Mechanics of transient platelet adhesion to von Willebrand factor under flow

Abstract

A primary and critical step in platelet attachment to injured vascular endothelium is the formation of reversible tether bonds between the platelet glycoprotein receptor Ibalpha and the A1 domain of surface-bound von Willebrand factor (vWF). Due to the platelet's unique ellipsoidal shape, the force mechanics involved in its tether bond formation differs significantly from that of leukocytes and other spherical cells. We have investigated the mechanics of platelet tethering to surface-immobilized vWF-A1 under hydrodynamic shear flow. A computer algorithm was used to analyze digitized images recorded during flow-chamber experiments and track the microscale motions of platelets before, during, and after contact with the surface. An analytical two-dimensional model was developed to calculate the motion of a tethered platelet on a reactive surface in linear shear flow. Through comparison of the theoretical solution with experimental observations, we show that attachment of platelets occurs only in orientations that are predicted to result in compression along the length of the platelet and therefore on the bond being formed. These results suggest that hydrodynamic compressive forces may play an important role in initiating tether bond formation.

FIGURE 1

Graphical results of the platelet tracking algorithm developed to analyze three-dimensional position of tethering platelets from digital movies. (A) Digital movie frames of a tethered platelet flipping on a vWF-coated surface showing platelet orientation at five different times (i–v) during the flip. (B) Corresponding diagrams of ellipsoidal mesh models rotated approximately three axes and its calculated two-dimensional projected shadow. (C) Regression of calculated shadow outline (represented by thick solid line) to experimental image outline (represented by ○).

FIGURE 2

Schematic of how the Stokes flow problem of a platelet flipping on a surface may be modeled as a two-dimensional analytical problem by decomposing it into the sum of two simpler cases. Flipping is a result of the hydrodynamic effect of shear flow on the platelet as it interacts with surface-bound vWF. (A) Platelet attached to the surface by GPIbα-vWF bond(s) and subjected to linear shear flow. (B) A stationary and rigid inclined fence subjected to linear shear flow. (C) A rigid, flat, hinged plate rotating at angular velocity ω toward the surface in a quiescent fluid.

FIGURE 3

Plot of analytically predicted and experimentally observed trajectories of bound platelets during platelet flips as a function of the dimensionless time. At time t = 0, the platelet is oriented at 90° to the surface. (Thick solid line represents the theoretical prediction; the symbols ⋄, △, □, and ○ represent four experimental flipping events at 8 dyn/cm²; the symbols ▹, ⋄, △, and □ represent four experimental flipping events at 1.5 dyn/cm²; x represents a flipping event at 1 dyn/cm².)

FIGURE 4

Plot of non-dimensionalized theoretical hydrodynamic radial bond force as a function of decreasing platelet orientation angle, compared with experimentally observed platelet attachment/detachment angles. (A) Schematic diagrams of three positions of a platelet during its flip, where α is the angle the platelet major axis makes with the surface, measured in counterclockwise direction. (B) Non-dimensionalized theoretical radial bond force, F/(2γμA), plotted as a function of platelet orientation angle where the angles vary from π to 0 as the platelet flips from one side to the other; the experimentally observed attachment angles (⋄) and detachment angles (○) obtained from experiments conducted at shear stresses of 1.0, 1.5, 2.0, 4.0, and 8.0 dyn/cm² are plotted with the theoretical bond force estimate. Note that the occurrence of attachment/detachment events corresponds to the negative/positive sign of the predicted radial force, respectively.

FIGURE 5

Plot of the experimentally measured average attachment (⋄) and detachment angles (○), as a function of wall shear stress.

FIGURE 6

Plot of the trajectories of free-stream platelets as predicted by the Jeffery orbits theory, and platelet trajectories from experiments conducted at 0.2 dyn/cm² shear stress. The experimental data (○, *, ▽, and △) are compared to the Jeffery orbit model for spheroid rotation in unbounded fluid (dashed line), and the theoretical prediction corrected to include the wall effect on plate rotational motion (thick solid line).

FIGURE 7

Plots of the analytically derived solution for force and torque acting on a stationary inclined fence subjected to linear shear flow (fence problem; Jeong and Kim, 1983), and the polynomial approximations fitted to the analytical solution by least-squares regression. (A) Plot of force values taken from the analytically derived solution (Eq. A5) (♦) and force calculated from the polynomial approximation (Eq. A7) (thick solid line). (B) Plot of torque values taken from the analytically derived solution (Eq. A6) (♦) and torque calculated from the polynomial approximation (Eq. A8) (thick solid line).