Diffusion, Cell Mobility, and Bandlimited Functions

Abstract

The mechanism by which leukocytes steer toward a chemical attractant is not fully resolved. Experimental data suggest that these cells detect differences in concentration of chemoattractant over their surface and “walk” up the gradient. The problem has been considered theoretically only in stationary media, where the distribution of attractant is determined solely by diffusion. Experimentally, bulk flow has been allowed only unintentionally. Since bulk flow is characteristic of real systems, we examine a simple two-dimensional model incorporating both diffusion and an additional drift. The latter problem leads to an integral equation which is central also in the study of weighted Hilbert spaces of bandlimited functions. We find asymptotic expressions for the required solution by a Wiener-Hopf method adapted to a finite interval. We conclude that, without drift, the concentration does not vary detectably around the cell, but that drift inceases this variation substantially. Thus over model suggests that drift may play an important role in the cell’s chemotactic response.