A probabilistic model for ligand-cytoskeleton transmembrane adhesion: predicting the behavior of microspheres on the surface of migrating cells

A theoretical model describing the attachment and cytoskeletal coupling of microspheres to the dorsal surface of motile cells was developed. Integral membrane receptors beneath a ligand-coated microsphere are allowed to be either free, attached to the microsphere, bound to the rearward moving actin network, or linked to both the bead and the cytoskeleton, and to switch between these four states. The binding transitions being modeled as chemical reactions governed by rate constants taken from literature, the chance for a receptor to be in each binding state over time is obtained by solving mass-balance equations for the probability functions. The population of n such receptors beneath the microsphere is accounted for by a binomial distribution for each state. Adhesion and transmembrane coupling (resulting in microsphere transport) being defined by a minimal number of ligand-receptor and receptor-cytoskeleton bonds, respectively, the probabilities of attachment and transport of the microsphere over time are expressed in terms of state probability distributions. It is found that increasing the ligand density raises the attachment and transport probabilities, in good quantitative agreement with recent experiments using optical tweezers and accurate position tracking. Increasing the bead size does not affect attachment, but raises the transport probability with a marked transition for bead diameter around 100 nm, as for experimental data. Increasing the restraining force decreases the transport probability, probably by inducing a rupture of receptor-cytoskeleton bonds. This study thus provides a framework that helps understand the process of cortical flow associated with cell locomotion.