Chemoreception of a Two-Dimensional Cell with Multilayer Diffusion

Abstract: Previously, Berg and Purcell found an expression for the diffusion current of particles into a set of receptors in their paper Physics of Chemoreception. These receptors were assumed to be uniformly distributed on a spherical cell's surface and the receptors where idealized as circular patches. For their model, the particles' diffusion constant was the same for all points outside of the cell. In this thesis, a model was made that mimics the scenario when there is a higher density of crowding material close to the cell's surface which would obstruct the particles from moving around. This makes the diffusion constant closer to the cell smaller than the diffusion constant further away. For computational reasons, two-dimensional geometry was considered. The model contained a two dimensional circular cell with diffusion constant D2 within a distance d from the cell's surface and a diffusion constant D1 further away from the cell. For a fully absorbing cell, the diffusion current was obtained both analytically and numerically. Furthermore, for a cell with equidistantly distributed receptors on its surface, where the remaining parts of the surface were perfectly reflecting, the diffusion current was obtained by numerically solving the diffusion equation. It was shown that the placement of receptors affected the diffusion current. Moreover, the ratio between D1 and D2 influenced the number of receptors needed to reach half of the maximum diffusion current.