Intrinsic noise, gene regulation and steady-state statistics in a two-gene network.

The intrinsic noise in a two-gene network model is analysed. The technique of the Fokker-Planck approximation is used to investigate the statistics of noise when the system state is near a stable equilibrium. This is called also the steady-state statistics. The relative size of noise is measured by the Fano factor that is defined as the ratio of the variance to the mean. Our main result shows that in general, the noise control in a two-gene network might be a very complicated process, but for the repressor-repressor system that is a very important case in investigating the genetic switch, the relative size of noise, i.e. the Fano factor, must be bigger than one for both the repressor proteins.

[1]  M. Thattai,et al.  Intrinsic noise in gene regulatory networks , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[2]  Ertugrul M. Ozbudak,et al.  Regulation of noise in the expression of a single gene , 2002, Nature Genetics.

[3]  M. Ehrenberg,et al.  Fluctuations in repressor control: thermodynamic constraints on stochastic focusing. , 2000, Biophysical journal.

[4]  A. Arkin,et al.  Stochastic mechanisms in gene expression. , 1997, Proceedings of the National Academy of Sciences of the United States of America.

[5]  J. Demongeot,et al.  Positive and negative feedback: striking a balance between necessary antagonists. , 2002, Journal of theoretical biology.

[6]  A. Keller,et al.  Model genetic circuits encoding autoregulatory transcription factors. , 1995, Journal of theoretical biology.

[7]  J. Hasty,et al.  Translating the noise , 2002, Nature Genetics.

[8]  Bruce Hannon,et al.  Positive and Negative Feedback , 1994 .

[9]  F R Adler,et al.  How to make a biological switch. , 2000, Journal of theoretical biology.

[10]  J. Collins,et al.  Construction of a genetic toggle switch in Escherichia coli , 2000, Nature.

[11]  J. Hasty,et al.  Noise-based switches and amplifiers for gene expression. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[12]  A. Arkin,et al.  Stochastic kinetic analysis of developmental pathway bifurcation in phage lambda-infected Escherichia coli cells. , 1998, Genetics.

[13]  Farren J. Isaacs,et al.  Prediction and measurement of an autoregulatory genetic module , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[14]  M. Ehrenberg,et al.  Random signal fluctuations can reduce random fluctuations in regulated components of chemical regulatory networks. , 2000, Physical review letters.

[15]  T. Kepler,et al.  Stochasticity in transcriptional regulation: origins, consequences, and mathematical representations. , 2001, Biophysical journal.

[16]  Peter G Wolynes,et al.  Stochastic gene expression as a many-body problem , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[17]  Yi Tao,et al.  Intrinsic and external noise in an auto-regulatory genetic network. , 2004, Journal of theoretical biology.

[18]  M. Ehrenberg,et al.  Stochastic focusing: fluctuation-enhanced sensitivity of intracellular regulation. , 2000, Proceedings of the National Academy of Sciences of the United States of America.