Receptor-mediated cell attachment and detachment kinetics. I. Probabilistic model and analysis.

The kinetics of receptor-mediated cell adhesion to a ligand-coated surface play a key role in many physiological and biotechnology-related processes. We present a probabilistic model of receptor-ligand bond formation between a cell and surface to describe the probability of adhesion in a fluid shear field. Our model extends the deterministic model of Hammer and Lauffenburger (Hammer, D.A., and D.A. Lauffenburger. 1987. Biophys. J. 52:475-487) to a probabilistic framework, in which we calculate the probability that a certain number of bonds between a cell and surface exists at any given time. The probabilistic framework is used to account for deviations from ideal, deterministic behavior, inherent in chemical reactions involving relatively small numbers of reacting molecules. Two situations are investigated: first, cell attachment in the absence of fluid stress; and, second, cell detachment in the presence of fluid stress. In the attachment case, we examine the expected variance in bond formation as a function of attachment time; this also provides an initial condition for the detachment case. Focusing then on detachment, we predict transient behavior as a function of key system parameters, such as the distractive fluid force, the receptor-ligand bond affinity and rate constants, and the receptor and ligand densities. We compare the predictions of the probabilistic model with those of a deterministic model, and show how a deterministic approach can yield some inaccurate results; e.g., it cannot account for temporally continuous cell attach mentor detachment, it can underestimate the time needed for cell attachment, it can overestimate the time required for cell detachment for a given level of force, and it can overestimate the force necessary for cell detachment.