Figure 4. Velocity, height, and force parameters of free-flowing and tethered neutrophils. (a) Average velocity of free-flowing neutrophils before and after tethering to adherent platelets as a function of wall shear rate. (b) Calculated gap distance between the neutrophil and the wall before and after tethering to a spread platelet. (c) Force balance on tethered neutrophil. L, the length of the tether; Fs, shear force on the cell; Fb, force on the tether bond; R, radius of the cell; g, gap distance between neutrophil and wall; h, distance of the cell centroid from wall; and ,, the measured average projection of the tether length. (d) Estimated force on tether bond as a function of wall shear rate. The rela- tionship between wall shear stress and force on the cell was esti- mated from Goldman’s equation (Fs 5 6pmRhgwC), where m, viscosity; R, cell radius; h, distance from the center of the cell to the wall; gw, wall shear rate; and C, a numerical factor that de- pends on h/R (Goldman et al., 1967). From geometry, Fs 5 Fb cos(u). Fb represents the case where the tether is bonded between point q on the platelet and point r on the neutrophil (i.e., u 5 tan21 (h2d/h)), where , is the measured tether length. Asterisk denotes the minimum force to pull a tether was obtained from Shao et al. (1998). ical results of Goldman et al. (1967). Fig. 4 b is a plot of the neutrophil distance from the surface with shear rate. The gap distance of the neutrophil above the wall after tether release was relatively constant at z0.2–0.3 mm. The gap distance of the approaching neutrophils captured by ad- herent platelets increased modestly from 0.7 to 1.7 mm, with an increasing shear rate from 100 to 250 s21, an obser- vation that may relate to the frequency of surface encoun- ter of the longest neutrophil microvilli or to very subtle lift forces that may exist (particle Reynolds number, z0.02). To estimate the force on the tether between the neutro- phil and platelet, a force balance was performed (Fig. 4, c and d). The relationship between wall shear stress and force on the cell was estimated from Goldman’s equation (Fs 5 6pmRhgwC), where m represents the viscosity, R rep- resents the cell radius, h represents the distance from the center of the cell to the wall, gw represents the wall shear rate, and C represents a numerical factor that depends on h/R. The relationship between the force on the cell and the force on the tethered bond was based upon a force balance Fbcosu 5 Fs. The force on the tether bond can be esti- mated by visualizing the projected length of the tether (,) and making the following assumptions that: (1) the tether began at the edge of the platelet (point q); (2) the gap dis- tance between the wall and the neutrophil was the height of the neutrophil after release (g z0.3 mm); and (3) the tether originated from the neutrophil at point r. Values for d and h were estimated from the height determined from the neutrophil’s approach and release velocities using the method of Goldman et al. (1967). Since the ratio of the tether growth velocity (vtether) to the cellular free flowing velocity (vflow) is typically below 1:20, the assumption of mechanical equilibrium is sufficiently accurate since the shear force is overestimated by ,5% for a correction fac- tor of 12vtether/vflow z 0.95. As the first available estimate of the P-selectin/PSGL-1 bond strength where both recep- tors reside in their natural cellular membranes, the force on the bond increased from 86 to 172 pN as the shear rate increased from 100 to 250 s21 (Fig. 4 d). Tether Formation Frequency and Antibody Blocking Experiments The percentage of initial adhesive events between flowing neutrophils and immobilized platelets, which resulted in the formation of elongated membrane tethers, as com- pared with transient pausing or rolling is shown in Fig 5. At a shear rate of 200 s21, 43 out of 139 collisions ob- served between free-flowing neutrophils and immobilized platelets resulted in a membrane tether (n 5 3 experi- ments with individual donors). To determine if the ob- served tether formation was due to P-selectin/PSGL-1 bonding, we studied platelet–neutrophil interactions in the presence of function-blocking mAbs to P-selectin and PSGL-1. Incubating adherent platelets with mAb G1, which binds to an epitope in the lectin domain of P-selec- tin and blocks binding of P-selectin to leukocytes (Ham- burger and McEver, 1990) and PSGL-1 (Moore et al., 1995), completely blocked tether formation (Fig. 5). Simi- larly, incubation of neutrophils with the mAb PL1, which binds to the NH2-terminal region of PSGL-1 and blocks P-selectin binding to this region (Moore et al., 1995), also resulted in the total inhibition of tether formation (Fig. 5). In contrast, incubation of neutrophils with either mAb IB4 Figure 5. Role of the P-selec- tin/PSGL-1 bond in neutro- phil tether formation with ad- herent platelets. Neutrophils were perfused over adherent platelets at 200 s21 in the ab- sence (n 5 3 experiments with individual donors) or the presence of mAbs, and the percentage of neutrophil– platelet collisions that re- sulted in membrane tether formation was determined. Incu- bation of platelets with anti–P-selectin antibody (G1), or neutrophils with anti–PSGL-1 (PL1) resulted in a complete inhi- bition of tether formation (n 5 2 experiments for each mAb). In contrast, the incubation of neutrophils with anti-CD18 antibody (IB4) (n 5 3 experiments) or with the metabolic inhibitor sodium azide did not prevent tether formation (n 5 3 experiments). Schmidtke and Diamond Neutrophil Tethering under Flow 723