Existing experimental and theoretical studies on the adhesion of molecular bond clusters are usually based on either displacement- or force-controlled loading conditions. Very few studies have addressed whether or not and how the loading conditions affect the stochastic behavior of clusters. By considering the reversible breaking and rebinding process of ligand–receptor bonds, we directly solve the master equation about reactions between receptor–ligand bonds and conduct the corresponding Monte Carlo simulation to investigate the rupture forces of adhesion molecular clusters under linearly incremented displacement and force loading, respectively. We find that the rupture force of clusters strongly depends on loading conditions. Bond breaking and rebinding are independent of each other under displacement-controlled loading, whereas the rupture force highly depends on the state of each single bond under force-controlled loading. The physical mechanism of the dependence of rupture force on loading rate is also analyzed. We identify three reaction regimes in terms of loading rate: the regimes of equilibrium breaking/rebinding reactions, near-equilibrium reaction, and far from equilibrium with only bond breaking. These findings can help improve the current understanding of the stochastic behaviors of the adhesion clusters of molecular bonds under dynamic loading conditions.

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