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 freestream 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 celladhesion applications.

Clonal Variants of Plasmodium falciparum Exhibit a Narrow Range of Rolling Velocities to Host Receptor CD36 under Dynamic Flow Conditions

“…Investigation of field isolates and CIDR recombinant proteins suggests there are low-and high-affinity CD36 binding variants (10,30), but there has been limited investigation of the range of pRBC-CD36 binding affinities. A variety of factors are likely to influence pRBC adhesion and rolling velocities, including the PfEMP1 surface expression levels, the strength of the receptorligand interaction, the bending modulus of the pRBC membrane, and the effective hydrodynamic radius of the rolling pRBC (48)(49)(50). Recently the density of knobs on the surface has been observed to vary both as pRBCs age and between parasite isolates (51,52).…”

Surface deformation and shear flow in ligand mediated cell adhesion

“…1, L = D 2 + |x| 2 is the length of a bond in a stretched configuration. The energy associated with a bond tilted from its vertical position is (1/2)λ θ α 2 0 , (κ θ being the torsion constant) and (Reboux et al 2008)…”

“…In the limit of small binding affinity and abundant ligands on the binding surface (i.e., A Tot K on, eq /K off, eq 1), the bond ligand density evolves in accordance with the pde (Dembo et al 1988;Hodges and Jensen 2002;Reboux et al 2008)…”

Review: Rheological properties of biological materials

“…Welldefined test-cases however are already within the reach of such approaches, as reviewed in [14]. For example, one can relate the microscopic detachment-formation of bonds at the molecular scale to describe how cells bind or roll alonga substrate [66,189] or how the molecular machinery comes into play to push the membrane forward in lamellipodia. Another important promising issue is to link the cellular (individual cell properties such as adhesive and mechanical effects [190]) and macroscopic scales (tissues) through homogeneization methods [e.g.…”