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Control, exploitation and tolerance of intracellular noise

Nature volume 420, pages 231–237 (2002)Cite this article

An Erratum to this article was published on 09 January 2003

Abstract

Noise has many roles in biological function, including generation of errors in DNA replication leading to mutation and evolution, noise-driven divergence of cell fates, noise-induced amplification of signals, and maintenance of the quantitative individuality of cells. Yet there is order to the behaviour and development of cells. They operate within strict parameters and in many cases this behaviour seems robust, implying that noise is largely filtered by the system. How can we explain the use, rejection and sensitivity to noise that is found in biological systems? An exploration of the sources and consequences of noise calls for the use of stochastic models.

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Figure 1: Comparison of the deterministic and stochastic solution for an isomerization reaction with dissociation constant Kd=1.
Figure 2: A comparison of the isomerization reaction with 10 and 100 molecules using a discrete stochastic model with k1=1 s−1 and k2=1 s−1.
Figure 3: Switches and chattering.
Figure 4: Construction of the synthetic positive feedback loop of Becksei and colleagues66.

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References

  1. Ko, M. S., Nakauchi, H. & Takahashi, N. The dose dependence of glucocorticoid-inducible gene expression results from changes in the number of transcriptionally active templates. EMBO J. 9, 2835–2842 (1990).

    CAS  PubMed  PubMed Central  Google Scholar 

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

    CAS  PubMed  Google Scholar 

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

    CAS  PubMed  Google Scholar 

  4. McAdams, H. H. & Arkin, A. Stochastic mechanisms in gene expression. Proc. Natl Acad. Sci. USA 94, 814–819 (1997).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  5. White, J. A., Rubinstein, J. T. & Kay, A. R. Channel noise in neurons. Trends Neurosci. 23, 131–137 (2000).

    CAS  PubMed  Google Scholar 

  6. Allen, C. & Stevens, C. F. An evaluation of causes for unreliability of synaptic transmission. Proc. Natl Acad. Sci. USA 91, 10380–10383 (1994).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  7. van Oudenaarden, A. & Theriot, J. A. Cooperative symmetry-breaking by actin polymerization in a model for cell motility. Nature Cell Biol. 1, 493–499 (1999).

    CAS  PubMed  Google Scholar 

  8. Simon, S. M., Peskin, C. S. & Oster, G. F. What drives the translocation of proteins? Proc. Natl Acad. Sci. USA 89, 3770–3774 (1992).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  9. Sternberg, P. W. & Felix, M. A. Evolution of cell lineage. Curr. Opin. Genet. Dev. 7, 543–550 (1997).

    CAS  PubMed  Google Scholar 

  10. Houchmandzadeh, B., Wieschaus, E. & Leibler, S. Establishment of developmental precision and proportions in the early Drosophila embryo. Nature 415, 798–802 (2002).

    ADS  CAS  PubMed  Google Scholar 

  11. Barkai, N. & Leibler, S. Robustness in simple biochemical networks. Nature 387, 913–917 (1997).

    ADS  CAS  PubMed  Google Scholar 

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

    ADS  CAS  PubMed  Google Scholar 

  13. Ptashne, M. A Genetic Switch : Phage Lambda and Higher Organisms (Cell Press, Blackwell Scientific Publications, Cambridge, MA, 1998).

    Google Scholar 

  14. Msadek, T. When the going gets tough: survival strategies and environmental signaling networks in Bacillus subtilis. Trends Microbiol. 7, 201–207 (1999).

    CAS  Google Scholar 

  15. Mayani, H., Dragowska, W. & Lansdorp, P. M. Lineage commitment in human hemopoiesis involves asymmetric cell division of multipotent progenitors and does not appear to be influenced by cytokines. J. Cell. Physiol. 157, 579–586 (1993).

    CAS  PubMed  Google Scholar 

  16. Spudich, J. L. & Koshland, D. E. Jr Non-genetic individuality: chance in the single cell. Nature 262, 467–471 (1976).

    ADS  CAS  PubMed  Google Scholar 

  17. Morgan, H. D., Sutherland, H. G., Martin, D. I. & Whitelaw, E. Epigenetic inheritance at the agouti locus in the mouse. Nature Genet. 23, 314–318 (1999).

    CAS  PubMed  Google Scholar 

  18. Connell, I. et al. Type 1 fimbrial expression enhances Escherichia coli virulence for the urinary tract. Proc. Natl Acad. Sci. USA 93, 9827–9832 (1996).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  19. Abraham, J. M., Freitag, C. S., Clements, J. R. & Eisenstein, B. I. An invertible element of DNA controls phase variation of type 1 fimbriae of Escherichia coli. Proc. Natl Acad. Sci. USA 82, 5724–5747 (1985).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  20. Mulvey, M. A., Schilling, J. D., Martinez, J. J. & Hultgren, S. J. Bad bugs and beleaguered bladders: interplay between uropathogenic Escherichia coli and innate host defenses. Proc. Natl Acad. Sci. USA 97, 8829–8835 (2000).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  21. Sauer, F. G., Mulvey, M. A., Schilling, J. D., Martinez, J. J. & Hultgren, S. J. Bacterial pili: molecular mechanisms of pathogenesis. Curr. Opin. Microbiol. 3, 65–72 (2000).

    CAS  PubMed  Google Scholar 

  22. Mehr, I. J. & Seifert, H. S. Differential roles of homologous recombination pathways in Neisseria gonorrhoeae pilin antigenic variation, DNA transformation and DNA repair. Mol. Microbiol. 30, 697–710 (1998).

    CAS  PubMed  Google Scholar 

  23. Ziebuhr, W. et al. A novel mechanism of phase variation of virulence in Staphylococcus epidermidis: evidence for control of the polysaccharide intercellular adhesin synthesis by alternating insertion and excision of the insertion sequence element IS256. Mol. Microbiol. 32, 345–356 (1999).

    CAS  PubMed  Google Scholar 

  24. Peak, I. R., Jennings, M. P., Hood, D. W., Bisercic, M. & Moxon, E. R. Tetrameric repeat units associated with virulence factor phase variation in Haemophilus also occur in Neisseria spp. and Moraxella catarrhalis. FEMS Microbiol. Lett. 137, 109–114 (1996).

    CAS  PubMed  Google Scholar 

  25. Wright, A. C., Powell, J. L., Kaper, J. B. & Morris, J. G. Jr Identification of a group 1-like capsular polysaccharide operon for Vibrio vulnificus. Infect. Immun. 69, 6893–6901 (2001).

    CAS  PubMed  PubMed Central  Google Scholar 

  26. Hallet, B. Playing Dr Jekyll and Mr Hyde: combined mechanisms of phase variation in bacteria. Curr. Opin. Microbiol. 4, 570–581 (2001).

    CAS  PubMed  Google Scholar 

  27. Arkin, A. P. Synthetic cell biology. Curr. Opin. Biotechnol. 12, 638–644 (2001).

    CAS  PubMed  Google Scholar 

  28. Slepchenko, B. M., Schaff, J. C., Carson, J. H. & Loew, L. M. Computational cell biology: spatiotemporal simulation of cellular events. Annu. Rev. Biophys. Biomol. Struct. 31, 423–441 (2002).

    CAS  PubMed  Google Scholar 

  29. Gardiner, C. W. Handbook of Stochastic Methods forPhysics, Chemistry, and the Natural Sciences (Springer, Berlin, 1990).

    Google Scholar 

  30. Kloeden, P. E. & Platen, E. Numerical Solution of Stochastic Differential Equations (Springer, Berlin, 1992).

    MATH  Google Scholar 

  31. Gillespie, D. T. The chemical Langevin equation. J. Chem. Phys. 113, 297–306 (2000).

    ADS  CAS  Google Scholar 

  32. Gillespie, D. T. The chemical Langevin equation and Fokker-Planck equation for the reverisble isomerization reaction. J. Phys. Chem. A 106, 5063–5071 (2002).

    CAS  Google Scholar 

  33. Kurtz, T. G. Approximation of Population Processes (SIAM, Philadelphia, 1981).

    MATH  Google Scholar 

  34. Kohn, K. W. Molecular interaction map of the mammalian cell cycle control and DNA repair systems. Mol. Biol. Cell 10, 2703–2734 (1999).

    CAS  PubMed  PubMed Central  Google Scholar 

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

    CAS  Google Scholar 

  36. Le Novere, N. & Shimizu, T. S. STOCHSIM: modelling of stochastic biomolecular processes. Bioinformatics 17, 575–576 (2001).

    CAS  PubMed  Google Scholar 

  37. Shimizu, T. S. & Bray, D. in Foundations of Systems Biology (ed. Kitano, H.) 213–232 (MIT Press, Cambridge, MA, 2001).

    Google Scholar 

  38. Gillespie, D. T. Approximate accelerated stochastic simulation of chemically reacting systems. J. Chem. Phys. 115, 1716–1733 (2001).

    ADS  CAS  Google Scholar 

  39. Gibson, M. A. & Bruck, J. Exact stochastic simulation of chemical systems with many species and many channels. J. Phys. Chem. A 105, 1876–1889 (2000).

    Google Scholar 

  40. Rao, C. V. & Arkin, A. Stochastic chemical kinetics and the quasi steady-state assumption: application to the Gillespie algorithm. J. Chem. Phys. (in the press).

  41. Haseltine, E. L. & Rawlings, J. B. Approximate simulation of coupled fast and slow reactions for stochastic chemical kinetics. J. Chem. Phys. 117, 6958–6969 (2002).

    ADS  Google Scholar 

  42. Arkin, A., Ross, J. & McAdams, H. H. Stochastic kinetic analysis of developmental pathway bifurcation in phage lambda-infected Escherichia coli cells. Genetics 149, 1633–1648 (1998).

    CAS  PubMed  PubMed Central  Google Scholar 

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

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  44. Kierzek, A. M., Zaim, J. & Zielenkiewicz, P. The effect of transcription and translation initiation frequencies on the stochastic fluctuations in prokaryotic gene expression. J. Biol. Chem. 276, 8165–8172 (2001).

    CAS  PubMed  Google Scholar 

  45. Kepler, T. B. & Elston, T. C. Stochasticity in transcriptional regulation: origins, consequences, and mathematical representations. Biophys J. 81, 3116–3136 (2001).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  46. Ozbudak, E. M., Thattai, M., Kurtser, I., Grossman, A. D. & van Oudenaarden, A. Regulation of noise in the expression of a single gene. Nature Genet. 31, 69–73 (2002).

    CAS  PubMed  Google Scholar 

  47. Elowitz, M. B., Levine, A. J., Siggia, E. D. & Swain, P. S. Stochastic gene expression in a single cell. Science 297, 1183–1186 (2002).

    ADS  CAS  PubMed  Google Scholar 

  48. Arkin, A. P. in Self-organized Biological Dynamics and Nonlineaer Control (ed. Walleczek, J.) 112–144 (Cambridge Univ. Press, London, 2000).

    Google Scholar 

  49. Samoilov, M., Arkin, A. & Ross, J. Signal processing by simple chemical systems. J. Phys. Chem. A (in the press).

  50. Detwiler, P. B., Ramanathan, S., Sengupta, A. & Shraiman, B. I. Engineering aspects of enzymatic signal transduction: photoreceptors in the retina. Biophys. J. 79, 2801–2817 (2000).

    CAS  PubMed  PubMed Central  Google Scholar 

  51. Thattai, M. & Van Oudenaarden, A. Attenuation of noise in ultrasensitive signaling cascades. Biophys. J. 82, 2943–2950 (2002).

    CAS  PubMed  PubMed Central  Google Scholar 

  52. Smolen, P., Baxter, D. A. & Byrne, J. H. Modeling transcriptional control in gene networks—methods, recent results, and future directions. Bull. Math. Biol. 62, 247–292 (2000).

    CAS  PubMed  MATH  Google Scholar 

  53. Fell, D. Understanding the Control of Metabolism (Portland, London, 1997).

    Google Scholar 

  54. Heinrich, R. & Schuster, S. The Regulation of Cellular Systems (Portland, London, 1996).

    MATH  Google Scholar 

  55. Becskei, A. & Serrano, L. Engineering stability in gene networks by autoregulation. Nature 405, 590–593 (2000).

    ADS  CAS  PubMed  Google Scholar 

  56. Yi, T. M., Huang, Y., Simon, M. I. & Doyle, J. Robust perfect adaptation in bacterial chemotaxis through integral feedback control. Proc. Natl Acad. Sci. USA 97, 4649–4653 (2000).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  57. McAdams, H. H. & Arkin, A. It's a noisy business! Genetic regulation at the nanomolar scale. Trends Genet. 15, 65–69 (1999).

    CAS  PubMed  Google Scholar 

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

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  59. Hartwell, L. H. & Weinert, T. A. Checkpoints: controls that ensure the order of cell cycle events. Science 246, 629–634 (1989).

    ADS  CAS  PubMed  Google Scholar 

  60. Rodnina, M. V. & Wintermeyer, W. Ribosome fidelity: tRNA discrimination, proofreading and induced fit. Trends Biochem. Sci. 26, 124–130 (2001).

    CAS  PubMed  Google Scholar 

  61. Wolf, D. M. & Arkin, A. P. Fifteen minutes of fim: control of type 1 pili expression in E. coli. Omics 6, 91–114 (2002).

    CAS  PubMed  Google Scholar 

  62. Morton-Firth, C. J. & Bray, D. Predicting temporal fluctuations in an intracellular signalling pathway. J. Theor. Biol. 192, 117–128 (1998).

    CAS  PubMed  Google Scholar 

  63. Bren, A. & Eisenbach, M. Changing the direction of flagellar rotation in bacteria by modulating the ratio between the rotational states of the switch protein FliM. J. Mol. Biol. 312, 699–709 (2001).

    CAS  PubMed  Google Scholar 

  64. Ferrell, J. E. Self-perpetuating states in signal transduction: positive feedback, double-negative feedback and bistability. Curr. Opin. Cell Biol. 14, 140–148 (2002).

    CAS  PubMed  Google Scholar 

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

    ADS  CAS  PubMed  MATH  PubMed Central  Google Scholar 

  66. Becskei, A., Seraphin, B. & Serrano, L. Positive feedback in eukaryotic gene networks: cell differentiation by graded to binary response conversion. EMBO J. 20, 2528–2535 (2001).

    CAS  PubMed  PubMed Central  Google Scholar 

  67. Gammaitoni, L., Hanggi, P., Jung, P. & Marchesoni, F. Stochastic resonance. Rev. Mod. Phys. 70, 223–287 (1998).

    ADS  CAS  Google Scholar 

  68. Russell, D. F., Wilkens, L. A. & Moss, F. Use of behavioural stochastic resonance by paddle fish for feeding. Nature 402, 291–294 (1999).

    ADS  CAS  PubMed  Google Scholar 

  69. Douglass, J. K., Wilkens, L., Pantazelou, E. & Moss, F. Noise enhancement of information transfer in crayfish mechanoreceptors by stochastic resonance. Nature 365, 337–340 (1993).

    ADS  CAS  PubMed  Google Scholar 

  70. Levin, J. E. & Miller, J. P. Broadband neural encoding in the cricket cercal sensory system enhanced by stochastic resonance. Nature 380, 165–168 (1996).

    ADS  CAS  PubMed  Google Scholar 

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

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  72. Elowitz, M. B. & Leibler, S. A synthetic oscillatory network of transcriptional regulators. Nature 403, 335–338 (2000).

    ADS  CAS  PubMed  Google Scholar 

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

    ADS  CAS  PubMed  Google Scholar 

  74. Barkai, N. & Leibler, S. Circadian clocks limited by noise. Nature 403, 267–268 (2000).

    ADS  CAS  PubMed  Google Scholar 

  75. Gonze, D., Halloy, J. & Goldbeter, A. Robustness of circadian rhythms with respect to molecular noise. Proc. Natl Acad. Sci. USA 99, 673–678 (2002).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  76. Vilar, J. M., Kueh, H. Y., Barkai, N. & Leibler, S. Mechanisms of noise-resistance in genetic oscillators. Proc. Natl Acad. Sci. USA 99, 5988–5992 (2002).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  77. Smolen, P., Baxter, D. A. & Byrne, J. H. Modeling circadian oscillations with interlocking positive and negative feedback loops. J. Neurosci. 21, 6644–6656 (2001).

    CAS  PubMed  PubMed Central  Google Scholar 

  78. Kastner, J., Solomon, J. & Fraser, S. Modeling a hox gene network in silico using a stochastic simulation algorithm. Dev. Biol. 246, 122–131 (2002).

    CAS  PubMed  Google Scholar 

  79. Levin, M. D., Morton-Firth, C. J., Abouhamad, W. N., Bourret, R. B. & Bray, D. Origins of individual swimming behavior in bacteria. Biophys. J. 74, 175–181 (1998).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  80. Morton-Firth, C. J., Shimizu, T. S. & Bray, D. A free-energy-based stochastic simulation of the Tar receptor complex. J. Mol. Biol. 286, 1059–1074 (1999).

    CAS  PubMed  Google Scholar 

  81. Alon, U., Surette, M. G., Barkai, N. & Leibler, S. Robustness in bacterial chemotaxis. Nature 397, 168–171 (1999).

    ADS  CAS  PubMed  Google Scholar 

  82. Meir, E., von Dassow, G., Munro, E. & Odell, G. M. Robustness, flexibility, and the role of lateral inhibition in the neurogenic network. Curr. Biol. 12, 778–786 (2002).

    CAS  PubMed  Google Scholar 

  83. Little, J. W., Shepley, D. P. & Wert, D. W. Robustness of a gene regulatory circuit. EMBO J. 18, 4299–4307 (1999).

    CAS  PubMed  PubMed Central  Google Scholar 

  84. Csete, M. E. & Doyle, J. C. Reverse engineering of biological complexity. Science 295, 1664–1669 (2002).

    ADS  CAS  PubMed  Google Scholar 

  85. Morohashi, M. et al. Robustness as a measure of plausibility in models of biochemical networks. J. Theor. Biol. 216, 19–30 (2002).

    MathSciNet  CAS  PubMed  Google Scholar 

  86. Hartwell, L. H., Hopfield, J. J., Leibler, S. & Murray, A. W. From molecular to modular cell biology. Nature 402, C47–C52 (1999).

    CAS  PubMed  Google Scholar 

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Authors and Affiliations

  1. Department of Bioengineering, Lawrence Berkeley National Laboratory, Howard Hughes Medical Institute, 1 Cyclotron Road, MS 3-144, Berkeley, 94720, California, USA

    Christopher V. Rao & Adam P. Arkin

  2. Department of Chemistry, University of California, Lawrence Berkeley National Laboratory, Howard Hughes Medical Institute, 1 Cyclotron Road, MS 3-144, Berkeley, 94720, California, USA

    Adam P. Arkin

  3. Department of Physical Biosciences Division, Lawrence Berkeley National Laboratory, Howard Hughes Medical Institute, 1 Cyclotron Road, MS 3-144, Berkeley, 94720, California, USA

    Denise M. Wolf & Adam P. Arkin

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Correspondence to Denise M. Wolf.

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Rao, C., Wolf, D. & Arkin, A. Control, exploitation and tolerance of intracellular noise. Nature 420, 231–237 (2002). https://doi.org/10.1038/nature01258

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