For disordered proteins, the dimensions of the chain are an important property that is sensitive to environmental conditions. We have used single-molecule Förster resonance energy transfer to probe the temperature-induced chain collapse of five unfolded or intrinsically disordered proteins. Because this behavior is sensitive to the details of intrachain and chain-solvent interactions, the collapse allows us to probe the physical interactions governing the dimensions of disordered proteins. We find that each of the proteins undergoes a collapse with increasing temperature, with the most hydrophobic one, λ-repressor, undergoing a reexpansion at the highest temperatures. Although such a collapse might be expected due to the temperature dependence of the classical "hydrophobic effect," remarkably we find that the largest collapse occurs for the most hydrophilic, charged sequences. Using a combination of theory and simulation, we show that this result can be rationalized in terms of the temperature-dependent solvation free energies of the constituent amino acids, with the solvation properties of the most hydrophilic residues playing a large part in determining the collapse.T he properties of unfolded proteins have recently attracted renewed interest (1), triggered in particular by the realization that a large fraction of naturally occurring polypeptides are unstructured under physiological conditions (2, 3). Some of them fold into well-defined structures upon interaction with a ligand or binding partner, whereas others may remain unstructured under all conditions. Many of these "intrinsically disordered proteins" (IDPs) are involved in cellular signaling networks and are thus of great medical interest (4). Given the presence of varying degrees of disorder in unbound and bound states (5), a general framework for the description of the physicochemical properties of IDPs will aid our understanding of the molecular mechanisms underlying their function. Such a framework is beginning to emerge from recent work in which concepts from polymer physics have been found to capture very successfully key aspects of the global conformational and dynamic properties of IDPs and unfolded proteins in general (6). These include the role of charge interactions (7, 8), protein-solvent interactions (9-13), scaling laws (14-16), reconfiguration dynamics (17), and the effect of internal friction (18)(19)(20)(21).An aspect that is less well understood is the effect of temperature on unfolded and intrinsically disordered proteins. Recent single-molecule Förster resonance energy transfer (FRET) experiments showed that the small cold shock protein from Thermotoga maritima (CspTm) and the IDP prothymosin α (ProTα) become more compact with increasing temperature (22), even after the effect of denaturant present in solution (23) is taken into account. The results were in good agreement with dynamic light-scattering experiments on unlabeled protein, demonstrating that the effect is independent of the presence of the fluorophores (22). This result is...

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.

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