Journal of Statistical Physics

, Volume 142, Issue 6, pp 1206–1217 | Cite as

Noise Filtering Strategies in Adaptive Biochemical Signaling Networks

Application to E. Coli Chemotaxis


Two distinct mechanisms for filtering noise in an input signal are identified in a class of adaptive sensory networks. We find that the high-frequency noise is filtered by the output degradation process through time-averaging; while the low-frequency noise is damped by adaptation through negative feedback. Both filtering processes themselves introduce intrinsic noises, which are found to be unfiltered and can thus amount to a significant internal noise floor even without signaling. These results are applied to E. coli chemotaxis. We show unambiguously that the molecular mechanism for the Berg-Purcell time-averaging scheme is the dephosphorylation of the response regulator CheY-P, not the receptor adaptation process as previously suggested. The high-frequency noise due to the stochastic ligand binding-unbinding events and the random ligand molecule diffusion is averaged by the CheY-P dephosphorylation process to a negligible level in E. coli. We identify a previously unstudied noise source caused by the random motion of the cell in a ligand gradient. We show that this random walk induced signal noise has a divergent low-frequency component, which is only rendered finite by the receptor adaptation process. For gradients within the E. coli sensing range, this dominant external noise can be comparable to the significant intrinsic noise in the system. The dependence of the response and its fluctuations on the key time scales of the system are studied systematically. We show that the chemotaxis pathway may have evolved to optimize gradient sensing, strong response, and noise control in different time scales.


Noise Adaptation Bacterial chemotaxis Signal transduction Networks 


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  1. 1.
    Berg, H.C., Purcell, E.M.: Biophys. J. 20, 193–219 (1977) CrossRefADSGoogle Scholar
  2. 2.
    Bialek, W., Setayeshgar, S.: Proc. Natl. Acad. Sci. USA 102, 10040–10045 (2005) CrossRefADSGoogle Scholar
  3. 3.
    Endres, R.G., Wingreen, N.S.: Phys. Rev. Lett. 103, 158101 (2009) CrossRefADSGoogle Scholar
  4. 4.
    Mora, T., Wingreen, N.S.: Phys. Rev. Lett. 104, 248101 (2010) CrossRefADSGoogle Scholar
  5. 5.
    Wang, K., Rappel, W.J., Kerr, R., Levine, H.: Phys. Rev. E, Stat. Nonlinear Soft Matter Phys. 75, 061905 (2007) CrossRefGoogle Scholar
  6. 6.
    Endres, R.G., Wingreen, N.S.: Proc. Natl. Acad. Sci. USA 105, 15749–15754 (2008) CrossRefADSGoogle Scholar
  7. 7.
    Berg, C.H., Brown, D.A.: Nature 239, 500–504 (1972) CrossRefADSGoogle Scholar
  8. 8.
    Torre, V., Ashmore, J.F., Lamb, T.D., Menini, A.: J. Neurosci. 15, 7757–7768 (1995) Google Scholar
  9. 9.
    Muzzey, D., Gmez-Uribe, C.A., Mettetal, J.T., van Oudenaarden, A.: Cell 138, 160–171 (2009) CrossRefGoogle Scholar
  10. 10.
    Yi, T.M., Huang, Y., Simon, M.I., Doyle, J.: Proc. Natl. Acad. Sci. USA 97, 4649–4653 (2000) CrossRefADSGoogle Scholar
  11. 11.
    Mello, B.A., Tu, Y.: Biophys. J. 92, 2329–2337 (2007) CrossRefADSGoogle Scholar
  12. 12.
    Andrews, B.W., Yi, T.M., Iglesias, P.A.: PLoS Comput. Biol. 2, e154 (2006) CrossRefADSGoogle Scholar
  13. 13.
    Tu, Y., Shimizu, T.S., Berg, H.C.: Proc. Natl. Acad. Sci. USA 105, 14855–14860 (2008) CrossRefADSGoogle Scholar
  14. 14.
    Ma, W., Trusina, A., El-Samad, H., Lim, W.A., Tang, C.: Cell 138, 760–773 (2009) CrossRefGoogle Scholar
  15. 15.
    Mello, B.A., Tu, Y.: Biophys. J. 84, 2943–2956 (2003) CrossRefADSGoogle Scholar
  16. 16.
    Sontag, E.D.: Syst. Control Lett. 50(2), 119–126 (2003) CrossRefMATHMathSciNetGoogle Scholar
  17. 17.
    Shimizu, T.S., Tu, Y., Berg, H.C.: Mol. Syst. Biol. 6, 382 (2010) CrossRefGoogle Scholar
  18. 18.
    van Kampen, N.G.: Stochastic Processes in Physics and Chemistry. Noth-Holland, Amsterdam (2007) Google Scholar
  19. 19.
    Landau, L.D., Lifshitz, E.M.: Statistical Physics: Part II. Pergamon Press, Oxford (1980) Google Scholar
  20. 20.
    Kim, K.K., Yokota, H., Kim, S.H.: Nature 400, 787–792 (1999) CrossRefADSGoogle Scholar
  21. 21.
    Ueda, M., Sako, Y., Tanaka, T., Devreotes, P., Yanagida, T.: Science 294, 864–867 (2001) CrossRefADSGoogle Scholar
  22. 22.
    Funamoto, S., Meili, R., Lee, S., Parry, L., Firtel, R.A.: Cell 109, 611–623 (2002) CrossRefGoogle Scholar
  23. 23.
    Berg, H.C.: Random Walks in Biology. Princeton University Press, Princeton (1993) Google Scholar
  24. 24.
    Yevgeniy, V., Jiang, L., Tu, Y., Wu, M.: Biophys. J. 96, 2439–2448 (2009) CrossRefGoogle Scholar
  25. 25.
    Jiang, L., Ouyang, Q., Tu, Y.: PLoS Comput. Biol. 6, e1000735 (2010) CrossRefMathSciNetGoogle Scholar
  26. 26.
    Strong, S.P., Freedman, B., Bialek, W., Koberle, R.: Phys. Rev. E 57, 4604–4617 (1998) CrossRefADSGoogle Scholar
  27. 27.
    Tu, Y., Grinstein, G.: Phys. Rev. Lett. 94, 208101 (2005) CrossRefADSGoogle Scholar
  28. 28.
    Korobkova, E., Emonet, T., Vilar, J.M., Shimizu, T.S., Cluzel, P.: Nature 428, 574–578 (2004) CrossRefADSGoogle Scholar
  29. 29.
    Emonet, T., Cluzel, P.: Proc. Natl. Acad. Sci. USA 105, 3304–3309 (2008) CrossRefADSGoogle Scholar
  30. 30.
    Kollmann, M., Lvdok, L.K.B., Timmer, J., Sourjik, V.: Nature 438, 504–507 (2005) CrossRefADSGoogle Scholar
  31. 31.
    Tostevin, F., Ten Wolde, P.R.: Phys. Rev. Lett. 102, 218101 (2009) CrossRefADSGoogle Scholar
  32. 32.
    Tanase-Nicola, S., Warren, P.B., Ten Wolde, P.R.: Phys. Rev. Lett. 97, 068102 (2006) CrossRefADSGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Max Planck Institute of Complex SystemsDresdenGermany
  2. 2.IBM T.J. Watson Research CenterYorktown HeightsUSA

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