Two-cell interactions in autologous chemotaxis.

Abstract

An advection-diffusion-reaction model for autologous chemotaxis of two cells in an interstitial flow is analyzed. Each cell secretes ligands uniformly over its surface; the ligands are absorbed by surface receptors anisotropically due to the flow and interaction between ligand fields around each cell. The absorption is quantified in terms of a vectorial anisotropy parameter, A, which is proportional to the first moment of the ligand concentration field about the surface of each cell. We consider the physiologically relevant limit of a weak interstitial flow, where the Péclet number, Pe, which characterizes the relative importance of ligand transport via advection to diffusion, is small. We further assume that the cells are separated at a distance that is large compared to the sum of their radii. These conditions allow us to utilize a reciprocal theorem and the method of reflections to construct an asymptotic approximation for A to first order in Pe for widely separated cells. We find that interactions between the cells: (i) reduce the flow-aligned ligand anisotropy around each cell and (ii) lead to a component of A that is perpendicular to the flow direction. The interaction is long ranged, decaying with the inverse distance between cells to leading order. We finally discuss how interactions between multiple cells could affect our findings.