Estimate of the sticking probability for cells in uniform shear flow with adhesion caused by specific bonds

A theory is developed for the aggregation rate of cells in uniform shear flow when the cell-cell adhesion is mediated by bonds between specific molecules on the cell surfaces such as antigen and antibody or lectin and carbohydrate. The theory is based on estimates of the frequency and duration of cell-cell collisions and of the number of bonds formed and required to hold the cells together. For high shear rates, the sticking probability is a function of a single dimensionless parameter, A, that is proportional to G-2, with G the shear rate. For low shear rates, the sticking probability is a function of a second dimensionless parameter, A' proportional to G-1. In either case the rate of cell-cell sticking is a maximum when A (or A') congruent to 1.0. For small values of A (or A') the cells collide frequently, but do not stick, whereas for large values of A (or A') the cells collide infrequently, but stick with larger probability. Studies in Couette viscometer or other flow having approximately uniform shear can test these models.