperativity between transcription factors UBF1 and SL1 mediates human ribosomal RNA synthesis Science 1988 241 4870 1192 1197
53. Ptashne M.
54. Bradley R., Basic properties of strong mixing conditions. A survey and some open questions Probability Surveys 2005 2 107 144
55. Cramer H., Leadbetter R., Stationary and Related Stochastic Processes 1967 New York, NY, USA John Wiley Sons
56. McNeil A., Frey R., Embrechts P., Quantitative Risk Management 2005 Princeton, NJ, USA Princeton University Press
57. Van Kampen N. G., Stochastic Processes in Physics and Chemistry 2006 Amsterdam, The Netherlands North Holland
58. Lorenz E. N., Deterministic nonperiodic flow Journal of the Atmospheric Sciences 2006 20 2 130 141
59. Gardiner C. W., Handbook of Stochastic Methods: For Physics, Chemistry, and the Natural Sciences 1983 Berlin, Germany Springer
60. McAdams H. H., Arkin A., Stochastic mechanisms in gene expression Proceedings of the National Academy of Sciences of the United States of America 1997 94 3 814 819
61. McAdams H. H.
62. Wu J., Mehta N. B., Zhang J., A flexible lognormal sum approximation method 6 Proceedings of the IEEE Global Telecommunications Conference (GLOBECOM 05) November-December 2005 St. Louis, Mo, USA Mitsubishi Electric Research Laboratories 3413 3417
63. Perko L., Differential Equations and Dynamical Systems 2001 Berlin, Germany Springer