A review of systems biology perspective on genetic regulatory networks with examples

Current Bioinformatics

Volumn 3, Issue 3, 2008, Pages 197-225

  Kulasiri, Don ^a   Nguyen, Lan K ^a   Samarasinghe, Sandhya ^a   Xie, Zhi ^a  

^a LINCOLN UNIVERSITY   (New Zealand)

Author keywords

Circadian rhythms; Genetic regulatory networks; Modelling; Noise; Systems biology

Indexed keywords

AMINO ACIDS; BIOLOGICAL SYSTEMS; DIGITAL STORAGE; FEEDBACK; MOLECULAR BIOLOGY;

CIRCADIAN RHYTHMS; EXTERNAL NOISE; FEEDBACK LOOPS; GENETIC REGULATORY NETWORKS; INTERNAL NOISE; LIVING SYSTEMS; MODELING; NOISE; RESEARCH ISSUES; SYSTEMS BIOLOGY;

ESCHERICHIA COLI;

ALGORITHM; CIRCADIAN RHYTHM; COMPUTER MODEL; DROSOPHILA; ENZYME INHIBITION; FEEDBACK SYSTEM; GENE EXPRESSION; GENE REGULATORY NETWORK; GENE REPRESSION; HUMAN; KINETICS; MATHEMATICAL MODEL; MOLECULAR BIOLOGY; NOISE; NOISE MEASUREMENT; NONHUMAN; NONLINEAR SYSTEM; PRIORITY JOURNAL; REVERSE ENGINEERING; REVIEW; STOCHASTIC MODEL; SYSTEMS BIOLOGY; TRANSCRIPTION REGULATION;

EID: 85005976913     PISSN: 15748936     EISSN: 2212392X     Source Type: Journal    
DOI: 10.2174/157489308785909214     Document Type: Review

References (159)

1. Fleischmann RD, Adams MD, White O, et al. Whole-genome random sequencing and assembly of Haemophilus influenzae Rd. Science 1995; 269: 496-512.
2. Venter JC, Adams MD, Myers EW, et al. The sequence of the human genome. Science 2001; 291: 1304-51.
3. Baldi P, Hatfield G. DNA microarrays and gene expression: from experiments to data analysis and modeling. Cambridge, Cambridge University Press, 2002, 200.
4. Zhu H, Bilgin M, Bangham R, et al. Global Analysis of Protein Activities Using Proteome Chips. Science 2001; 293: 2101-2105.
5. Uetz P, Giot L, Cagney G, et al. A comprehensive analysis of protein- protein interactions in Saccharomyces cerevisiae. Nature 2000; 403: 623-7.
6. Kitano H. Systems biology: a brief overview. Science New York, N.Y. 2002; 295: 1662-4.
7. Wiener N. Cybernetics Or Control And Communication In The Animal And The Machine New York, Wiley, 1948.
8. Lewin B, Genes VIII. Instructor’s ed. Upper Saddle River, N.J., Pearson Prentice Hall, 2004, xxi, 1027.
9. von Hippel PH. Biochemistry. Completing the view of transcriptional regulation. Science 2004; 305: 350-2.
10. Stamatoyannopoulos JA. The genomics of gene expression. Genomics 2004; 84(3): 449-57.
11. Bower JM, Bolouri H. Computational modeling of genetic and biochemical Net-works, MIT Press, Cambridge, MA 2001.
12. Goldbeter A. A model for circadian oscillations in the Drosophila period protein (PER). Proc Biol Sci 1995; 261: 319-24.
13. Xie Z, Kulasiri D. Modelling of circadian rhythms in Drosophila incorporating the interlocked PER/TIM and VRI/PDP1 feedback loops. J Theor Biol 2007; 245: 290-304.
14. Novak B, Pataki Z, Ciliberto A, Tyson JJ. Mathematical model of the cell division cycle of fission yeast. Chaos 2001; 11: 277-286.
15. Bootman MD, Lipp P, Berridge MJ. The organisation and functions of local Ca(2+) signals. J Cell Sci 2001; 114: 2213-22.
16. Becskei A, Seraphin B, Serrano L. Positive feedback in eukaryotic gene networks: cell differentiation by graded to binary response conversion. EMBO J 2001; 20: 2528-35.
17. Smolen P, Baxter DA, Byrne JH. Mathematical modeling of gene networks. Neuron 2000; 26: 567-80.
18. Elowitz MB, Leibler S. A synthetic oscillatory network of transcriptional regulators. Nature 2000; 403: 335-8.
19. Angeli D, Ferrell JE, Jr., Sontag ED. Detection of multistability, bifurcations, and hysteresis in a large class of biological positivefeedback systems. Proc Natl Acad Sci USA 2004; 101: 1822-7.
20. Pomerening JR, Sontag ED, Ferrell JE, Jr. Building a cell cycle oscillator: hysteresis and bistability in the activation of Cdc2. Nat Cell Biol 2003; 5: 346-51.
21. Delbruck M. The Burst Size Distribution in the Growth of Bacterial Viruses (Bacteriophages). J Bacteriol 1945; 50: 131-5.
22. Powell EO. An outline of the pattern of bacterial generation times. J Gen Microbiol 1958; 18: 382-417.
23. Singh UN. Polyribosomes and unstable messenger RNA: a stochastic model of protein synthesis. J Theor Biol 1969; 25: 444-60.
24. Singh UN, Gupta RS. Polyribosomes and unstable messenger RNA. II. Some further implications of the tape theory of protein synthesis. J Theor Biol 1971; 30: 603-19.
25. Rigney DR, Schieve WC. Stochastic model of linear, continuous protein synthesis in bacterial populations. J Theor Biol 1977; 69:761-6.
26. Ozbudak EM, Thattai M, Kurtser I, Grossman AD, van Oudenaarden A. Regulation of noise in the expression of a single gene. Nat Genet 2002; 31: 69-73.
27. Elowitz MB, Levine AJ, Siggia ED, Swain PS. Stochastic gene expression in a single cell. Science 2002; 297: 1183-6.
28. Blake WJ, Kaern M, Cantor CR, Collins JJ. Noise in eukaryotic gene expression. Nature 2003; 422: 633-7.
29. Raser JM, O’Shea EK. Control of stochasticity in eukaryotic gene expression. Science 2004; 304: 1811-4.
30. Pedraza JM, van Oudenaarden A. Noise propagation in gene networks. Science 2005; 307: 1965-9.
31. Austin DW, Allen MS, McCollum JM, et al. Gene network shaping of inherent noise spectra. Nature 2006; 439: 608-11.
32. Dublanche Y, Michalodimitrakis K, Kummerer N, Foglierini M, Serrano L. Noise in transcription negative feedback loops: simulation and experimental analysis. Mol Syst Biol 2006; 2: 41.
33. Kepler TB, Elston TC. Stochasticity in transcriptional regulation:Origins, consequences, and mathematical representations. Biophys J 2001; 81: 3116.
34. Swain PS, Elowitz MB, Siggia ED. Intrinsic and extrinsic contributions to stochasticity in gene expression. Proc Natl Acad Sci USA 2002; 99: 12795-800.
35. Paulsson J. Summing up the noise in gene networks. Nature 2004; 427: 415-8.
36. Tao Y. Intrinsic and external noise in an auto-regulatory genetic network. J Theor Biol 2004; 229: 147-56.
37. Longo D, Hasty J. Dynamics of single-cell gene expression. Mol Syst Biol 2006; 2: 64.
38. McAdams H, Arkin A. It’s a noisy business! Genetic regulation at the nanomolar scale. Trends Genet 1999; 15: 65-9.
39. Benzer S. Induced synthesis of enzymes in bacteria analyzed at the cellular level. Biochim Biophys Acta 1953; 11: 383-95.
40. Maloney PC, Rotman B. Distribution of suboptimally induces -Dgalactosidase in Escherichia coli. The enzyme content of individual cells. J Mol Biol 1973; 73: 77-91.
41. Novick A, Weiner M. Enzyme Induction as an All-or-None Phenomenon. Proc Natl Acad Sci USA 1957; 43: 553-66.
42. Spudich JL, Koshland DE, Jr. Non-genetic individuality: chance in the single cell. Nature 1976; 262: 467-71.
43. Hasty J, Pradines J, Dolnik M, Collins JJ. Noise-based switches and amplifiers for gene expression. Proc Natl Acad Sci USA 2000; 97: 2075-2080.
44. McAdams HH, Arkin A. Stochastic mechanisms in gene expression. Proc Natl Acad Sci USA 1997; 94: 814-819.
45. Rosenfeld N, Young JW, Alon U, Swain PS, Elowitz MB. Gene regulation at the single-cell level. Science 2005; 307: 1962-5.
46. Volfson D, Marciniak J, Blake WJ, Ostroff N, Tsimring LS, Hasty J. Origins of extrinsic variability in eukaryotic gene expression. Nature 2006; 439: 861-4.
47. Colman-Lerner A, Gordon A, Serra E, et al. Regulated cell-to-cell variation in a cell-fate decision system. Nature 2005; 437: 699-706.
48. Kaern M, Elston TC, Blake WJ, Collins JJ. Stochasticity in gene expression: from theories to phenotypes. Nat Rev Genet 2005; 6:451-64.
49. Bar-Even A, Paulsson J, Maheshri N, et al. Noise in protein expression scales with natural protein abundance. Nat Genet 2006; 38: 636-43.
50. Becskei A, Kaufmann BB, van Oudenaarden A. Contributions of low molecule number and chromosomal positioning to stochastic gene expression. Nat Genet 2005; 37: 937-44.
51. Lewis K. Programmed death in bacteria. Microbiol Mol Biol Rev 2000; 64: 503-14.
52. Maughan H, Nicholson WL. Stochastic processes influence stationary- phase decisions in Bacillus subtilis. J Bacteriol 2004; 186:2212-4.
53. Thattai M, van Oudenaarden A. Stochastic gene expression in fluctuating environments. Genetics 2004; 167: 523-30.
54. Fraser HB, Hirsh AE, Giaever G, Kumm J, Eisen MB. Noise minimization in eukaryotic gene expression. PLoS Biol 2004; 2:e137.
55. Kurakin A. Self-organization vs Watchmaker: stochastic gene expression and cell differentiation. Dev Genes Evol 2005; 215: 46-52.
56. Paldi A. Stochastic gene expression during cell differentiation:order from disorder? Cell Molec Life Sci 2003; 60: 1775-8.
57. Hooshangi S, Thiberge S, Weiss R. Ultrasensitivity and noise propagation in a synthetic transcriptional cascade. Proc Natl Acad Sci USA 2005; 102: 3581-6.
58. Hooshangi S, Weiss R. The effect of negative feedback on noise propagation in transcriptional gene networks. Chaos 2006; 16:026108.
59. Giaever G, Chu AM, Ni L, et al. Functional profiling of the Saccharomyces cerevisiae genome. Nature 2002; 418: 387-91.
60. Barkai N, Leibler S. Robustness in simple biochemical networks. Nature 1997; 387: 913-7.
61. von Dassow G, Meir E, Munro EM, Odell GM. The segment polarity network is a robust developmental module. Nature 2000; 406:188-92.
62. Dunlap JC. Molecular bases for circadian clocks. Cell 1999; 96:271-90.
63. Gonze D, Halloy J, Goldbeter A. Robustness of circadian rhythms with respect to molecular noise. Proc Natl Acad Sci USA 2002; 99:673-8.
64. Rao CV, Wolf DM, Arkin AP. Control, exploitation and tolerance of intracellular noise. Nature 2002; 420: 231-7.
65. Vilar JM, Kueh HY, Barkai N, Leibler S. Mechanisms of noiseresistance in genetic oscillators. Proc Natl Acad Sci USA 2002; 99:5988-92.
66. Krishna S, Andersson AM, Semsey S, Sneppen K. Structure and function of negative feedback loops at the interface of genetic and metabolic networks. Nucleic Acids Res 2006; 34: 2455-62.
67. Freeman M. Feedback control of intercellular signalling in development. Nature 2000; 408: 313-9.
68. Smolen P, Baxter D, Byrne J. Modeling transcriptional control in gene networks--methods, recent results, and future directions. Bull Math Biol 2000; 62: 247-92.
69. Becskei A, Serrano L. Engineering stability in gene networks by autoregulation. Nature 2000; 405: 590-3.
70. Yi TM, Huang Y, Simon MI, Doyle J. Robust perfect adaptation in bacterial chemotaxis through integral feedback control. Proc Natl Acad Sci USA 2000; 97: 4649-53.
71. Raser JM, O’Shea EK. Noise in gene expression: origins, consequences, and control. Science 2005; 309: 2010-3.
72. Doncic A, Ben-Jacob E, Barkai N. Noise resistance in the spindle assembly checkpoint. Mol Syst Biol 2006; 2: 2006. 0027.
73. Yuh CH, Bolouri H, Davidson EH. Cis-regulatory logic in the endo16 gene: switching from a specification to a differentiation mode of control. Development 2001; 128: 617-629.
74. McAdams HH, Shapiro L. Circuit simulation of genetic networks. Science 1995; 269: 650-6.
75. Pritchard L, Kell DB. Schemes of flux control in a model of Saccharomyces cerevisiae glycolysis. Eur J Biochem 2002; 269: 3894-904.
76. Arkin AP. Synthetic cell biology. Curr Opin Biotechnol 2001; 12:638-44.
77. Heinrich R, Rapoport SM, Rapoport TA. Metabolic regulation and mathematical models. Prog Biophys Mol Biol 1977; 32: 1-82.
78. Savageau MA. Biochemical systems analysis. I. Some mathematical properties of the rate law for the component enzymatic reactions. J Theor Biol 1969; 25: 365-9.
79. Savageau MA, Voit EO. Recasting nonlinear differential equations as S-systems: a canonical nonlinear form. Math Biosci 1987; 87:83-115.
80. Kampen V, Stochastic processes in physics and chemistry. Rev. and enl. ed. Amsterdam; New York, Elsevier Science Pub Co, 2001, xiv, 465.
81. Haseltine EL, Rawlings JB. Approximate simulation of coupled fast and slow reactions for stochastic chemical kinetics. J Chem Phys 2002; 117: 6959-6969.
82. Rao CV, Arkin AP. Stochastic chemical kinetics and the quasisteady- state assumption: Application to the Gillespie algorithm. J Chem Phys 2003; 118: 4999-5010.
83. Cao Y, Gillespie DT, Petzold LR. The slow-scale stochastic simulation algorithm. J Chem Phys 2005; 122: 14116.
84. Takahashi K, Kaizu K, Hu B, Tomita M. A multi-algorithm, multitimescale method for cell simulation. Bioinformatics 2004; 20:538-46.
85. Kauffman S. A proposal for using the ensemble approach to understand genetic regulatory networks. J Theor Biol 2004; 230: 581-90.
86. Armstrong NJ, van de Wiel MA. Microarray data analysis: from hypotheses to conclusions using gene expression data. Cell Oncol 2004; 26: 279-90.
87. Endy D, Brent R. Modelling cellular behaviour. Nature 2001; 409:391-5.
88. Kauffman SA. Homeostasis and differentiation in random genetic control networks. Nature 1969; 224: 177-178.
89. Kauffman SA. The large scale structure and dynamics of gene control circuits: an ensemble approach. J Theor Biol 1974; 44: 167-90.
90. Huang S. Gene expression profiling, genetic networks, and cellular states: an integrating concept for tumorigenesis and drug discovery. J Mol Med 1999; 77: 469-80.
91. Kauffman SA. The origins of order: self-organization and selection in evolution. New York, Oxford University Press, 1993.
92. Kauffman SA. Antichaos and adaptation: biological evolution may have been shaped by more than just natural selection, computer models suggest that certain complex systems tend toward selforganization. Sci Am 1991; 265: 78.
93. Somogyi R, Sniegoski C. Modeling the complexity of genetic networks: understanding multigenic and pleiotropic regulation. Complexity 1996;1: 45-63.
94. Szallasi Z, Liang S. Modeling the Normal and Neoplastic Cell Cycle With “Realistic Boolean Genetic Networks”: Their Application for Understanding Carcinogenesis and Assessing Therapeutic Strategies. in Proc Pac Symp Biocomput. Singapore: World Scientific Publishing, 1998.
95. Serra R, Villani M, Graudenzi A, Kauffman SA. Why a simple model of genetic regulatory networks describes the distribution of avalanches in gene expression data. J Theor Biol 2007; 246: 449-60.
96. Bolouri H, Davidson EH. Modeling transcriptional regulatory networks. BioEssays 2002; 24: 1118.
97. Hill AV. The possible effects of the aggregation of the molecules of haemoglobin on its oxygen dissociation curve. J Physiol 1910; 40: 4-7.
98. De Jong H. Modeling and simulation of genetic regulatory systems:a literature review. J Comput Biol 2002; 9: 67-103.
99. Gillespie DT. Exact stochastic simulation of coupled chemical reactions. J Phys Chem 1977: 2340-2361.
100. Gillespie DT, Markov processes: an introduction for physical scientists. Boston, Academic Press, 1992.
101. McQuarrie DA. Stochastic approach to chemical kinetics. J Appl Prob 1967; 4: 417-478.
102. Gillespie DT. Approximate accelerated stochastic simulation of chemically reacting systems. J Chem Phys 2001; 115: 1716-1733.
103. Kampen V. The expansion of the Master equation. Adv Chem Phys 1976; 34: 245.
104. Paulsson J. Models of stochastic gene expression. Phys Life Rev 2005; 2: 157-175.
105. Thattai M, van Oudenaarden A. Intrinsic noise in gene regulatory networks. Proc Natl Acad Sci USA 2001; 98: 8614-9.
106. Kaufmann BB, van Oudenaarden A. Stochastic gene expression:from single molecules to the proteome. Curr Opin Genet Dev 2007; 17: 107-112.
107. Scott M, Ingalls B, Kaern M. Estimations of intrinsic and extrinsic noise in models of nonlinear genetic networks. Chaos 2006; 16:026107.
108. Vohradsky J. Neural model of the genetic network. J Biol Chem 2001; 276: 36168-73.
109. Wahde M, Hertz J. Coarse-grained reverse engineering of genetic regulatory networks. Biosystems 2000; 55: 129-36.
110. Friedman N, Linial M, Nachman I, Pe’er D. Using Bayesian networks to analyze expression data. J Comput Biol 2000; 7: 601-20.
111. Hartemink AJ, Gifford DK, Jaakkola TS, Young RA. Using graphical models and genomic expression data to statistically validate models of genetic regulatory networks. Pac Symp Biocomput 2001: 422-33.
112. Nagarajan R, Aubin JE, Peterson CA. Modeling genetic networks from clonal analysis. J Theor Biol 2004; 230: 359-73.
113. Sachs K, Perez O, Pe’er D, Lauffenburger DA, Nolan GP. Causal protein-signaling networks derived from multiparameter single-cell data. Science 2005; 308: 523-9.
114. Tegner J, Yeung MK, Hasty J, Collins JJ. Reverse engineering gene networks: integrating genetic perturbations with dynamical modeling. Proc Natl Acad Sci USA 2003; 100: 5944-9.
115. Yeung MK, Tegner J, Collins JJ. Reverse engineering gene networks using singular value decomposition and robust regression. Proc Natl Acad Sci USA 2002; 99: 6163-8.
116. Chen T, He HL, Church GM. Modeling gene expression with differential equations. Pac Symp Biocomput 1999: 29-40.
117. Lee F, Yanofsky C. Transcription termination at the trp operon attenuators of Escherichia coli and Salmonella typhimurium: RNA secondary structure and regulation of termination. Proc Natl Acad Sci USA 1977; 74: 4365-9.
118. Yanofsky C. Transcription attenuation: once viewed as a novel regulatory strategy. J Bacteriol 2000; 182: 1-8.
119. Santillan M, Zeron ES. Dynamic influence of feedback enzyme inhibition and transcription attenuation on the tryptophan operon response to nutritional shifts. J Theor Biol 2004; 231: 287-98.
120. Birge EA. Bacterial and Bacteriophage Genetics. 5 ed, Springer New York, 2006.
121. Santillan M, Zeron ES. Analytical study of the multiplicity of regulatory mechanisms in the tryptophan operon. Bull Math Biol 2006; 68: 343-59.
122. Pittendrigh CS. Circadian rhythms and the circadian organization of living systems. Cold Spring Harb Symp Quant Biol 1960; 25:159-84.
123. Panda S, Hogenesch JB, Kay SA. Circadian rhythms from flies to human. Nature 2002; 417: 329-35.
124. Van Gelder RN, Herzog ED, Schwartz WJ, Taghert PH. Circadian Rhythms: In the Loop at Last. Science 2003; 300: 1534-1535.
125. Nitabach MN. Circadian rhythms: clock coordination. Nature 2005; 438: 173-5.
126. Schoning JC, Staiger D. At the pulse of time: protein interactions determine the pace of circadian clocks. FEBS Lett 2005; 579: 3246-52.
127. Hardin PE. The circadian timekeeping system of Drosophila. Curr Biol 2005; 15: R714-22.
128. Konopka RJ, Benzer S. Clock mutants of Drosophila melanogaster. Proc Natl Acad Sci USA 1971; 68: 2112-6.
129. Crews ST, Thomas JB, Goodman CS. The Drosophila singleminded gene encodes a nuclear protein with sequence similarity to the per gene product. Cell 1988; 52: 143-51.
130. Hoffman EC, Reyes H, Chu FF, et al. Cloning of a factor required for activity of the Ah (dioxin) receptor. Science 1991; 252: 954-8.
131. Huang ZJ, Edery I, Rosbash M. PAS is a dimerization domain common to Drosophila period and several transcription factors. Nature 1993; 364: 259-62.
132. Gekakis N, Saez L, Delahaye-Brown AM, et al. Isolation of timeless by PER protein interaction: defective interaction between timeless protein and long-period mutant PERL. Science 1995; 270: 811-5.
133. Myers MP, Wager-Smith K, Wesley CS, Young MW, Sehgal A. Positional cloning and sequence analysis of the Drosophila clock gene, timeless. Science 1995; 270: 805-8.
134. Sehgal A, Price JL, Man B, Young MW. Loss of circadian behavioral rhythms and per RNA oscillations in the Drosophila mutant timeless. Science 1994; 263: 1603-6.
135. Hardin PE, Hall JC, Rosbash M. Feedback of the Drosophila period gene product on circadian cycling of its messenger RNA levels. Nature 1990; 343: 536-40.
136. Sehgal A, Rothenfluh-Hilfiker A, Hunter-Ensor M, Chen Y, Myers MP, Young MW. Rhythmic expression of timeless: a basis for promoting circadian cycles in period gene autoregulation. Science 1995; 270: 808-10.
137. Hao H, Allen DL, Hardin PE. A circadian enhancer mediates PERdependent mRNA cycling in Drosophila melanogaster. Mol Cell Biol 1997; 17: 3687-93.
138. McDonald MJ, Rosbash M. Microarray analysis and organization of circadian gene expression in Drosophila. Cell 2001; 107: 567-78.
139. Darlington TK, Wager-Smith K, Ceriani MF, et al. Closing the circadian loop: CLOCK-induced transcription of its own inhibitors per and tim. Science 1998; 280: 1599-603.
140. Bae K, Lee C, Sidote D, Chuang KY, Edery I. Circadian regulation of a Drosophila homolog of the mammalian Clock gene: PER and TIM function as positive regulators. Mol Cell Biol 1998; 18: 6142-51.
141. Glossop NR, Lyons LC, Hardin PE. Interlocked feedback loops within the Drosophila circadian oscillator. Science 1999; 286: 766-8.
142. Glossop NR, Houl JH, Zheng H, Ng FS, Dudek SM, Hardin PE. VRILLE feeds back to control circadian transcription of Clock in the Drosophila circadian oscillator. Neuron 2003; 37: 249-61.
143. Cyran SA, Buchsbaum AM, Reddy KL, et al. vrille, Pdp1, and dClock form a second feedback loop in the Drosophila circadian clock. Cell 2003; 112: 329-41.
144. Zerr DM, Hall JC, Rosbash M, Siwicki KK. Circadian fluctuations of period protein immunoreactivity in the CNS and the visual system of Drosophila. J Neurosci 1990; 10: 2749-62.
145. Zeng H, Qian Z, Myers MP, Rosbash M. A light-entrainment mechanism for the Drosophila circadian clock. Nature 1996; 380:129-35.
146. Lee C, Bae K, Edery I. The Drosophila CLOCK protein undergoes daily rhythms in abundance, phosphorylation, and interactions with the PER-TIM complex. Neuron 1998; 21: 857-67.
147. Price JL, Blau J, Rothenfluh A, Abodeely M, Kloss B, Young MW. double-time is a novel Drosophila clock gene that regulates PERIOD protein accumulation. Cell 1998; 94: 83-95.
148. Leloup J-C, Goldbeter A. Toward a detailed computational model for the mammalian circadian clock. Proc Natl Acad Sci USA 2003; 100: 7051-7056.
149. Locke JC, Southern MM, Kozma-Bognar L, et al. Extension of a genetic network model by iterative experimentation and mathematical analysis. Mol Syst Biol 2005; 1: 2005-13.
150. Goldbeter A. Computational approaches to cellular rhythms. Nature 2002; 420: 238-45.
151. Leloup JC, Goldbeter A. A model for circadian rhythms in Drosophila incorporating the formation of a complex between the PER and TIM proteins. J Biol Rhythms 1998; 13: 70-87.
152. Leloup JC, Goldbeter A. Modeling the molecular regulatory mechanism of circadian rhythms in Drosophila. Bioessays 2000; 22: 84-93.
153. Tyson JJ, Hong CI, Thron CD, Novak B. A Simple Model of Circadian Rhythms Based on Dimerization and Proteolysis of PER and TIM. Biophys J 1999; 77: 2411-2417.
154. Ueda HR, Hagiwara M, Kitano H. Robust oscillations within the interlocked feedback model of Drosophila circadian rhythm. J Theor Biol 2001; 210: 401-6.
155. Smolen P, Hardin PE, Lo BS, Baxter DA, Byrne JH. Simulation of Drosophila Circadian Oscillations, Mutations, and Light Responses by a Model with VRI, PDP-1, and CLK. Biophys J 2004; 86: 2786-2802.
156. Ruoff P, Christensen MK, Sharma VK. PER/TIM-mediated amplification, gene dosage effects and temperature compensation in an interlocking-feedback loop model of the Drosophila circadian clock. J Theor Biol 2005; 237: 41-57.
157. Hida A, Koike N, Hirose M, Hattori M, Sakaki Y, Tei H. The human and mouse Period1 genes: five well-conserved E-boxes additively contribute to the enhancement of mPer1 transcription. Genomics 2000; 65: 224-33.
158. Murray JD, Mathematical biology. 3rd ed. Interdisciplinary applied mathematics. New York, Springer, 2002.
159. Hynne F, Dano S, Sorensen PG. Full-scale model of glycolysis in Saccharomyces cerevisiae. Biophys Chem 2001; 94: 121-63.