Perfect adaptation in eukaryotic gradient sensing using cooperative allosteric binding

Eukaryotic cells generally sense chemical gradients using the binding of chemical ligands to membrane receptors. 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 tradeoff between adaptation time and gradient sensing accuracy.