Strength of adhesion clusters under shared linear loading

A cluster of N ligand-receptor pairs between two parallel surfaces under an applied force F=Γt with a constant loading rate Γ is considered. Our theoretical and numerical studies show that there is a characteristic force f_c and a characteristic loading rate Γ_c. At Γ<Γ_c, the mean rupture force F_r of the cluster is close to but lower than Nf_c. In this regime, cluster dissociation can be modeled as a one-dimensional barrier crossing process and F_r scales like Nf_c-F_r-N1 ^/3[ln(Γ_c/Γ)]2^/3. At Γ=Γ_c, the cluster dissociation occurs at F _r=Nf_c. At ΓΓ_c, F_r for clusters with large N is well predicted by the rate equation because the fluctuations of the number of closed bonds are unimportant. Our study shows that f_c and Γ_c are important emergent properties for understanding the mechanical response of adhesion clusters.