Simulations of Chemotaxis and Random Motility in Finite Domains

Abstract

ABSTRACTRational design and selection of candidate porous biomaterials to serve as tissue engineering constructs rests on our ability to understand the influence of the porous microarchitecture on the transport of chemical species (e.g., nutrients and signaling compounds), fluid flow, and cellular locomotion and growth. We have begun to study the behavior of chemotactically mobile cells in response to unsteady signaling molecule concentration fields using a computational simulation-based model. The model couples fully time-dependent finite-difference solution of a reaction-diffusion equation for the concentration field of a generic chemoattractant to biased random walks representing individual moving cells. This model is a first step in building a quantitative, pore-level model of mass and cellular transport in porous tissue-engineered constructs. In these proceedings, we focus on our recent findings regarding the influence of flux-reactive boundary conditions in heterogeneous 2D domains on the chemotactic response of otherwise randomly moving cells. In particular, we find that, when cells are forced to “crawl” around obstacles in order to approach a point source of chemoattractant, the reactivity of the obstacle surface with respect to the chemoattractant strongly determines the morphology of the cells' paths of locomotion. Cells crawl along non-reactive surfaces and strongly avoid reactive surfaces, due to the nature of the chemoattractant concentration gradients near the surface. We show further that tuning the reactivity of the surfaces of two obstacles defining a gap can control the passage of cells through the gap. From our work, we infer the importance of a proper treatment of boundary conditions in any future pore-level quantitatve modeling of mass transport and cellular response in porous media.