# Perfect adaptation in eukaryotic gradient sensing using cooperative allosteric binding

## TL;DR

This paper models eukaryotic gradient sensing as a cooperative allosteric process, showing cells can adapt to various ligand concentrations and achieve near-optimal chemotaxis, with accuracy influenced by diffusion and reaction rates.

## Contribution

It introduces a novel allosteric model for gradient sensing that explains adaptation and accuracy trade-offs in eukaryotic chemotaxis.

## Key findings

- Cells can adapt receptor affinity to achieve 50% receptor binding across concentrations.
- Chemotactic accuracy approaches optimal over a broad concentration range.
- Diffusion of allosteric compounds significantly impacts sensing accuracy.

## Abstract

Eukaryotic cells generally sense chemical gradients using the binding of chemical ligands to membrane receptors. In order to perform chemotaxis effectively in different environments, cells need to adapt to different concentrations. We present a model of gradient sensing where the affinity of receptor-ligand binding is increased when a protein binds to the receptor's cytosolic side. This interior protein (allosteric factor) alters the sensitivity of the cell, allowing the cell to adapt to different ligand concentrations. We propose a reaction scheme where the cell alters the allosteric factor's availability to adapt the average fraction of bound receptors to 1/2. We calculate bounds on the chemotactic accuracy of the cell, and find that the cell can reach near-optimal chemotaxis over a broad range of concentrations. We find that the accuracy of chemotaxis depends strongly on the diffusion of the allosteric compound relative to other reaction rates. From this, we also find a trade-off between adaptation time and gradient sensing accuracy.