Adhesion Cluster — Stochastic Bond Rebinding

Bell model + rebinding: cooperative rupture & catch-bond behaviour (Erdmann & Schwarz 2004)

Bond Parameters

Total bonds N 20

Off-rate k₀ 1.0

Force sensitivity γ 0.5

On-rate κ_on 2.0

Applied Force

Total force F 5.0

State

Bound bonds n: —

Force/bond f: —

Avg lifetime τ: —

Stochastic Adhesion Cluster Model

In cell adhesion, clusters of molecular bonds (integrins, selectins) bear load collectively. Each bond ruptures at rate k_off(f) = k₀·exp(γ·f/n) (Bell 1978) where f/n is the force per bond. Broken bonds rebind at rate κ_on·(N−n)/N.

The mean-field transition: for small F the cluster is stable (rebinding wins); above a critical force F_c = n·k_BT/γ·ln(κ_on/k₀), rupture cascades and the cluster fails. This cooperative failure explains the sharp force-dependent lifetime of adhesion patches observed in AFM measurements.

Catch bonds (selectins) show the opposite: k_off decreases with force over some range, giving longer lifetimes under moderate loads — critical for rolling adhesion in blood vessels.