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.
- Pieter Rein ten Wolde
- Giulia Malaguti
The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.
- Raymond E Goldstein, University of Cambridge, United Kingdom
- Received: August 28, 2020
- Accepted: February 12, 2021
- Accepted Manuscript published: February 17, 2021 (version 1)
© 2021, Malaguti & ten Wolde
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