Abstract
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.
Similar content being viewed by others
References
Berg, H.C., Purcell, E.M.: Biophys. J. 20, 193–219 (1977)
Bialek, W., Setayeshgar, S.: Proc. Natl. Acad. Sci. USA 102, 10040–10045 (2005)
Endres, R.G., Wingreen, N.S.: Phys. Rev. Lett. 103, 158101 (2009)
Mora, T., Wingreen, N.S.: Phys. Rev. Lett. 104, 248101 (2010)
Wang, K., Rappel, W.J., Kerr, R., Levine, H.: Phys. Rev. E, Stat. Nonlinear Soft Matter Phys. 75, 061905 (2007)
Endres, R.G., Wingreen, N.S.: Proc. Natl. Acad. Sci. USA 105, 15749–15754 (2008)
Berg, C.H., Brown, D.A.: Nature 239, 500–504 (1972)
Torre, V., Ashmore, J.F., Lamb, T.D., Menini, A.: J. Neurosci. 15, 7757–7768 (1995)
Muzzey, D., Gmez-Uribe, C.A., Mettetal, J.T., van Oudenaarden, A.: Cell 138, 160–171 (2009)
Yi, T.M., Huang, Y., Simon, M.I., Doyle, J.: Proc. Natl. Acad. Sci. USA 97, 4649–4653 (2000)
Mello, B.A., Tu, Y.: Biophys. J. 92, 2329–2337 (2007)
Andrews, B.W., Yi, T.M., Iglesias, P.A.: PLoS Comput. Biol. 2, e154 (2006)
Tu, Y., Shimizu, T.S., Berg, H.C.: Proc. Natl. Acad. Sci. USA 105, 14855–14860 (2008)
Ma, W., Trusina, A., El-Samad, H., Lim, W.A., Tang, C.: Cell 138, 760–773 (2009)
Mello, B.A., Tu, Y.: Biophys. J. 84, 2943–2956 (2003)
Sontag, E.D.: Syst. Control Lett. 50(2), 119–126 (2003)
Shimizu, T.S., Tu, Y., Berg, H.C.: Mol. Syst. Biol. 6, 382 (2010)
van Kampen, N.G.: Stochastic Processes in Physics and Chemistry. Noth-Holland, Amsterdam (2007)
Landau, L.D., Lifshitz, E.M.: Statistical Physics: Part II. Pergamon Press, Oxford (1980)
Kim, K.K., Yokota, H., Kim, S.H.: Nature 400, 787–792 (1999)
Ueda, M., Sako, Y., Tanaka, T., Devreotes, P., Yanagida, T.: Science 294, 864–867 (2001)
Funamoto, S., Meili, R., Lee, S., Parry, L., Firtel, R.A.: Cell 109, 611–623 (2002)
Berg, H.C.: Random Walks in Biology. Princeton University Press, Princeton (1993)
Yevgeniy, V., Jiang, L., Tu, Y., Wu, M.: Biophys. J. 96, 2439–2448 (2009)
Jiang, L., Ouyang, Q., Tu, Y.: PLoS Comput. Biol. 6, e1000735 (2010)
Strong, S.P., Freedman, B., Bialek, W., Koberle, R.: Phys. Rev. E 57, 4604–4617 (1998)
Tu, Y., Grinstein, G.: Phys. Rev. Lett. 94, 208101 (2005)
Korobkova, E., Emonet, T., Vilar, J.M., Shimizu, T.S., Cluzel, P.: Nature 428, 574–578 (2004)
Emonet, T., Cluzel, P.: Proc. Natl. Acad. Sci. USA 105, 3304–3309 (2008)
Kollmann, M., Lvdok, L.K.B., Timmer, J., Sourjik, V.: Nature 438, 504–507 (2005)
Tostevin, F., Ten Wolde, P.R.: Phys. Rev. Lett. 102, 218101 (2009)
Tanase-Nicola, S., Warren, P.B., Ten Wolde, P.R.: Phys. Rev. Lett. 97, 068102 (2006)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Sartori, P., Tu, Y. Noise Filtering Strategies in Adaptive Biochemical Signaling Networks. J Stat Phys 142, 1206–1217 (2011). https://doi.org/10.1007/s10955-011-0169-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10955-011-0169-z