Hybrid modeling of noise reduction by a negatively autoregulated system

Bulletin of Mathematical Biology

Volumn 71, Issue 4, 2009, Pages 1006-1024

  Zeiser, Stefan ^a   Franz, Uwe ^b,c   Müller, Johannes ^d   Liebscher, Volkmar ^e  

^a INSTITUTE OF EPIDEMIOLOGY   (Germany)

^b UNIVERSITÉ DE FRANCHE COMTÉ   (France)

^c TOHOKU UNIVERSITY   (Japan)

^d TECHNICAL UNIVERSITY OF MUNICH   (Germany)

^e UNIVERSITY OF GREIFSWALD   (Germany)

Author keywords

Hybrid modeling; Negative feedback loop; Noise attenuation; Stationary distribution

Indexed keywords

ARTICLE; BIOLOGICAL MODEL; FEEDBACK SYSTEM; GENE EXPRESSION REGULATION; GENETIC TRANSCRIPTION; HOMEOSTASIS; PROMOTER REGION;

FEEDBACK; GENE EXPRESSION REGULATION; HOMEOSTASIS; MODELS, GENETIC; PROMOTER REGIONS, GENETIC; TRANSCRIPTION, GENETIC;

EID: 64449085131     PISSN: 00928240     EISSN: 15229602     Source Type: Journal    
DOI: 10.1007/s11538-008-9391-5     Document Type: Article

References (26)

1. A. Becskei L. Serrano 2000 Engineering stability in gene networks by autoregulation Nature 405 590 593
2. A. Becskei B. Séraphin L. Serrano 2001 Positive feedback in eukaryotic gene networks: cell differentiation by graded to binary response conversion EMBO J. 20 2528 35
3. A. Belle A. Tanay L. Bitincka R. Shamir E.K. O'Shea 2006 Quantification of protein half-lives in the budding yeast proteome Proc. Natl. Acad. Sci. USA 103 13004 13009
4. M.H.A. Davis 1984 Piecewise-deterministic Markov processes: A general class of non-diffusion stochastic models J. R. Stat. Soc. B 46 353 388
5. M.B. Elowitz A.J. Levine E.D. Siggia P.S. Swain 2002 Stochastic gene expression in a single cell Science 297 1183 1186
6. S. Godstein 1951 On diffusion by discontinuous movements and on the telegraph equation Q. J. Mech. Appl. Math. 4 129 156
7. K.P. Hadeler 1998 Reaction transport equations in biological modeling Math. Comput. Model. 31 75 81
8. P.E. Hardin J.C. Hall M. Rosbash 1990 Feedback of the Drosophila period gene product on circadian cycling of its messenger RNA levels Nature 343 536 540
9. H. Hirata S. Yoshiura T. Ohtsuka Y. Bessho T. Harada K. Yoshikawa R. Kageyama 2002 Oscillatory expression of the bHLH factor Hes1 regulated by a negative feedback loop Science 298 840 843
10. J.E. Ferrell Jr. E.M. Machleder 1998 The biochemical basis of an all-or-none cell fate switch in xenopus oocytes Science 280 895 898
11. M. Kac 1974 A stochastic model related to the telegrapher's equation Rocky Mt. J. Math. 4 497 509 Reprinted
12. T.B. Kepler T.C. Elstondagger 2001 Stochasticity in transcriptional regulation: Origins, consequences, and mathematical representations Biophys. J. 81 3116 3136
13. H. Kwon S. Park S. Lee D.-K. Lee C.-H. Yang 2001 Determination of binding constant of transcription factor AP-1 and DNA Eur. J. Biochem. 268 565 572
14. H.H. McAdams A. Arkin 1997 Stochastic mechanisms in gene expression Proc. Natl. Acad. Sci. USA 94 814 819
15. J. Müller C. Kuttler B.A. Hense S. Zeiser V. Liebscher 2008 Transcription, intercellular variability and correlated random walk Math. Biosci. 216 30 39
16. J. Peccoud B. Ycart 1995 Markovian modelling of gene products synthesis Theor. Popul. Biol. 48 222 234
17. A. Raj C.S. Peskin D. Tranchina D.Y. Vargas S. Tyagi 2006 Stochastic mRNA synthesis in mammalian cells PLoS Biol. 4 1707 1719
18. M.A. Savageau 1974 Comparison of classical and autogenous systems of regulation in inducible operons Nature 252 546 549
19. D.B. Schulman D.R. Setzera 2002 Identification and characterization of transcription factor IIIA from Schizosaccharomyces pombe Nucleic Acids Res. 30 2772 2781
20. Slater, L.J., 1966. Generalized Hypergeometric Functions. Cambridge University Press, Cambridge.
21. W.K. Smits C.C. Eschevins K.A. Susanna S. Bron O.P. Kuipers L.W. Hamoen 2005 Stripping Bacillus: ComK auto-stimulation is responsible for the bistable response in competence development Mol. Microbiol. 56 604 14
22. M.A. Sørensen S. Pedersen 1991 Absolute in vivo translation rates of individual codons in Escherichia coli. The two glutamic acid codons GAA and GAG are translated with a threefold difference in rate J. Mol. Biol. 222 265 280
23. J.J. Tyson H.G. Othmer 1978 The dynamics of feedback control circuits in biochemical pathways Prog. Theor. Biol. 5 1 62
24. van Kampen, N.G., 1992. Stochastic Processes in Physics and Chemistry. North-Holland-Elsevier, Amsterdam.
25. D.M. Wolf F.H. Eeckman 1998 On the relationship between genomic regulatory element organization and gene regulatory dynamics J. Theor. Biol. 195 167 186
26. S. Zeiser U. Franz O. Wittich V. Liebscher 2008 Simulation of genetic networks modelled by piecewise deterministic Markov processes IET Syst. Biol. 2 113 135