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Multiple barriers in forced rupture of protein complexes

Curvatures in the most probable rupture force ($f^*$) versus log-loading rate ($\log{r_f}$) observed in dynamic force spectroscopy (DFS) on biomolecular complexes are interpreted using a one-dimensional free energy profile with multiple barriers or a single barrier with force-dependent transition state. Here, we provide a criterion to select one scenario over another. If the rupture dynamics occurs by crossing a single barrier in a physical free energy profile describing unbinding, the exponent $ν$, from $(1- f^*/f_c)^{1/ν}\sim(\log r_f)$ with $f_c$ being a critical force in the absence of force, is restricted to $0.5 \leq ν\leq 1$. For biotin-ligand complexes and leukocyte-associated antigen-1 bound to intercellular adhesion molecules, which display large curvature in the DFS data, fits to experimental data yield $ν<0.5$, suggesting that ligand unbinding is associated with multiple-barrier crossing.