Population-scale modelling of cellular chemotaxis and aggregation
AbstractMotivated by chemotaxis of, and especially aggregation within, populations of cells, we examine an extension of the Becker–Döring aggregation equations in which monomers undergo diffusion and advection in one spatial dimension, as well as attaching themselves to clusters of all sizes. We restrict our attention to irreversible aggregation, particularly for power-law rate coefficients. We examine the large-time behaviour of the initial-value problem on an infinite domain, both in the purely diffusive case and with advection. We also determine the large-time behaviour on a semi-infinite domain, with a non-zero Dirichlet condition imposed on the monomer concentration at the boundary. The asymptotic results are confirmed by numerical simulations.