Triangulation sensing: how cells recover a source from diffusing particles in three dimensions

TL;DR

This paper investigates how cells can determine the position of a source emitting diffusing particles in three dimensions by analyzing receptor fluxes, revealing the minimum number of receptors needed and the limits of localization accuracy.

Contribution

It introduces a method to recover 3D source location from receptor fluxes, showing at least three receptors are necessary and quantifying localization accuracy limits.

Findings

At least three receptors are needed for source triangulation.

Source cannot be accurately located if it is far from the cell.

Localization precision improves with more receptors.

Abstract

How can cells embedded into a gradient concentration triangulate the position of the source and migrate toward their final destination? The source triangulation requires to recover the three dimensional coordinates of the source from the fluxes of diffusing cues at narrow windows (receptors) located on the surface of a cell. We develop here a method to address this question and we show in the limit of fast binding rate to the receptors, that at least three receptors are necessary. We solve the steady-state diffusion equation using an asymptotic approach, which agrees with hybrid stochastic-analytical simulations. Interestingly, with an accuracy of few percent, the source cannot be located if it is located at a distance tens of time the size of the cell. Finally, the precision of the source recovery increases with the number of receptors.