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The energy–speed–accuracy trade-off in sensory adaptation

Nature Physics volume 8, pages 422–428 (2012)Cite this article

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Abstract

Adaptation is the essential process by which an organism becomes better suited to its environment. The benefits of adaptation are well documented, but the cost it incurs remains poorly understood. Here, by analysing a stochastic model of a minimum feedback network underlying many sensory adaptation systems, we show that adaptive processes are necessarily dissipative, and continuous energy consumption is required to stabilize the adapted state. Our study reveals a general relation among energy dissipation rate, adaptation speed and the maximum adaptation accuracy. This energy–speed–accuracy relation is tested in the Escherichia coli chemosensory system, which exhibits near-perfect chemoreceptor adaptation. We identify key requirements for the underlying biochemical network to achieve accurate adaptation with a given energy budget. Moreover, direct measurements confirm the prediction that adaptation slows down as cells gradually de-energize in a nutrient-poor medium without compromising adaptation accuracy. Our work provides a general framework to study cost-performance trade-offs for cellular regulatory functions and information processing.

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Figure 1: Schematic model of adaptive feedback systems.
Figure 2: Energetics and kinetics of adaptation.
Figure 3: The E. coli chemotaxis adaptation.
Figure 4: The cost–performance relationship.
Figure 5: Adaptation dynamics of starving E. coli cells.

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Acknowledgements

We thank J. Tersoff, T. Theis and K. Schwarz for comments. This work is partially supported by a National Institutes of Health (NIH) grant (R01GM081747 to Y.T.), a Deutsche Forschungsgemeinschaft (DFG) grant (SO 421/3-3 to V.S.), and a Cajamadrid fellowship to P.S.

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Author notes

  1. Ganhui Lan

    Present address: Present address: NCI Physical Sciences—Oncology Center, Johns Hopkins University, 3400 N Charles St., Maryland 21218, USA,

  2. Ganhui Lan and Pablo Sartori: These authors contributed equally to this work

Authors and Affiliations

  1. IBM T.J. Watson Research Center, Yorktown Heights, New York 10598, PO Box 218, USA

    Ganhui Lan & Yuhai Tu

  2. Max Planck Institute for the Physics of Complex Systems, Nothnitzer Str. 38, 01187 Dresden, Germany

    Pablo Sartori

  3. Zentrum fur Molekulare Biologie der Universitat Heidelberg, 69120 Heidelberg, Germany

    Silke Neumann & Victor Sourjik

Authors
  1. Ganhui Lan
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Contributions

Y.T. initiated the work; G.L., P.S. and Y.T. carried out the theoretical calculations; S.N. and V.S. performed the experiments; G.L. did the data analysis; all authors wrote the paper.

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Correspondence to Yuhai Tu.

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Lan, G., Sartori, P., Neumann, S. et al. The energy–speed–accuracy trade-off in sensory adaptation. Nature Phys 8, 422–428 (2012). https://doi.org/10.1038/nphys2276

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