A model for the kinetics of homotypic cellular aggregation under static conditions

We present the formulation and testing of a mathematical model for the kinetics of homotypic cellular aggregation. The model considers cellular aggregation under no-flow conditions as a two-step process. Individual cells and cell aggregates 1) move on the tissue culture surface and 2) collide with other cells (or aggregates). These collisions lead to the formation of intercellular bonds. The aggregation kinetics are described by a system of coupled, nonlinear ordinary differential equations, and the collision frequency kernel is derived by extending Smoluchowski's colloidal flocculation theory to cell migration and aggregation on a two-dimensional surface. Our results indicate that aggregation rates strongly depend upon the motility of cells and cell aggregates, the frequency of cell-cell collisions, and the strength of intercellular bonds. Model predictions agree well with data from homotypic lymphocyte aggregation experiments using Jurkat cells activated by 33B6, an antibody to the beta 1 integrin. Since cell migration speeds and all the other model parameters can be independently measured, the aggregation model provides a quantitative methodology by which we can accurately evaluate the adhesivity and aggregation behavior of cells.