Accuracy of direct gradient sensing by single cells

TL;DR

This paper develops a theoretical framework for understanding the physical limits of gradient sensing in cells, comparing models of absorbing and monitoring spheres, and explaining cellular adaptations like signal degrading enzymes.

Contribution

It introduces a new theory for the physical limits of cellular gradient sensing using sphere models, highlighting the superiority of absorbing spheres and aligning with experimental data.

Findings

Absorbing sphere model outperforms monitoring sphere in sensing accuracy.

Cells operate near the physical limits of gradient detection.

Presence of signal degrading enzymes explained by model superiority.

Abstract

Many types of cells are able to accurately sense shallow gradients of chemicals across their diameters, allowing the cells to move towards or away from chemical sources. This chemotactic ability relies on the remarkable capacity of cells to infer gradients from particles randomly arriving at cell-surface receptors by diffusion. Whereas the physical limits of concentration sensing by cells have been explored, there is no theory for the physical limits of gradient sensing. Here, we derive such a theory, using as models a perfectly absorbing sphere and a perfectly monitoring sphere, which, respectively, infer gradients from the absorbed surface particle density or the positions of freely diffusing particles inside a spherical volume. We find that the perfectly absorbing sphere is superior to the perfectly monitoring sphere, both for concentration and gradient sensing, since previously observed particles are never remeasured. The superiority of the absorbing sphere helps explain the presence at the surfaces of cells of signal degrading enzymes, such as PDE for cAMP in Dictyostelium discoideum (Dicty) and BAR1 for mating factor alpha in Saccharomyces cerevisiae (budding yeast). Quantitatively, our theory compares favorably to recent measurements of Dicty moving up a cAMP gradient, suggesting these cells operate near the physical limits of gradient detection.