Simulations of Chemotaxis and Random Motility in 2D Random Porous Domains

Abstract

We discuss a generic computational model of eukariotic chemotaxis in 2D random porous domains. The model couples the fully time-dependent finite-difference solution of a reaction–diffusion equation for the concentration field of a chemoattractant to biased random walks representing individual chemotactic cells. We focus in particular on the influence of consumption of chemoattractant by the boundaries of obstacles with irregular shapes which are distributed randomly in the domain on the chemotactic response of the cells. Cells are stimulated to traverse a field of obstacles by a line source of chemoattractant. We find that the reactivity of the obstacle boundaries with respect to the chemoattractant strongly determines the transit time of cells through two primary mechanisms. The channeling effect arises because cells are effectively repelled from surfaces which consume chemoattractant, and opposing surfaces therefore act to keep cells in the middle of channels. This reduces traversal times relative to the case with unreactive boundaries, provided that the appropriate Péclet number relating the strength of reactivity to diffusion in governing chemoattractant transport is neither too low nor too high. The dead-zone effect arises due to a realistic threshold on the chemotactic response, which at steady state results in portions of the domain having no detectable gradient. Of these two, the channeling effect is responsible for 90% of the sensitivity of transit times to boundary reactivity. Based on these results, we speculate that it may be possible to tune the rates of cellular penetration into porous domains by engineering the reactivity of the internal surfaces to cytokines.