No Access Submitted: 20 November 2017 Accepted: 05 January 2018 Published Online: 24 January 2018
J. Chem. Phys. 148, 123325 (2018);
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  • J. Nicholas Taylor
  • Menahem Pirchi
  • Gilad Haran
  • Tamiki Komatsuzaki
Hierarchical features of the energy landscape of the folding/unfolding behavior of adenylate kinase, including its dependence on denaturant concentration, are elucidated in terms of single-molecule fluorescence resonance energy transfer (smFRET) measurements in which the proteins are encapsulated in a lipid vesicle. The core in constructing the energy landscape from single-molecule time-series across different denaturant concentrations is the application of rate-distortion theory (RDT), which naturally considers the effects of measurement noise and sampling error, in combination with change-point detection and the quantification of the FRET efficiency-dependent photobleaching behavior. Energy landscapes are constructed as a function of observation time scale, revealing multiple partially folded conformations at small time scales that are situated in a superbasin. As the time scale increases, these denatured states merge into a single basin, demonstrating the coarse-graining of the energy landscape as observation time increases. Because the photobleaching time scale is dependent on the conformational state of the protein, possible nonequilibrium features are discussed, and a statistical test for violation of the detailed balance condition is developed based on the state sequences arising from the RDT framework.
J.N.T. and T.K. would like to thank Chun-Biu Li, Hiroshi Teramoto, Jason R. Green, and Schuyler B. Nicholson for helpful discussions. This work was supported by Grant-in-Aid for Young Scientists (B) (No. 15K18511) (to J.N.T.), Grant-in-Aid for Scientific Research (B) (No. 17H02940) (to T.K.), Grant-in-Aid for Specially Promoted Research (B) (No. 15KT0055) (to T.K.), Grant-in-Aid for Exploratory Research (No. 16K14703), JSPS (to T.K.), Grant-in-Aid for Scientific Research on Innovative Areas (No. 16H01525), MEXT (to T.K.), and a grant from the Israel Science Foundation (686/14) (to G.H.). The authors also thank the workshop “Macromolecular dynamics: structure, function and diseases,” Kavli Institute for Theoretical Physics, Beijing, China, (2014) through which this work was initiated.
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