Robust perfect adaptation in bacterial chemotaxis through integral feedback control
Integral feedback control is a basic engineering strategy for ensuring that the output of a system robustly tracks its desired value independent of noise or variations in system parameters. In biological systems, it is common for the response to an extracellular stimulus to return to its prestimulus value even in the continued presence of the signal-a process termed adaptation or desensitization. Barkai, Alon, Surette, and Leibler have provided both theoretical and experimental evidence that the precision of adaptation in bacterial chemotaxis is robust to dramatic changes in the levels and kinetic rate constants of the constituent proteins in this signaling network [Alon. U., Surette, M. G., Barkai. N. & Leibler, S. (1998) Nature (London) 397, 168-171]. Here we propose that the robustness of perfect adaptation is the result of this system possessing the property of integral feedback control. Using techniques from control and dynamical systems theory, we demonstrate that integral control is structurally inherent in the Barkai-Leibler model and identify and characterize the key assumptions of the model. Most importantly, we argue that integral control in some form is necessary for a robust implementation of perfect adaptation. More generally, integral control may underlie the robustness of many homeostatic mechanisms.
Additional Information© 2000 by the National Academy of Sciences. Contributed by Melvin I. Simon, February 7, 2000. We acknowledge valuable discussions with Drs. S. Lall, H. Berg, D. Petrasek, U. Alon, N. Barkai, and S. Leibler. Special thanks to Drs. U. Alon, H. Berg, J. Stock, and P. Iglesias for comments on the manuscript. This work was supported by an Air Force Office of Scientific Research (AFOSR)/DDRE MURI AFS-5X-F496209610471 grant entitled "Uncertainty Management in Complex Systems" and Defense Advanced Research Planning Agency/AFOSR grant AFS-5-F4962098-L0487. T.-M.Y. was supported by a fellowship from the Caltech Initiative in Computational Molecular Biology funded by the Burroughs–Wellcome Foundation. The publication costs of this article were defrayed in part by page charge payment. This article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. §1734 solely to indicate this fact.
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