Selectin receptor-ligand bonds: Formation limited by shear rate and dissociation governed by the Bell model

Abstract

We have studied the principles that govern the formation and dissociation of an adhesive bond between a cell moving in shear flow and a substrate and tested different theories of how force affects bond dissociation. Viscosity relates the kinematics of fluid movement (shear rate, units of time(-1)) to shear stress (units of force/area, the product of shear rate and viscosity). At different medium viscosities, the formation of receptor-ligand bonds between a cell in the flowstream and P-selectin on the vessel wall showed a similar efficiency as a function of shear rate but not of shear stress. Therefore, bond formation was a function of shear rate and hence of the kinematics of receptor and ligand movement. By contrast, the kinetics of bond dissociation was a function of shear stress and hence of force on the bond. The different requirements for bond formation and dissociation allowed dissociation kinetics to be measured at higher forces on the bond by increasing medium viscosity. Data over an extended range of forces on the bond therefore could be collected that enabled five different proposed equations, relating force to bond dissociation, to be compared for fit to experimental data. The relationship proposed by Bell [Bell, G. I. (1978) Science 200, 618-627] fit the data significantly the best and also predicted an off-rate in the absence of force that best matched an independent measurement [Mehta, P., Cummings, R. D. & McEver, R. P. (1998) J. Biol. Chem. 273, 32506-32513].

Figure 1

Hydrodynamic velocities of neutrophils near the substrate at different viscosities. Neutrophils were infused into the flow chamber in Hanks' balanced salt solution/Hepes buffer containing 2 mM Ca²⁺ and 0, 3, and 6% Ficoll. The velocity of the cells was measured in the microscopic focal plane near the lower wall of the flow chamber.

Figure 2

Frequency of tethering in shear flow of neutrophils to P-selectin at three different viscosities. Transient tether frequency on P-selectin diluted 1:40,000 was determined as the number of tethering events per second divided by the number of cells in the field of view near the wall of substrate in Hanks' balanced salt solution/Hepes buffer containing 2 mM Ca²⁺ and 0, 3, and 6% of Ficoll. The same data are plotted vs. wall shear stress (A) and shear rate (B).

Figure 3

The kinetics of dissociation of transiently tethered neutrophils at different viscosities. The number of cells remaining transiently tethered as a function of time after tether initiation was measured on P-selectin at 1 (A), 1.8 (B), and 2.6 cP (C). Lines show the fits to first-order dissociation kinetics by the method of least squares.

Figure 4

Instantaneous force on the bond and rate of force loading. (A) Instantaneous force, f_b. The first time point is at the time when the peak force is loaded, as determined by the hydrodynamic velocity of the cell and the lever arm (see text); thereafter, f_b is shown after each video-frame time interval (0.033 s). (B) Force loading rate. The rate was calculated as described in the text.

Figure 5

Fit to five theoretical predictions of the effect of F_b on k_off. (A) Arithmetic fit. (B) Logarithmic fit, using the difference between the logs of the predicted and observed k_off values. The k_off data of tethered neutrophils on P-selectin measured in 0, 3, or 6% Ficoll are plotted vs. the average force on bond, F_b. The pooled data of k_off at different viscosities were fit to the indicated theoretical models. DHW, deep harmonic well; SBD, spontaneous bond dissociation.