Theory for the optimal detection of time-varying signals in cellular sensing systems

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Abstract

Living cells often need to measure chemical concentrations that vary in time, yet how accurately they can do so is poorly understood. Here, we present a theory that fully specifies, without any adjustable parameters, the optimal design of a canonical sensing system, in terms of two elementary design principles: (1) there exists an optimal integration time, which is determined by the input statistics and the number of receptors; (2) in the optimally designed system, the number of independent concentration measurements as set by the number of receptors and the optimal integration time, equals the number of readout molecules that store these measurements, and equals the work to store these measurements reliably; no resource is then in excess and hence wasted. Applying our theory to the E.coli chemotaxis system indicates that its integration time is not only optimal for sensing shallow gradients, but also necessary to enable navigation in these gradients.

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All data generated or analysed during this study are included in the manuscript and supporting files.

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Giulia Malaguti

Living Matter Department, AMOLF, Amsterdam, Netherlands

Competing interests
The authors declare that no competing interests exist.
Pieter Rein ten Wolde

Living Matter Department, AMOLF, Amsterdam, Netherlands

For correspondence
tenwolde@amolf.nl

Competing interests
The authors declare that no competing interests exist.

"This ORCID iD identifies the author of this article:" 0000-0001-9933-4016

Funding

Nederlandse Organisatie voor Wetenschappelijk Onderzoek

Pieter Rein ten Wolde

Nederlandse Organisatie voor Wetenschappelijk Onderzoek

Giulia Malaguti

The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.

Copyright

This article is distributed under the terms of the Creative Commons Attribution License permitting unrestricted use and redistribution provided that the original author and source are credited.