ArticleNature2013
Single-molecule fluorescence probes dynamics of barrier crossing.
Article in Nature, 2013. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 93 papers.
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Who cites it
93 citing papers in PubMed.
- Cooperative Native Contact Formation Facilitates Free Energy Barrier Crossing in Protein Folding.Physical review letters · 2026Article
- Multiscale tracking of emulsion dynamics by aggregation-induced emission.National science review · 2025Article
- Three-color single-molecule maximum likelihood analysis of folding and binding of diffusing molecules.Biophysical journal · 2025Article
- Model-free photon analysis of diffusion-based single-molecule FRET experiments.Nature communications · 2025Article
- Extrinsic and intrinsic effects setting viscosity in complex fluids and life processes: the role of fundamental physical constants.The European physical journal. E, Soft matter · 2025Article
- The Thermodynamic and Kinetic Properties of the dA-rU DNA-RNA Hybrid Base Pair Investigated via Molecular Dynamics Simulations.Molecules (Basel, Switzerland) · 2024Article
- An optofluidic antenna for enhancing the sensitivity of single-emitter measurements.Nature communications · 2024Article
- Time-resolved burst variance analysis.Biophysical reports · 2023Article
- Constraints on fundamental physical constants from bio-friendly viscosity and diffusion.Science advances · 2023Article
- Fast protein folding is governed by memory-dependent friction.Proceedings of the National Academy of Sciences of the United States of America · 2023Article
- Robust membrane protein tweezers reveal the folding speed limit of helical membrane proteins.eLife · 2023Article
- Anisotropic Friction in a Ligand-Protein Complex.Nano letters · 2023Article
- The Effect of Time Resolution on Apparent Transition Path Times Observed in Single-Molecule Studies of Biomolecules.The journal of physical chemistry. B · 2022Article
- Real-time Exchange of the Lipid-bound Intermediate and Post-fusion States of the HIV-1 gp41 Ectodomain.Journal of molecular biology · 2022Article
- Theory and Analysis of Single-Molecule FRET Experiments.Methods in molecular biology (Clifton, N.J.) · 2022Article
- Observing the base-by-base search for native structure along transition paths during the folding of single nucleic acid hairpins.Proceedings of the National Academy of Sciences of the United States of America · 2021Article
- Learning non-stationary Langevin dynamics from stochastic observations of latent trajectories.Nature communications · 2021Article
- Does Electric Friction Matter in Living Cells?The journal of physical chemistry. B · 2021Article
- Extraction of rapid kinetics from smFRET measurements using integrative detectors.Cell reports. Physical science · 2021Article
- Energy landscapes of fast-folding proteins pushing the limits of atomic force microscope (AFM) pulling.Proceedings of the National Academy of Sciences of the United States of America · 2021Article
33 more citing papers are in PubMed but not listed here.
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Abstract
Kramers developed the theory on how chemical reaction rates are influenced by the viscosity of the medium. At the viscosity of water, the kinetics of unimolecular reactions are described by diffusion of a Brownian particle over a free-energy barrier separating reactants and products. For reactions in solution this famous theory extended Eyring's transition state theory, and is widely applied in physics, chemistry and biology, including to reactions as complex as protein folding. Because the diffusion coefficient of Kramers' theory is determined by the dynamics in the sparsely populated region of the barrier top, its properties have not been directly measured for any molecular system. Here we show that the Kramers diffusion coefficient and free-energy barrier can be characterized by measuring the temperature- and viscosity-dependence of the transition path time for protein folding. The transition path is the small fraction of an equilibrium trajectory for a single molecule when the free-energy barrier separating two states is actually crossed. Its duration, the transition path time, can now be determined from photon trajectories for single protein molecules undergoing folding/unfolding transitions. Our finding of a long transition path time with an unusually small solvent viscosity dependence suggests that internal friction as well as solvent friction determine the Kramers diffusion coefficient for α-helical proteins, as opposed to a breakdown of his theory, which occurs for many small-molecule reactions. It is noteworthy that the new and fundamental information concerning Kramers' theory and the dynamics of barrier crossings obtained here come from experiments on a protein rather than a much simpler chemical or physical system.
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