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J. Math. Biol. (2007) 55:413431 DOI 10.1007/s00285-007-0090-x
Mathematical Biology
Modeling stochastic gene expression under repression
G. C. P. Innocentini J. E. M. Hornos
Received: 27 June 2006 / Revised: 14 March 2007 / Published online: 22 May 2007 Springer-Verlag 2007
Abstract Intrinsic transcriptional noise induced by operator uctuations is investigated with a simple spin-like stochastic model. The effects of transcriptional uctuations in protein synthesis are probed by coupling transcription and translation by an amplicative interaction. In the presence of repression a new term contributes to the noise, which depends on the rate of mRNA production. If the switch decay time is small compared with the mRNA life time, the noise is also small. In general the damping of protein production by a repressive agent occurs linearly but uctuations can show a maximum at intermediate repression. The discrepancy among the switch decay time, the mRNA degradation, and protein degradation is crucial for the repressive control in translation without large uctuations. The noise proles obtained here are in quantitative agreement with recent experiments.
Keywords Transcriptional regulation Expression Stochasticity Fluctuations
Mathematics Subject Classication (2000) 92B05
1 Introduction
The remarkable simplicity of the relation between genetic information and protein synthesis in the ribosomes, resulting in a symmetrical and almost universal genetic
Work was supported by FAPESP and CNPq, Brazil.
G. C. P. Innocentini J. E. M. Hornos (B)
Instituto de Fsica de So Carlos, Universidade de So Paulo, Caixa Postal 369, 13560-970, So Carlos, SP, Brazile-mail: [email protected]
G. C. P. Innocentinie-mail: [email protected]
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code, is the result of a complex process involving a large number of chemical reactions. The gene transcription is assisted by the enzymatic action of regulatory proteins which can enhance or repress the production of mRNA molecules. The amino-acid assembling in the ribosome ends the cycle and proteins are produced and folded to a functional form. The pioneer work on lambda phage [25] has shown the crucial role of regulatory proteins in the control of such genetic networks [20] and intense experimental and theoretical investigations [25,7,8,11,16,17,26,27] have been dedicated to the understanding of this web of interactions.
Despite the fact that we are dealing with biosystems composed by a large number of genes, with complex gene-gene interactions...