A Traveling Wave Model for Invasion by Precursor and Differentiated Cells

Abstract

We develop and investigate a continuum model for invasion of a domain by cells that migrate, proliferate and differentiate. The model is applicable to neural crest cell invasion in the developing enteric nervous system, but is presented in general terms and is of broader applicability. Two cell populations are identified and modeled explicitly; a population of precursor cells that migrate and proliferate, and a population of differentiated cells derived from the precursors which have impaired migration and proliferation. The equation describing the precursor cells is based on Fisher's equation with the addition of a carrying-capacity limited differentiation term. Two variations of the prolif..