Structural-elastic Determination of the Lifetime of Biomolecules under Force

The lifetime of protein domains and ligand-receptor complexes under force is crucial for both mechanochemistry and mechanobiology. However, how force affects the lifetime remains poorly understood. Currently, most of the models are derived based on a presumed shape of the energy surface, which restricts the scope of their applications to explain experimental data. Here we report a novel analytical expression of the force-dependent rate (the reciprocal of lifetime) of protein unfolding or ligand-receptor complex rupturing based on the structural-elastic properties of the molecules. This new model is able to fit a wide scope of experimentally measured force-dependent rates, including many experimental data showing complex derivation from Bell’s model, such as the "catch-to-slip" behaviour. Most importantly, the best-fitting parameters of our model directly inform us of the differential structural-elastic properties of the molecules between the transition and native states. Further, combined with the structural-elastic properties of the native state that can be obtained from the molecular structure and all-atom molecular dynamics simulations, the structural-elastic properties of the transition state of the molecule can be uniquely determined from the values of fitting parameters.