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Biophys J, March 1999, p. 1280-1292, Vol. 76, No. 3
School of Chemical Engineering, Cornell University, Ithaca, New York 14853 USA
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.
Biophys J, March 1999, p. 1280-1292, Vol. 76, No. 3
© 1999 by the Biophysical Society 0006-3495/99/03/1280/13 $2.00
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