**Parameters of rolling adhesion under flow.** (A) The rolling motions of a microsphere or neutrophil of radius *r* are governed by the balance of the resultant force (*F*_{s}) and torque (*T*_{s}) exerted by the flowing fluid, the tether force (*F*_{t}) applied through L-selectin–PSGL-1 bonds, and the contact force (*F*_{c}). The conversion of wall shear stress to *F*_{t} using the indicated variables is described in Materials and methods. Elevating the viscosity by addition of 6% Ficoll increases shear stress by 2.6-fold and therefore increases *F*_{t} on a sphere of constant size, as illustrated by the comparative lengths of the thin and thick vectors for *F*_{t} on the small sphere. At the same shear stress, *F*_{t} is ninefold greater for a sphere of 3-μm radius than for a sphere of 1-μm radius, as illustrated by the comparative lengths of the thin vectors for *F*_{t} on the large and small spheres. (B) A rolling sphere stops when the adhesive bond sustains the full load required to balance the maximum *F*_{t} and *T*_{s}. After the bond dissociates, the sphere accelerates as it pivots on a newly formed bond upstream and then decelerates as force develops in the bond. The sphere stops again if the new bond has sufficient strength to withstand the full load and lives long enough to survive loading, or it accelerates if the bond dissociates prematurely.

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