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Modeling stochastic gene expression under repression

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Abstract

Intrinsic transcriptional noise induced by operator fluctuations is investigated with a simple spin-like stochastic model. The effects of transcriptional fluctuations in protein synthesis are probed by coupling transcription and translation by an amplificative 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 fluctuations 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 fluctuations. The noise profiles obtained here are in quantitative agreement with recent experiments.

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References

  1. Abramowitz, M., Stegun, I.A.: Handbook of mathematical functions with formulas, graphs and mathematical tables. Nat. Bur. Standards Appl. Series, 55, U.S. Government Printing Office, Washington, D.C. (paperback edition published by Dover, New York) (1964)

  2. Ackers G.K., Johnson A.D. and Shea M.A. (1982). Quantitative model for gene regulation by λ phage repressor. Proc. Natl. Acad. Sci. USA 79: 1129–1133

    Article  Google Scholar 

  3. Becskei A. and Serrano L. (2000). Engineering stability in gene networks by autoregulation. Nature 405: 590–593

    Article  Google Scholar 

  4. Berg O.G. (1978). A model for the statistical fluctuations of protein numbers in a microbial population. J. Theor. Biol. 71: 587–603

    Article  Google Scholar 

  5. Bhalla U.S. and Iyengar R. (1999). Emergent properties of networks of biological signaling pathways. Science 283: 381–387

    Article  Google Scholar 

  6. Blake W.J., Kaern M., Cantor C.R. and Collins J.J. (2003). Noise in eukaryotic gene expression. Nature 422: 633–637

    Article  Google Scholar 

  7. Cook D.L., Gerber A.N. and Tapscott S.J. (1998). Modeling stochastic gene expression: Implications for haploinsufficiency. Proc. Natl. Acad. Sci. USA 95: 15641–15646

    Article  Google Scholar 

  8. von Dassow G., Meir E., Munro E.M. and Odell G.M. (2000). The segment polarity network is a robust developmental module. Nature 406: 188–192

    Article  Google Scholar 

  9. Elowitz M.B. and Leibler S. (2000). A synthetic oscillatory network of transcriptional regulators. Nature 403: 335–338

    Article  Google Scholar 

  10. Gardner T.S., Cantor C.R. and Collins J.J. (2000). Construction of genetic toggle switch in Escherichia coli. Nature 403: 339–342

    Article  Google Scholar 

  11. Gillespie D.T. (1977). Exact stochastic simulation of coupled chemical reactions. J. Phys. Chem. 81: 2340–2361

    Article  Google Scholar 

  12. Hasty J., Pradines J., Dolnik M. and Collins J.J. (2000). Noise-based switches and amplifiers for gene expression. Proc. Natl. Acad. Sci. USA 97: 2075–2080

    Article  Google Scholar 

  13. Hornos J.E.M., Schultz D., Innocentini G.C.P., Wang J., Walczak A.M., Onuchic J.N. and Wolynes P.G. (2005). Self-regulating gene: An exact solution. Phys. Rev. E 72: 051907

    Article  MathSciNet  Google Scholar 

  14. Innocentini, G.C.P., Hornos, J.E.M.: Stochastic gene expression: approaching the equilibrium (in preparation)

  15. van Kampen N.G. (1992). Stochastic Processes in Physics and Chemistry. North-Holland, Amsterdam

    Google Scholar 

  16. Kennell D. and Riezman H. (1977). Transcription and translation initiation frequencies of the escherichia coli lac operon. J. Mol. Biol. 114: 1–21

    Article  Google Scholar 

  17. Ko M.S.H. (1991). A stochastic model for gene induction. J. Theor. Biol. 153: 181–194

    Article  Google Scholar 

  18. McAdams H.H. and Arkin A. (1997). Stochastic mechanisms in gene expression. Proc. Natl. Acad. Sci. USA 94: 814–819

    Article  Google Scholar 

  19. McAdams H.H. and Arkin A. (1999). Its a noisy business! genetic regulation at the nanomolar scale. Trends Genet. 15: 65–69

    Article  Google Scholar 

  20. Monod J. and Jacob F. (1961). Genetic regulatory mechanisms in synthesis of protein. J. Mol. Biol. 3: 318–356

    Google Scholar 

  21. Ozbudak E.M., Thattai M., Kurtser I., Grossman A.D. and van Oudenaarden A. (2002). Regulation of noise in the expression of single gene. Nat. Genet. 31: 69–73

    Article  Google Scholar 

  22. Paulsson J. (2004). Summing up the noise in gene networks. Nature 427: 415–418

    Article  Google Scholar 

  23. Paulsson J., Berg O.G. and Ehrenberg M. (2000). Stochastic focusing: Fluctuation-enhanced sensitivity of intracellular regulation. Proc. Natl. Acad. Sci. USA 97: 7148–7153

    Article  Google Scholar 

  24. Pedraza J.M. and van Oudenaarden A. (2005). Noise propagation in gene networks. Science 307: 1965–1969

    Article  Google Scholar 

  25. Ptashne M. (1992). A Genetic Switch: Phage λ and Higher Organisms. Cell Press/Blackwell, Cambridge

    Google Scholar 

  26. van de Putte P. and Goosen N. (1992). Dna inversions in phages and bacteria. Trends Genet. 8: 457–462

    Article  Google Scholar 

  27. Siegele D.A. and Hu J.C. (1997). Gene expression from plasmids containing the araBAD promoter at subsaturating inducer concentrations represents mixed populations. Proc. Natl. Acad. Sci.USA 94: 8168–8172

    Article  Google Scholar 

  28. Thattai M. and van Oudenaarden A. (2001). Intrinsic noise in gene regulatory networks. Proc. Natl. Acad. Sci. USA 98: 8614–8619

    Article  Google Scholar 

  29. Walczak A.M., Sasai M. and Wolynes P.G. (2005). Self-consistent proteomic field theory of stochastic gene switches. Biophys. J. 88: 828–850

    Article  Google Scholar 

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Correspondence to J. E. M. Hornos.

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Work was supported by FAPESP and CNPq, Brazil.

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Innocentini, G.C.P., Hornos, J.E.M. Modeling stochastic gene expression under repression. J. Math. Biol. 55, 413–431 (2007). https://doi.org/10.1007/s00285-007-0090-x

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  • DOI: https://doi.org/10.1007/s00285-007-0090-x

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