Figure 1. Simulation geometry.

(A) A Cartesian coordinate system was employed. Flow was applied in the X-direction with a linear shear rate, S. A three dimensional sphere with a fixed radius, R, was coated with receptors, and each anchor point of the base of the receptor's tether region to the surface of the sphere is shown as a black dot. Only the receptors within an unstressed receptor/ligand contour length of the surface, λ, were allowed to form bonds. This region has been highlighted in yellow. The gap between the base of the sphere and the surface, δ, was allowed to vary. The diffusion of the sphere was included in the simulation. The diffusion had six components with the inclusion of rotation in the sphere's motion. Motion perpendicular to the flow direction, along the Y-axis, is referred to as “wobble” in the text. (B,C) Two different models of reactivity for molecules in the contact volume were included in the simulations. For contact patch confinement, described mathematically by (1), all of the receptors on the sphere within an unstressed receptor/ligand contour length of the surface were assumed to react with a constant rate. For molecular area confinement, described mathematically by (2), receptors immobilized on portions of the sphere closest to the surface were allowed to form bonds with an increased rate proportional to the area of the projection of the molecular contour length onto the XY plane. The colors in (B,C) depict the relative reaction rate of receptors, and warmer colors indicate an increased reaction rate.