An Investigation of the Channel Capacity of Bacterial Chemotactic Sensors for Low Chemoattractant Concentrations

Bacterial chemotactic sensing converts noisy chemical signals into running and tumbling. We analyze the static sensing limits of mixed Tar/Tsr chemoreceptor clusters in individual Escherichia coli cells using a heterogeneous Monod--Wyman--Changeux (MWC) model. Across a seven-dimensional parameter sweep, we compute three sensing-performance metrics -- channel capacity, dynamic range, and effective Hill coefficient -- in the limit that the cells are constantly in such low concentrations of chemoattractant that they need not adapt to new baseline chemoattractant concentration levels. What results are an upper bound on the trajectory mutual information rate given by the static capacity divided by a finite perceptual timescale, a quantitative understanding of the tight connection between channel capacity and dynamic range, and the finding that in this regime channel capacity is well described by a closed-form ceiling depending only on the receptor's baseline activity, which every wild-type and mutant strain in our sample achieves to within a few percent. In more realistic scenarios, adaptation plays a larger role and so do the exact temporal dynamics of chemoattractant concentrations seen by bacteria as they swim. This manuscript thus points to the importance of mapping out naturalistic chemoattractant concentration statistics in the wild as has been done for natural scene statistics.