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Chaos / Volume 21 / Issue 4 / FOCUS ISSUE: NONLINEAR AND STOCHASTIC PHYSICS IN BIOLOGY
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Chaos 21, 047523 (2011); http://dx.doi.org/10.1063/1.3658618 (12 pages)

A common repressor pool results in indeterminacy of extrinsic noise

Michail Stamatakis1, Rhys M. Adams2, and Gábor Balázsi2

1Department of Chemical and Biomolecular Engineering, Rice University, Houston, Texas 77005, USA
2Department of Systems Biology – Unit 950, The University of Texas MD Anderson Cancer Center, Houston, Texas 77054, USA

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(Received 21 July 2011; accepted 17 October 2011; published online 29 December 2011)

For just over a decade, stochastic gene expression has been the focus of many experimental and theoretical studies. It is now widely accepted that noise in gene expression can be decomposed into extrinsic and intrinsic components, which have orthogonal contributions to the total noise. Intrinsic noise stems from the random occurrence of biochemical reactions and is inherent to gene expression. Extrinsic noise originates from fluctuations in the concentrations of regulatory components or random transitions in the cell’s state and is imposed to the gene of interest by the intra- and extra-cellular environment. The basic assumption has been that extrinsic noise acts as a pure input on the gene of interest, which exerts no feedback on the extrinsic noise source. Thus, multiple copies of a gene would be uniformly influenced by an extrinsic noise source. Here, we report that this assumption falls short when multiple genes share a common pool of a regulatory molecule. Due to the competitive utilization of the molecules existing in this pool, genes are no longer uniformly influenced by the extrinsic noise source. Rather, they exert negative regulation on each other and thus extrinsic noise cannot be determined by the currently established method.

© 2011 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. INTRINSIC AND EXTRINSIC NOISE: AN OVERVIEW
  3. MATHEMATICAL MODELING AND STOCHASTIC SIMULATIONS
    1. Competitive repressor utilization
      1. Formulation of the model
      2. Fast-operator-fluctuations approximation
      3. Solution of the Master equation for LacI and its target operators
      4. Stochastic simulations
      5. Calculation of extrinsic and intrinsic noise
    2. Non-competitive repressor utilization
  4. SUMMARY

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KEYWORDS and PACS

Keywords

genetics, indeterminancy, noise, random processes, stochastic processes

PACS

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.3658618

PUBLICATION DATA

ISSN

1054-1500 (print)  
1089-7682 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

  1. H. C. Berg , Random Walks in Biology (Princeton University, Princeton, NJ, 1993).
  2. A. Einstein, Ann. Phys. 17, 549 (1905). [ISI]
  3. A. Pikovsky, M. Rosenblum, and J. Kurths , Synchronization: A Universal Concept in Nonlinear Sciences (Cambridge University Press, Cambridge, UK, 2003).
  4. S. H. Strogatz , Nonlinear Dynamics And Chaos: With Applications To Physics, Biology, Chemistry, And Engineering (Westview Press, Cambridge, MA, USA, 2001).
  5. V. S. Anishchenko, V. Astakhov, A. Neiman, T. Vadivasova, and L. Schimansky-Geier , Nonlinear Dynamics of Chaotic and Stochastic Systems: Tutorial and Modern Developments, 2nd ed. (Springer, New York, 2007).
  6. A.-L. Barabási , Linked: How Everything Is Connected to Everything Else and What It Means (Plume, New York, NY, USA, 2003).
  7. A. L. Barabási and Z. N. Oltvai, Nat. Rev. Genet. 5(2), 101 (2004). [MEDLINE]
  8. K. Wiesenfeld and F. Moss, Nature (London) 373(6509), 33 (1995). [MEDLINE]
  9. G. Balázsi, A. van Oudenaarden, and J. J. Collins, Cell 144(6), 910 (2011).
  10. A. Eldar and M. B. Elowitz, Nature (London) 467(7312), 167 (2010).
  11. M. Kaern, T. C. Elston, W. J. Blake, and J. J. Collins, Nat. Rev. Genet. 6(6), 451 (2005).
  12. N. Maheshri and E. K. O'Shea, Annu. Rev. Biophys. Biomol. Struct. 36, 413 (2007). [MEDLINE]
  13. A. Raj and A. van Oudenaarden, Cell 135(2), 216 (2008). [MEDLINE]
  14. C.V. Rao, D. M. Wolf, and A. P. Arkin, Nature (London) 420(6912), 231 (2002). [MEDLINE]
  15. K. F. Murphy, G. Balázsi, and J. J. Collins, Proc. Natl Acad. Sci. U.S.A. 104(31), 12726 (2007). [MEDLINE]
  16. K. F. Murphy, R. M. Adams, X. Wang, G. Balázsi, and J. J. Collins, Nucleic. Acids Res. 38(8), 2712 (2010).
  17. P. S. Swain, M. B. Elowitz, and E. D. Siggia, Proc. Natl Acad. Sci. U.S.A. 99(20), 12795 (2002).
  18. M. B. Elowitz, A. J. Levine, E. D. Siggia, and P. S. Swain, Science 297(5584), 1183 (2002). [MEDLINE]
  19. M. Thattai and A. van Oudenaarden, Proc. Natl. Acad. Sci. U. S. A. 98(15), 8614 (2001). [ISI] [MEDLINE]
  20. J. J. Tyson and H. G. Othmer, Prog.Theor. Biol., 5, 1 (1978).
  21. C. Tan, P. Marguet, and L. C. You,. Nat. Chem. Biol., 5(11), 842 (2009).
  22. F. J. Isaacs, J. Hasty, C. R. Cantor, and J. J. Collins, Proc. Natl Acad. Sci. U.S.A. 100(13), 7714 (2003). [ISI] [MEDLINE]
  23. P. Guptasarma, BioEssays 17(11), 987 (1995). [ISI] [MEDLINE]
  24. D. Normanno, F. Vanzi, and F. S. Pavone,. Nucleic Acids Res. 36(8), 2505 (2008).
  25. W. Bialek, F. Rieke, R. R. de Ruyter van Steveninck, and D. Warland, Science 252(5014), 1854 (1991). [ISI] [MEDLINE]
  26. J. K. Douglass et al., Nature (London) 365(6444), 337 (1993). [MEDLINE]
  27. Z. Gingl, L. B. Kiss, and F. Moss, Europhys. Lett. 29(3), 191 (1995). [Inspec] [ISI]
  28. K. Wiesenfeld, D. Pierson, E. Pantazelou, C. Dames, and F. Moss, Phys. Rev. Lett. 72(14), 2125 (1994). [MEDLINE]
  29. S. M. Bezrukov and I. Vodyanoy, Nature (London) 378(6555), 362 (1995). [MEDLINE]
  30. P. C. Gailey, A. Neiman, J. J. Collins, and F. M. Moss, Phys. Rev. Lett. 79(23), 4701 (1997). [ISI]
  31. J. J. Collins, C. C. Chow, and T. T. Imhoff, Nature (London) 376(6537), 236 (1995). [Inspec] [ISI] [MEDLINE]
  32. E. M. Ozbudak, M. Thattai, I. Kurtser, A. D. Grossman, and A. van Oudenaarden, Nat. Genet. 31(1), 69 (2002). [MEDLINE]
  33. T. M. Neildez-Nguyen, A. Parisot, C. Vignal, P. Rameau, D. Stockholm, J. Picot, V. Allo, C. Le Bec, C. Laplace, and A. Paldi, Differentiation 76(1), 33 (2008).
  34. A. Raj, C. S. Peskin, D. Tranchina, D. Y. Vargas, and S. Tyagi, PLoS Biol. 4(10), e309 (2006).
  35. J. M. Raser and E. K. O'Shea,. Science 304(5678), 1811 (2004).
  36. A. Becskei, B. B. Kaufmann, and A. van Oudenaarden,. Nat. Genet. 37(9), 937 (2005). [MEDLINE]
  37. D. Volfson, J. Marciniak, W. J. Blake, N. Ostroff, L. S. Tsimring, and J. Hasty, Nature (London) 439(7078), 861 (2006). [MEDLINE]
  38. W. J. Blake, G. Balazsi, M. A. Kohanski, F. J. Isaacs, K. F. Murphy, Y. Kuang, C. R. Cantor, D. R. Walt, and J. J. Collins, Mol. Cell 24(6), 853 (2006). [MEDLINE]
  39. W. J. Blake, M. Kærn, C. R. Cantor, and J. J. Collins, Nature 422(6932), 633 (2003). [ISI] [MEDLINE]
  40. M. Stamatakis and N. V. Mantzaris, Biophys. J. 96(3), 887 (2009).
  41. D. T. Gillespie, J. Comput. Phys. 22(4), 403 (1976).
  42. D. T. Gillespie, J. Phys. Chem. 81(25), 2340 (1977).
  43. N. G. van Kampen , Stochastic Processes in Physics and Chemistry (North-Holland-Personal-Library, New York, Amsterdam, 1992).
  44. C. V. Rao and A. P. Arkin, J. Chem. Phys. 118(11), 4999 (2003)JCPSA6000118000011004999000001. [ISI]
  45. C. Z. Jiang and B. F. Pugh, Nat. Rev. Genet. 10(3), 161 (2009).

Figures (5) Tables (3)

Figures (click on thumbnails to view enlargements)

FIG.1
A gene could be viewed as a noisy machine that accepts a random signal as input (extrinsic noise E) and transforms it through an inherently stochastic process (intrinsic noise, I), thereby generating a noisy output signal (f(E,I)). Consequently, the latter contains two orthogonal noise components: extrinsic, due to the input noise, and intrinsic due to the noise produced within the “machine.” In our discussion, the output is the protein expression level: f(E,I) = P(E,I).

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FIG.2
Schematic representation of the interactions taken into account in the two promoter-reporter system. For species notation see Table 1.

FIG.2 Download High Resolution Image (.zip file) | Export Figure to PowerPoint

FIG.3
Comparison of the analytical math(ɛ) approximation for the stationary probability math0s(LacT) with simulation results. Panel (a): plot of Eq. ( 38 ) and of the stationary LacT probability estimate from samples obtained from Gillespie simulations. Panel (b): sampling error falls with the inverse square root of the sample size.

FIG.3 Download High Resolution Image (.zip file) | Export Figure to PowerPoint

FIG.4
(Color) Scatter plots of the Yfp versus Cfp concentration assuming constant repressor content (kLac = 0 nM/min, λLac = 0 min−1). Panel (a): total LacI content equal to 1 molecule; parameter values: kr = 10 (nM·min)−1, k−r = 1 min−1, km = 10 min−1, kp = 10 min−1, λm = 0.4 min−1, λp = 0.1 min−1. Panel (b): total LacI content equal to 4 molecules; parameter values: kr = 50 (nM·min)−1, k−r = 1 min−1, km = 10 min−1, kp = 1000 min−1, λm = 0.4 min−1, λp = 0.1 min−1. Colors indicate relative density of points on the Yfp-Cfp plane: warmer colors correspond to higher densities.

FIG.4 Download High Resolution Image (.zip file) | Export Figure to PowerPoint

FIG.5
Plots of the intrinsic (panel a) and extrinsic (panel b) noise for given q = LacT concentration as calculated from Eqs. ( 42 , 43 ).

FIG.5 Download High Resolution Image (.zip file) | Export Figure to PowerPoint

Tables

Table I. Symbols used for the species.

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Table II. Kinetic constants (deterministic and stochastic).

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Table III. Reaction network and propensity functions.

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