FIGURE 2.

Parameters of cell tethering under flow. (A) The fluid velocity v of a Couette flow field bordered with a solid surface (xy plane) is parallel to the surface and increases linearly with the distance from the surface (z direction). The shear rate is reciprocal to the slope of the velocity profile. Fluid-mechanics theory predicts that the translational velocity V and angular velocity Ω of a sphere of radius r freely moving above a surface in an otherwise Couette flow are proportional to and , respectively (29). The sphere bottom has a positive velocity V_s ≡ V – rΩ ∝ relative to the surface (13). The sphere and the surface are coated with receptors and ligands, respectively, whose combined length l_m sets a contact threshold. When the gap distance l_i between the sphere bottom and the surface is <l_m, the two are in contact with an area A_i = 2πr(l_m − l_i). (B) Due to its small size, the sphere is susceptible to thermal excitations that cause Brownian motion. This produces fluctuations in velocity components parallel to the surface, which can be directly observed (cf. Fig. 3 A), as well as those perpendicular to the surface, which are depicted by the wavy trajectory of the sphere shown at five different times and positions. By randomly modulating the gap distance above and below the contact threshold z = l_m (horizontal line), Brownian motion causes discontinuous contacts of different portions of the sphere with different portions of the surface, with alternating intervals of contact (t_i) and noncontact (t_j). A productive contact results in a tethering event, but many contacts are nonproductive. As schematically shown for one receptor and one ligand by the movements along the two-sided arrows (lighter colors), the binding sites of L-selectin and PSGL-1 can undergo rotational diffusion even though portions of the molecules are anchored to the respective sphere surface and chamber floor. To ensure that only first-time tethering events were observed, the chamber floor upstream to the microscope field of view was coated with HSA to allow measurement of the distance traveled by the sphere from the demarcation line to the location where tethering occurs. The cell, contact area, and molecular sizes are not drawn to scale.