An Estimate of the Numbers and Density of Low-Energy Structures (or Decoys) in the Conformational Landscape of Proteins

The conformational energy landscape of a protein, as calculated by known potential energy functions, has several minima, and one of these corresponds to its native structure. It is however difficult to comprehensively estimate the actual numbers of low energy structures (or decoys), the relationships between them, and how the numbers scale with the size of the protein.We have developed an algorithm to rapidly and efficiently identify the low energy conformers of oligo peptides by using mutually orthogonal Latin squares to sample the potential energy hyper surface. Using this algorithm, and the ECEPP/3 potential function, we have made an exhaustive enumeration of the low-energy structures of peptides of different lengths, and have extrapolated these results to larger polypeptides.We show that the number of native-like structures for a polypeptide is, in general, an exponential function of its sequence length. The density of these structures in conformational space remains more or less constant and all the increase appears to come from an expansion in the volume of the space. These results are consistent with earlier reports that were based on other models and techniques

Hydrogen-Bond Driven Loop-Closure Kinetics in Unfolded Polypeptide Chains

Characterization of the length dependence of end-to-end loop-closure kinetics in unfolded polypeptide chains provides an understanding of early steps in protein folding. Here, loop-closure in poly-glycine-serine peptides is investigated by combining single-molecule fluorescence spectroscopy with molecular dynamics simulation. For chains containing more than 10 peptide bonds loop-closing rate constants on the 20–100 nanosecond time range exhibit a power-law length dependence. However, this scaling breaks down for shorter peptides, which exhibit slower kinetics arising from a perturbation induced by the dye reporter system used in the experimental setup. The loop-closure kinetics in the longer peptides is found to be determined by the formation of intra-peptide hydrogen bonds and transient β-sheet structure, that accelerate the search for contacts among residues distant in sequence relative to the case of a polypeptide chain in which hydrogen bonds cannot form. Hydrogen-bond-driven polypeptide-chain collapse in unfolded peptides under physiological conditions found here is not only consistent with hierarchical models of protein folding, that highlights the importance of secondary structure formation early in the folding process, but is also shown to speed up the search for productive folding events