Probing static disorder in protein unfolding and chemical reactions by single-molecule force spectroscopy

The work presented in this dissertation focuses on the kinetics of biomolecular reactions under mechanical force, including protein unfolding and disulfide-bond reduction, probed at the single-molecule level. The advent of single-molecule force spectroscopy has allowed the direct measure of force-dependent reaction rates, providing a powerful approach to extract the kinetic information and to characterize the underlying energy landscape that governs the reaction. The widely accepted two-state kinetic model for protein unfolding describes that the protein unfolds by crossing over a single energy barrier, with the implicit assumption of a single transition state and a well-defined activation energy barrier. Based on this assumption, the ensemble-averaged survival probability is expected to follow single exponential time dependence. However, it has become increasingly clear that the saddle point of the free-energy surface in most reactions is populated by ensembles of conformations, leading to nonexponential kinetics. Here we present a theory that generalizes the two-state model to include static disorder of conformational degrees of freedom to fully account for a diverse set of unfolding pathways. Using single-molecule force-clamp spectroscopy, we study the nonexponential kinetics of single ubiquitin proteins unfolding under constant forces. We find that the measured variance in the barrier heights has a quadratic dependence on force. Our study illustrates a novel adaptation of the classical Arrhenius equation that accounts for the microscopic origins of nonexponential kinetics. Our theory provides a direct approach in determining the variance in the barrier heights of a reaction. We extend our theoretical model to investigate the kinetics of two different reactions, protein unfolding and disulfide-bond reduction, both occurring within the same protein molecule. We measure the variance of the barrier heights, which quantifies the heterogeneity of the reaction pathway for both reactions. In contrast to protein unfolding, we find that the variance of the barrier heights for disulfide-bond reduction is close to zero, reflecting the differences between these two reactions. These results strongly suggest that the transition state for a disulfide-bond reduction is well defined, as opposed to protein unfolding. The Bell model assumes that the distance to the transition state is force independent. However, in many systems, it has been observed that the transition state moves toward the destabilized state upon perturbation. This effect, known as the Hammond effect, would predict that the distance to the transition state decreases with force. This hypothesis remains unexplored in protein unfolding under force. To elucidate the conformational plasticity of the transition state structure upon the application of force, we probe the unfolding kinetics of ubiquitin and NuG2 over a broad range of forces. We use the force-ramp assay to measure probability distribution of unfolding forces. Based on the standard two-state model, the force-dependent lifetimes can be obtained by transforming the probability distribution of unfolding forces. However, this formalism is invalid for proteins exhibiting the dispersed kinetics, as we observed in ubiquitin. By measuring the lifetimes over a wide range of forces, we discover that the distance to the transition state for NuG2 exhibits a weak force dependency. The measured value of the distance to the transition state is 0.22 nm, comparable to the size of a water molecule. The observed non-Hammond behavior revealed an integral structural role of water molecules bridging the unfolding transition state, constraining the movement of the unfolding transition state. Finally, in order to test the Kramers theory that would predict that the distance to the transition state continuously decreases with force, we explore the kinetics of disulfide bond reduction by hydroxide anions over a wide range of forces. On the contrary to the Kramers prediction, we observe that the reduction rate exhibits two distinct exponential dependencies on the pulling force, revealing a discontinuous shift in the distance to the transition state. The experimental data show that the distance to the transition state is ~ 0.5 Å in the low-force regime (< 500 pN), and changes to a much shorter value of ~ 0.1 Å in the high-force regime (> 500 pN). We propose a plausible molecular scenario that is consistent with our experimental results. We suggest that the substrate disulfide bond undergoes a conformational change under a stretching force above 500 pN. Our results show the first observation that the application of a mechanical force to the protein disulfide bond causes an abrupt change in reactivity.