Probabilistic Modeling of Shear-Induced Formation and Breakage of Doublets Cross-Linked by Receptor-Ligand Bonds

Abstract

A model was constructed to describe previously published experiments of shear-induced formation and breakage of doublets of red cells and of latexes cross-linked by receptor-ligand bonds (Tees et al. 1993. Biophys. J. 65:1318–1334; Tees and Goldsmith. 1996. Biophys. J. 71:1102–1114; Kwong et al. 1996. Biophys. J. 71:1115–1122). The model, based on McQuarrie’s master equations (1963. J. Phys. Chem. 38:433–436), provides unifying treatments for three distinctive time periods in the experiments of particles in a Couette flow in which a doublet undergoes 1) formation upon two-body collision between singlets; 2) evolution of bonds at low shear rate; and 3) break-up at high shear rate. Neglecting the applied force at low shear rate, the probability of forming a doublet per collision as well as the evolution of probability distribution of bonds in a preformed doublet were solved analytically and found to be in quite good agreement with measurements. At high shear rate with significant force acting to accelerate bond dissociation, the predictions for break-up of doublets were obtained numerically and compared well with data in both individual and population studies. These comparisons enabled bond kinetic parameters for three types of particles cross-linked by two receptor-ligand systems to be calculated, which agreed well with those computed from Monte Carlo simulations. This work can be extended to analyze kinetics of receptor-ligand binding in cell aggregates, such as those of neutrophils and platelets in the circulation.