Inferring directionality of diffusive sources from short time fluxes to membrane receptors.

Identifying the directionality of signaling sources from noisy input to membrane receptors is an essential task performed by many cell types. As the limits of experimental measurements have expanded, effective directional sensing has been observed at very low concentrations, often corresponding to just a few receptor binding events. We consider the scenario of a single cell seeking the directionality of a point source of diffusing molecules. We analyze a simple mechanism in which a cell adopts the direction associated with the first few receptor binding events. This is an example of an extreme statistic where the relevant biological timescale is set by the minimum of many i.i.d. realizations. The accuracy of this approach is validated and shown to be effective, provided the source is not too distant. An important biological implication of this mechanism is that source recovery can be accomplished while making minimal assumptions on the computational capacities of the cell. Numerical simulations verify the effectiveness of the method in both two and three dimension.