Bond tilting and sliding friction in a model of cell adhesion

Abstract

As a simple theoretical model of a cell adhering to a biological interface, we consider a rigid cylinder moving in a viscous shear flow near a wall. Adhesion forces arise through intermolecular bonds between receptors on the cell and their ligands on the wall, which form flexible tethers that can stretch and tilt as the base of the cell moves past the wall; binding kinetics is assumed to follow a standard model for slip bonds. By introducing a finite resistance to bond tilting, we use our model to explore the territory between previous theoretical models that allow for either zero or infinite resistance to bond rotation. A microscale calculation (for two parallel sliding plates) reveals a nonlinear force–speed relation arising from bond formation, tilting and breakage. Two distinct types of macroscale cell motion are then predicted: either bonds adhere strongly and the cell rolls (or tank treads) over the wall without slipping, or the cell moves near its free-stream speed with bonds providing weak frictional resistance to sliding. The model predicts bistability between these two states, implying that at critical shear rates the system can switch abruptly between rolling and free sliding, and suggesting that sliding friction arising through bond tilting may play a significant dynamical role in some cell-adhesion applications.

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ORCID for Giles Richardson: orcid.org/0000-0001-6225-8590

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