Single-molecule experiments can reveal fundamentally novel and unique information on the structure, dynamics, and interactions of individual biomolecules. Single-molecule protein folding. Protein folding is often described as diffusion on a free energy surface. We have developed and quantified diffusion models of protein folding (1). These fully quantitative models showed that the approximations frequently made in the analysis of single-molecule experiments are reasonably accurate, at least for the small model proteins we could study by coarse-grained molecular simulations. Hydrodynamics at the molecular scale. In solution, the translational motions, associated for instance with binding and dissociation of complexes, are affected by so-called hydrodynamic interactions. We have quantified these hydrodynamic interactions for a model system and showed that simple hydrodynamic models such as the Oseen tensor and their refinements indeed capture the gross effects, but with significant deviations at the molecular scale (2). Folding transition path times. Transition paths are a distinct single-molecule property that separate out transition events. Arguably, they contain all mechanistic information relevant for a transition such as protein and nucleic-acid folding. In commenting on experimental studies of transition path time distributions, we have examined the theory and single-molecule experimental approaches used to study these mechanistically important events (3). 1. R. B. Best, G. Hummer, Diffusion models of protein folding, Phys. Chem. Chem. Phys. 13, 16902-16911 (2011). 2. J. Mittal, G. Hummer, Pair diffusion, hydrodynamic interactions, and available volume in dense fluids, J. Chem. Phys. 137, 034110 (2012). 3. G. Hummer, W. A. Eaton, Viewpoint: Transition path times for DNA and RNA folding from force spectroscopy, Physics 5, 87 (2012).

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Mittal, Jeetain; Hummer, Gerhard (2012) Pair diffusion, hydrodynamic interactions, and available volume in dense fluids. J Chem Phys 137:034110
Best, Robert B; Hummer, Gerhard (2011) Diffusion models of protein folding. Phys Chem Chem Phys 13:16902-11
Hummer, Gerhard (2010) Catching a protein in the act. Proc Natl Acad Sci U S A 107:2381-2
Hummer, Gerhard; Szabo, Attila (2010) Free energy profiles from single-molecule pulling experiments. Proc Natl Acad Sci U S A 107:21441-6
Frewen, Thomas A; Hummer, Gerhard; Kevrekidis, Ioannis G (2009) Exploration of effective potential landscapes using coarse reverse integration. J Chem Phys 131:134104
Berezhkovskii, Alexander; Hummer, Gerhard; Szabo, Attila (2009) Reactive flux and folding pathways in network models of coarse-grained protein dynamics. J Chem Phys 130:205102
Best, Robert B; Hummer, Gerhard (2009) Biochemistry. Unfolding the secrets of calmodulin. Science 323:593-4
Dudko, Olga K; Hummer, Gerhard; Szabo, Attila (2008) Theory, analysis, and interpretation of single-molecule force spectroscopy experiments. Proc Natl Acad Sci U S A 105:15755-60