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Exact protein distributions for stochastic models of gene expression using partitioning of Poisson processes

Hodjat Pendar*

Thierry Platini†

Rahul V. Kulkarni‡

  • Department of Engineering Science and Mechanics, Virginia Tech, Blacksburg, Virginia 24061, USA

  • Applied Mathematics Research Center, Coventry University, Coventry, CV1 5FB, England

  • Department of Physics, University of Massachusetts, Boston, Massachusetts USA

  • *Electronic address: hpendar@vt.edu
  • †Electronic address: thierry.platini@coventry.ac.uk
  • ‡Electronic address: rahul.kulkarni@umb.edu
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Phys. Rev. E 87, 042720 – Published 26 April, 2013

DOI: https://doi.org/10.1103/PhysRevE.87.042720

Abstract

Stochasticity in gene expression gives rise to fluctuations in protein levels across a population of genetically identical cells. Such fluctuations can lead to phenotypic variation in clonal populations; hence, there is considerable interest in quantifying noise in gene expression using stochastic models. However, obtaining exact analytical results for protein distributions has been an intractable task for all but the simplest models. Here, we invoke the partitioning property of Poisson processes to develop a mapping that significantly simplifies the analysis of stochastic models of gene expression. The mapping leads to exact protein distributions using results for mRNA distributions in models with promoter-based regulation. Using this approach, we derive exact analytical results for steady-state and time-dependent distributions for the basic two-stage model of gene expression. Furthermore, we show how the mapping leads to exact protein distributions for extensions of the basic model that include the effects of posttranscriptional and posttranslational regulation. The approach developed in this work is widely applicable and can contribute to a quantitative understanding of stochasticity in gene expression and its regulation.

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References (29)

  1. G. Balázsi, A. van Oudenaarden, and J. Collins, Cell 144, 910 (2011).
  2. A. Raj and A. van Oudenaarden, Cell 135, 216 (2008).
  3. O. Gefen, C. Gabay, M. Mumcuoglu, G. Engel, and N. Balaban, Proc. Natl. Acad. Sci. USA 105, 6145 (2008).
  4. L. Weinberger, J. Burnett, J. Toettcher, A. Arkin, and D. Schaffer, Cell 122, 169 (2005).
  5. J. Raser and E. O’Shea, Science 304, 1811 (2004).
  6. J. Paulsson, Phys. Life Rev. 2, 157 (2005).
  7. Á. Sánchez and J. Kondev, Proc. Natl. Acad. Sci. USA 105, 5081 (2008).
  8. A. Coulon, O. Gandrillon, and G. Beslon, BMC Syst. Biol. 4, 2 (2010).
  9. A. Singh, B. Razooky, R. Dar, and L. Weinberger, Mol. Syst. Biol. 8, 607 (2012).
  10. T. To and N. Maheshri, Science 327, 1142 (2010).
  11. Y. Taniguchi, P. Choi, G. Li, H. Chen, M. Babu, J. Hearn, A. Emili, and X. Xie, Science 329, 533 (2010).
  12. M. Ferguson, D. Le Coq, M. Jules, S. Aymerich, O. Radulescu, N. Declerck, and C. Royer, Proc. Natl. Acad. Sci. USA 109, 155 (2012).
  13. J. Peccoud and B. Ycart, Theoret. Pop. Biol. 48, 222 (1995).
  14. A. Raj, C. Peskin, D. Tranchina, D. Vargas, and S. Tyagi, PLoS Biol. 4, e309 (2006).
  15. S. Iyer-Biswas, F. Hayot, and C. Jayaprakash, Phys. Rev. E 79, 031911 (2009).
  16. J. Zhang, L. Chen, and T. Zhou, Biophys. J. 102, 1247 (2012).
  17. A. Stinchcombe, C. Peskin, and D. Tranchina, Phys. Rev. E 85, 061919 (2012).
  18. J. E. M. Hornos, D. Schultz, G. C. P. Innocentini, J. Wang, A. M. Walczak, J. N. Onuchic, and P. G. Wolynes, Phys. Rev. E 72, 051907 (2005).
  19. A. F. Ramos, G. C. P. Innocentini, and J. E. M. Hornos, Phys. Rev. E 83, 062902 (2011).
  20. N. Friedman, L. Cai, and X. Xie, Phys. Rev. Lett. 97, 168302 (2006).
  21. V. Shahrezaei and P. Swain, Proc. Natl. Acad. Sci. USA 105, 17256 (2008).
  22. P. Bokes, J. King, A. Wood, and M. Loose, J. Math. Biol. 64, 829 (2012).
  23. S. Ross, Introduction to Probability Models (Academic Press, New York, 2006).
  24. D. Bratsun, D. Volfson, L. Tsimring, and J. Hasty, Proc. Natl. Acad. Sci. USA 102, 14593 (2005).
  25. L. Lafuerza and R. Toral, Phys. Rev. E 84, 051121 (2011).
  26. J. Miękisz, J. Poleszczuk, M. Bodnar, and U. Foryś, Bull. Math. Biol. 73, 2231 (2011).
  27. B. Munsky, G. Neuert, and A. van Oudenaarden, Science 336, 183 (2012).
  28. Y. Lan, P. G. Wolynes, and G. A. Papoian, J. Chem. Phys. 125, 124106 (2006).
  29. D. Larson, Curr. Opin. Genet. Dev. 21, 591 (2011).

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Phys. Rev. E 87, 042720– Published 26 April, 2013
  • Received 16 February 2013
Article part of CHORUS

©2013 American Physical Society

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