Single-molecule fluorescence probes dynamics of barrier crossing

ABSTRACT Kramers developed the theory on how chemical reaction rates are influenced by the viscosity of the medium1,2. 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 folding3,4. 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 transitions5. 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 reactions2. 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. Access through your institution Buy or subscribe This is a preview of subscription content, access via

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LEVEL Article 28 March 2024 TRANSIENT BINDING AND JUMPING DYNAMICS OF P53 ALONG DNA REVEALED BY SUB-MILLISECOND RESOLVED SINGLE-MOLECULE FLUORESCENCE TRACKING Article Open access 13 August

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account for two-probe folding kinetics of protein α3D. _J. Chem. Phys._ 130, 061101 (2009) Article  ADS  Google Scholar  Download references ACKNOWLEDGEMENTS We are particularly indebted to

J. M. Louis for the preparation, dye labelling and purification of the protein used in this work, with technical assistance from A. Aniana. We also thank R. Best, G. Hummer and A. Szabo for

discussions and comments on the manuscript, and D.E. Shaw Research for providing access to their molecular dynamics trajectories for the calculations by R. Best. This work was supported by

the Intramural Research Program of the National Institute of Diabetes and Digestive and Kidney Diseases, National Institutes of Health. AUTHOR INFORMATION AUTHORS AND AFFILIATIONS *

Laboratory of Chemical Physics, National Institute of Diabetes and Digestive and Kidney Diseases, National Institutes of Health, Bethesda, 20892-0520, Maryland, USA Hoi Sung Chung & 

William A. Eaton Authors * Hoi Sung Chung View author publications You can also search for this author inPubMed Google Scholar * William A. Eaton View author publications You can also search

for this author inPubMed Google Scholar CONTRIBUTIONS H.S.C. and W.A.E. designed the research and wrote the manuscript; H.S.C. collected and analysed the experimental data. CORRESPONDING

AUTHORS Correspondence to Hoi Sung Chung or William A. Eaton. ETHICS DECLARATIONS COMPETING INTERESTS The authors declare no competing financial interests. EXTENDED DATA FIGURES AND TABLES

EXTENDED DATA FIGURE 1 AMINO ACID SEQUENCES OF POLYPEPTIDES CONTAINING PROTEIN Α3D. Dyes were attached to the cysteine residues (red) and a biotin molecule was attached to the lysine residue

(blue) in the AviTag sequence. EXTENDED DATA FIGURE 2 PHOTON TRAJECTORY AND KINETICS MODELS. A, The definition of photon indices and time interval of a photon trajectory with a folding

transition. B, C, Photon trajectories were analysed using the two-state model to determine kinetics parameters (B) or the three-state model to determine the average transition path times

(_t_TP  = 1/2_k_S) (C). EXTENDED DATA FIGURE 3 FRET EFFICIENCY HISTOGRAMS OF Α3D IN 2.25 M GDMCL SOLUTION AT DIFFERENT TEMPERATURES. The FRET efficiency histograms were constructed from 1-ms

bins in the trajectories with the mean photon count rate >40 ms−1. Wide and narrow bars are the experimental histograms and the histograms constructed from re-coloured photon

trajectories using the parameters obtained from the maximum likelihood method with the two-state model (Extended Data Table 1), respectively. The agreement between the two histograms

validates the description of α3D as a two-state folder8. The similar ratio of the integral of the folded (high FRET) and the unfolded (low FRET) distributions indicates that the equilibrium

constant is unchanged over the temperature range of the measurement, as shown more precisely in the maximum likelihood analysis. At high temperature and low pH, where the 11 glutamates and 1

aspartate are protonated, more than two states are observed37,38. EXTENDED DATA FIGURE 4 DONOR–ACCEPTOR CROSS-CORRELATION FUNCTIONS AT DIFFERENT TEMPERATURES. Black solid lines are

exponential functions that best fit the data. The fitting parameters are listed in Extended Data Table 1. EXTENDED DATA FIGURE 5 FRET EFFICIENCY HISTOGRAMS OF Α3D AT VARIOUS SOLVENT

VISCOSITIES. The FRET efficiency histograms were constructed from 1-ms bins in the trajectories with the mean photon count rate >50 ms−1 for 2.25 M and 3.2 M GdmCl and from 2-ms bins in

the trajectories with the mean photon count rate >30 ms−1 for 4.6 M, 4.3 M and 3.8 M GdmCl concentrations. At the relative viscosity (_η_/_η_0) 1, 10 and 38, the higher concentration of

GdmCl was used to counteract the stabilization of proteins by glycerol to maintain the ratio of folded to unfolded molecules as close to unity as practically possible. The similar ratio of

the integral of the folded (high FRET) and the unfolded (low FRET) distributions indicates that the equilibrium constant is unchanged at these conditions, as shown more precisely in the

maximum likelihood analysis. EXTENDED DATA FIGURE 6 DONOR–ACCEPTOR CROSS-CORRELATION OF THE SEGMENTS OF THE FLUORESCENCE TRAJECTORIES CORRESPONDING TO THE UNFOLDED STATE (REF. 24). A, Black

solid lines are exponential functions that best fit the data. The fitting parameters are listed in Extended Data Table 2. B, The unfolded state dynamics are slowed approximately linearly by

the solvent viscosity as previously observed at high denaturant concentrations24. The relaxation time at _η_/ _η_0 = 1 (aqueous solution) is too fast to be measured by this method.

POWERPOINT SLIDES POWERPOINT SLIDE FOR FIG. 1 POWERPOINT SLIDE FOR FIG. 2 POWERPOINT SLIDE FOR FIG. 3 POWERPOINT SLIDE FOR FIG. 4 RIGHTS AND PERMISSIONS Reprints and permissions ABOUT THIS

ARTICLE CITE THIS ARTICLE Chung, H., Eaton, W. Single-molecule fluorescence probes dynamics of barrier crossing. _Nature_ 502, 685–688 (2013). https://doi.org/10.1038/nature12649 Download

citation * Received: 15 May 2013 * Accepted: 12 September 2013 * Published: 23 October 2013 * Issue Date: 31 October 2013 * DOI: https://doi.org/10.1038/nature12649 SHARE THIS ARTICLE Anyone

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