Effect of viscous drag on multiple receptor-ligand bonds rupture force

Abstract

Monte Carlo simulation of the rupture of multiple receptor-ligand bonds between two PMN cells suspended in a Newtonian fluid is performed. We demonstrate via micro-mechanical model of two cells adhered by multiple receptor-ligand bonds that viscous drag caused by relative motion of cell suspended in a Newtonian fluid modulates transmission of an applied external load to bonds. Specifically, it is demonstrated that at any time the intermolecular bond force is not equivalent to the instantaneous applied force. The difference in the instantaneous applied force and the intermolecular bond force depends on the viscosity of fluid, the size of cell, the applied loading rate, and the number of bonds at any instant of time. Viscous drag acting on cell reduces average bond rupture forces.

Figure 1

Schematic of two PMN cells detachment (not drawn to scale) through binding between PSGL-1 (receptor) and L-selectin (ligand) molecules concentrated on the tip of PMN microvillus.

Figure 2

Time variation of the cell velocity (solid lines) and the number of bonds (dashed lines) obtained from micro-mechanical model simulation at loading rate R_f = 10⁷ pN/s for the initial number of bonds N₀ = 5.

Figure 3

Time variation of drag force acting on cell (a) for N₀ = 2 at three different R_f (b) for N₀ = 1, 2, 5, 10 at R_f = 10⁷ pN/s obtained from micro-mechanical model simulations for the model parameters listed in Table 1.

Figure 4

Time variation of applied force (solid line) and intermolecular bond force for N₀ = 1 (dashed lines), N₀ = 2 (dashed dot lines), N₀ = 5 (long dashed lines), and N₀ = 10 (dashed dot dot lines) at (a) R_f = 10³ pN/s (b) R_f = 10⁵ pN/s (c) R_f = 10⁷ pN/s obtained from micro-mechanical model simulations for the model parameters listed in Table 1. Panel (d) shows time variation of applied force (solid line) and intermolecular bond force for N₀ = 2 at R_f = 10⁷ pN/s and η = 1 cP (dashed lines), η = 2 cP (dashed dot lines), η = 3 cP (long dashed lines), and η = 4 cP (dashed dot dot lines).

Figure 5

Average bond rupture force as a function of loading rate for (a) N₀ = 1, (b) N₀ = 2, (c) N₀ = 5, and (d) N₀ = 10 obtained from the micro-mechanical model simulations utilizing the Bell model for the model parameters listed in Table 1.

Figure 6

Average bond rupture force as a function of loading rate for (a) N₀ = 1, (b) N₀ = 2, (c) N₀ = 5, and (d) N₀ = 10 obtained from the micro-mechanical model simulations utilizing the two-state (catch-slip) model for the model parameters listed in Table 1.

Figure 7

Effect of bond spring constant on the average bond rupture force as a function of loading rate for N₀ = 10 at σ = 4 dyn/cm (solid lines), σ = 2 dyn/cm (dashed lines), and σ = 1 dyn/cm (dashed dot lines) obtained from the micro-mechanical model simulations utilizing the Bell model for the model parameters listed in Table 1.

Figure 8

Number of bonds as a function of time obtained from the deterministic model simulation (solid lines) at R_f = 10⁷ pN/s, N₀ = 100. A few representative trajectories for the number of bonds as a function of time obtained from the Monte Carlo simulation at R_f = 10⁷ pN/s, N₀ = 100 are shown as dashed lines.

Figure 9

Solid lines: deterministic results for (a) cluster lifetime T_cluster and (b) cluster rupture force F_cluster for the case of vanishing rebinding and in absence of both inertia and viscous drag as a function of μ=N₀ for N₀ = 10, 10², and 10³. Broken lines: curves for all three scaling regimes.

Figure 10

Solid lines: deterministic results for (a) cluster lifetime T_cluster and (b) cluster rupture force F_cluster for the case of vanishing rebinding and in absence of both inertia and viscous drag as a function of μ=N₀ for N₀ = 10, 10², and 10³. Symbols: corresponding results in presence of both inertia and viscous drag.