Coarse grained description of the protein folding

We consider two- and three-dimensional lattice models of proteins which were characterized previously. We coarse grain their folding dynamics by reducing it to transitions between effective states. We consider two methods of selection of the effective states. The first method is based on the steepest descent mapping of states to underlying local energy minima and the other involves an additional projection to maximally compact conformations. Both methods generate connectivity patterns that allow to distinguish between the good and bad folders. Connectivity graphs corresponding to the folding funnel have few loops and are thus tree-like. The Arrhenius law for the median folding time of a 16-monomer sequence is established and the corresponding barrier is related to easily identifiable kinetic trap states.Comment: REVTeX, 9 pages, 15 EPS figures, to appear in Phys. Rev.

Modeling study on the validity of a possibly simplified representation of proteins

The folding characteristics of sequences reduced with a possibly simplified representation of five types of residues are shown to be similar to their original ones with the natural set of residues (20 types or 20 letters). The reduced sequences have a good foldability and fold to the same native structure of their optimized original ones. A large ground state gap for the native structure shows the thermodynamic stability of the reduced sequences. The general validity of such a five-letter reduction is further studied via the correlation between the reduced sequences and the original ones. As a comparison, a reduction with two letters is found not to reproduce the native structure of the original sequences due to its homopolymeric features.Comment: 6 pages with 4 figure

Inferring stabilizing mutations from protein phylogenies : application to influenza hemagglutinin

One selection pressure shaping sequence evolution is the requirement that a protein fold with sufficient stability to perform its biological functions. We present a conceptual framework that explains how this requirement causes the probability that a particular amino acid mutation is fixed during evolution to depend on its effect on protein stability. We mathematically formalize this framework to develop a Bayesian approach for inferring the stability effects of individual mutations from homologous protein sequences of known phylogeny. This approach is able to predict published experimentally measured mutational stability effects (ΔΔG values) with an accuracy that exceeds both a state-of-the-art physicochemical modeling program and the sequence-based consensus approach. As a further test, we use our phylogenetic inference approach to predict stabilizing mutations to influenza hemagglutinin. We introduce these mutations into a temperature-sensitive influenza virus with a defect in its hemagglutinin gene and experimentally demonstrate that some of the mutations allow the virus to grow at higher temperatures. Our work therefore describes a powerful new approach for predicting stabilizing mutations that can be successfully applied even to large, complex proteins such as hemagglutinin. This approach also makes a mathematical link between phylogenetics and experimentally measurable protein properties, potentially paving the way for more accurate analyses of molecular evolution

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

Probing the urea dependence of residual structure in denatured human α-lactalbumin

Backbone 15N relaxation parameters and 15N–1HN residual dipolar couplings (RDCs) have been measured for a variant of human α-lactalbumin (α-LA) in 4, 6, 8 and 10 M urea. In the α-LA variant, the eight cysteine residues in the protein have been replaced by alanines (all-Ala α-LA). This protein is a partially folded molten globule at pH 2 and has been shown previously to unfold in a stepwise non-cooperative manner on the addition of urea. 15N R2 values in some regions of all-Ala α-LA show significant exchange broadening which is reduced as the urea concentration is increased. Experimental RDC data are compared with RDCs predicted from a statistical coil model and with bulkiness, average area buried upon folding and hydrophobicity profiles in order to identify regions of non-random structure. Residues in the regions corresponding to the B, D and C-terminal 310 helices in native α-LA show R2 values and RDC data consistent with some non-random structural propensities even at high urea concentrations. Indeed, for residues 101–106 the residual structure persists in 10 M urea and the RDC data suggest that this might include the formation of a turn-like structure. The data presented here allow a detailed characterization of the non-cooperative unfolding of all-Ala α-LA at higher concentrations of denaturant and complement previous studies which focused on structural features of the molten globule which is populated at lower concentrations of denaturant