A FUNCTIONAL DIFFERENTIAL EQUATION MODEL FOR BIOLOGICAL CELL SORTING DUE TO DIFFERENTIAL ADHESION

Abstract

This paper presents a mathematical model to describe the sorting of two different types of cells, arising from differential adhesion mechanisms within biological tissue. The model is based on a continuum approach that takes into account individual cell behavior including aspects of the cell-migration process, dynamics of the adhesions between contacting cells, and finite cell size. Numerical solutions and bifurcation analyses for the case of a collection of two different cell types show a variety of behaviors observed in experiments, including spatially uniform mixing of cells and the formation of two distinct, containing both types of cells or just one. The mathematical model, which is in the form of a set of functional differential equations, represents a novel approach to continuum modeling of cell sorting and migration within biological tissue.