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Free energy surfaces from single-distance information

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P. Schuetz; R. Wuttke; B. Schuler; A. Caflisch

Journal: J. Phys. Chem. B
Year: 2010
Volume: 114
Issue: 46
Pages: 15227-15235
DOI: 10.1021/jp1053698
Type of Publication: Journal Article

Fluorescence Resonance Energy Transfer; Kinetics; Molecular Dynamics Simulation; Peptides; Protein Conformation; Protein Denaturation; Protein Folding; Thermodynamics


We propose a network-based method for determining basins and barriers of complex free energy surfaces (e.g., the protein folding landscape) from the time series of a single intramolecular distance. First, a network of transitions is constructed by clustering the points of the time series according to the short-time distribution of the signal. The transition network, which reflects the short-time kinetics, is then used for the iterative determination of individual basins by the minimum-cut-based free energy profile, a barrier-preserving one-dimensional projection of the free energy surface. The method is tested using the time series of a single C(β)-C(β) distance extracted from equilibrium molecular dynamics (MD) simulations of a structured peptide (20 residue three-stranded antiparallel β-sheet). Although the information of only one distance is employed to describe a system with 645 degrees of freedom, both the native state and the unfolding barrier of about 10 kJ/mol are determined with remarkable accuracy. Moreover, non-native conformers are identified by comparing long-time distributions of the same distance. To examine the applicability to single-molecule Förster resonance energy transfer (FRET) experiments, a time series of donor and acceptor photons is generated using the MD trajectory. The native state of the β-sheet peptide is determined accurately from the emulated FRET signal. Applied to real single-molecule FRET measurements on a monomeric variant of λ-repressor, the network-based method correctly identifies the folded and unfolded populations, which are clearly separated in the minimum-cut-based free energy profile.