Local models of cell aggregation kinetics

Abstract

Mathematical models of the phenomena of the sorting out of embryonic cells are derived which predict multiple clustering of like cell types into many small islands. The experiments of Trinkaus and Lentz, and other essentially two-dimensional cell sorting results, provide examples. Two continuous models are introduced, both based on the Smoluchowski theory of Brownian motion. A mass-interaction model predicts local clumping of the internally segregating cell type within a continuum of the other type. A diffusion model simulates the suspension-aggregate experiments of Roth and Weston. A discrete model of sorting out, the exchange model, is re-derived in a clearer manner than before, and certain recent criticisms are responded to. Results in recent two-dimensional cell sorting experiments are discussed and a stability criterion for patterns of multiple clusters is introduced. The site frequency model is re-examined and criticized in terms of its application to the Roth-Weston experiments.