The Forward Rate of Binding of Surface-Tethered Reactants: Effect of Relative Motion between Two Surfaces

Abstract

The reaction of molecules confined to two dimensions is of interest in cell adhesion, specifically for the reaction between cell surface receptors and substrate-bound ligand. We have developed a model to describe the overall rate of reaction of species that are bound to surfaces under relative motion, such that the Peclet number is order one or greater. The encounter rate between reactive species is calculated from solution of the two-dimensional convection-diffusion equation. The probability that each encounter will lead to binding depends on the intrinsic rate of reaction and the encounter duration. The encounter duration is obtained from the theory of first passage times. We find that the binding rate increases with relative velocity between the two surfaces, then reaches a plateau. This plateau indicates that the increase in the encounter rate is counterbalanced by the decrease in the encounter duration as the relative velocity increases. The binding rate is fully described by two dimensionless parameters, the Peclet number and the Damköhler number. We use this model to explain data from the cell adhesion literature by incorporating these rate laws into "adhesive dynamics" simulations to model the binding of a cell to a surface under flow. Leukocytes are known to display a "shear threshold effect" when binding selectin-coated surfaces under shear flow, defined as an increase in bind rate with shear; this effect, as calculated here, is due to an increase in collisions between receptor and ligand with increasing shear. The model can be used to explain other published data on the effect of wall shear rate on the binding of cells to surfaces, specifically the mild decrease in binding within a fixed area with increasing shear rate.

Dynamic states of cells adhering in shear flow: From slipping to rolling

“…One immediate advantage of our method is that it avoids a flow rate-dependent rate of bond formation [45]. In order to be able to spatially resolve both ligands and receptors, it is necessary to include the Brownian motion of the cell.…”

Affinity and Kinetic Analysis of Fcγ Receptor IIIa (CD16a) Binding to IgG Ligands

“…A major physical difference between the two-and three-dimensional binding is that, instead of approaching one another by free diffusion in the three-dimensional case, molecules in two-dimensional interactions are brought together (and apart) by cells to which they are anchored. Cells are 1,000 times the size of the molecules; and thereby their motions dictate the transport of the reacting molecules prior (and post) to their intrinsic binding (34,35). The difference between the three-dimensional k off values measured via the SPR technique and the two-dimensional k off values measured by the micropipette technique has been highlighted in a recent study (36).…”

Selectin catch–slip kinetics encode shear threshold adhesive behavior of rolling leukocytes

“…Stable rolling through L-selectin requires a threshold level of fluid shear stress, an unexpected but important consequence that prevents homotypic aggregation and inappropriate adhesion in low-shear environments (2)(3)(4). Much attention has focused on the underlying molecular kinetics to understand this behavior, with particular emphasis on the role of convective transport (5)(6)(7)(8) and the molecular response to mechanical strain (9,10). Several studies have now firmly established that fluid shear rate controls the tethering rate at which cells initially adhere to the substrate (6)(7)(8).…”