Long ligands reinforce biological adhesion under shear flow

In this work, computer modeling has been used to show that longer ligands allow biological cells (e.g., blood platelets) to withstand stronger flows after their adhesion to solid walls. A mechanistic model of polymer-mediated ligand-receptor adhesion between a microparticle (cell) and a flat wall has been developed. The theoretical threshold between adherent and non-adherent regimes has been derived analytically and confirmed by simulations. These results lead to a deeper understanding of numerous biophysical processes, e.g., arterial thrombosis, and to the design of new biomimetic colloid-polymer systems.

Figure 1

Illustration of polymer-mediated adhesion mechanics. (a) In the shear flow a spherical particle is rolling and translating along the wall within distance $h$. The tether can stick to the sphere (b), and if the tether is long enough, it develops a sufficient tension force $Tcos\alpha$ to hold the sphere against the drag force $F$. Yet if $\alpha$ is too big, then the maximum tension $T_{\max }$ is reached and the tether detaches (a).

Figure 2

(a) Three types of particles used in this work. (b) The drag on a sphere held against the flow with constant velocity $U$. Numerical results (squares for the smaller sphere, circles for the bigger one) agree with Stokes's law (lines).

Figure 3

Drag force (left) and torque (right) on the immobile sphere ($R=0.64\mu \mathrm{m}$) near a wall in shear flow. Symbols correspond to simulation results for different distances $h$ between the sphere and the wall; lines correspond to the analytical formulas from [51, 59].

Figure 4

Adhesion regimes diagram: red crosses correspond to cases where the tether was unable to hold the sphere, green circles to where the sphere remained attached until the end of the simulation, orange triangles to rolling with stops, and light green diamonds to adhesion when the tethering occurred on the second (or third, etc.) approach. The dashed line corresponds to Eq. (1) and the dash-dotted line to Eq. (2). The solid red line is a visual guide for the boundary between adhesive and non-adhesive regimes.

Figure 5

(a) Series of simulation shots for $R=0.64$ $\mu \mathrm{m}$, $N=20$, and $\dot{\gamma }={10}^3{s}^{-1}$. (b) Mean velocity of the sphere ($R=0.64$) plotted against shear rate for different $N$. Dashed line corresponds to the theoretical velocity $V=\dot{\gamma }(R+h)$ of a free-flowing sphere at distance $h=0.15$ $\mu \mathrm{m}$ from the wall. (c) Distance traveled by the sphere ($R=0.64$ $\mu \mathrm{m}$) before stopping in cases of durable adhesion for different $N$.

Figure 6

Mean velocity of a sphere plotted against the shear rate for different $N$ and $R$. Lines correspond to theoretical velocity of a free-flowing sphere.

Figure 7

(a) Simulation of the platelet motion before adhering to a wall via binding with grafted von Willebrand factor chain. (b) Diagram comparing the maximum shear rate sustained by the platelet (yellow) and the equivolume sphere (blue). For the platelet, the error bars correspond to deviation due to its initial placement (different orientation of symmetry axes), and for the sphere, to a systematic uncertainty (50 ${\mathrm{s}}^{-1}$) caused by the step change of shear rate between two consequent simulations.