Role of spatial averaging in multicellular gradient sensing

TL;DR

This paper investigates how spatial averaging affects the precision of multicellular gradient sensing, revealing that in simple models, increased transverse size can decrease accuracy, but a new REGI mechanism can recover the benefits of averaging.

Contribution

It demonstrates that spatial averaging can reduce gradient sensing precision in simple models and introduces REGI as a mechanism to overcome this limitation.

Findings

Transverse averaging decreases gradient sensing precision in simple LEGI models.

REGI mechanism restores the benefits of spatial averaging in gradient sensing.

Optimal detector shapes predicted by REGI align with natural cell populations.

Abstract

Gradient sensing underlies important biological processes including morphogenesis, polarization, and cell migration. The precision of gradient sensing increases with the length of a detector (a cell or group of cells) in the gradient direction, since a longer detector spans a larger range of concentration values. Intuition from analyses of concentration sensing suggests that precision should also increase with detector length in the direction transverse to the gradient, since then spatial averaging should reduce the noise. However, here we show that, unlike for concentration sensing, the precision of gradient sensing decreases with transverse length for the simplest gradient sensing model, local excitation--global inhibition (LEGI). The reason is that gradient sensing ultimately relies on a subtraction of measured concentration values. While spatial averaging indeed reduces the noise in these measurements, which increases precision, it also reduces the covariance between the measurements, which results in the net decrease in precision. We demonstrate how a recently introduced gradient sensing mechanism, regional excitation--global inhibition (REGI), overcomes this effect and recovers the benefit of transverse averaging. Using a REGI-based model, we compute the optimal two- and three-dimensional detector shapes, and argue that they are consistent with the shapes of naturally occurring gradient-sensing cell populations.