Molecule concentrations are the building blocks of information transmission in living organisms. Thanks to their molecule receptors, cells are able to sense concentration gradients with high accuracy. For example, small motile bacteria such as E. coli detect spatial gradients indirectly by measuring concentration ramps (temporal concentration changes) as they swim, and can respond to concentrations as low as 3.2 nM - about three molecules per cell volume. The noise arising from the small number of detected molecules sets a fundamental physical limit on the accuracy of concentration sensing, as originally shown in the seminal work of Berg and Purcell, but up to now no theory existed for the physical limit of ramp sensing, which is what bacteria actually do. I will show how such a bound can be derived for different measurement devices, from a single receptor to an entire cell. I will then present a plausible implementation of that bound by a realistic (bio)chemical network, similar to the adaptation system of E. coli. Finally I will show how energy consumption at the level of the receptors can be used to increase the accuracy by a twofold factor over a passive scheme where no energy is consumed.
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