Protein folding rate is one of the important properties of a protein. Protein folding rate prediction is useful for understanding protein folding process and guiding protein design. In this study, we developed a support vector machine (SVM) based method to predict protein folding kinetic types (two-state or non-two-state) and the real-value folding rate using the features calculated from the three-dimensional structure such as contact order, various properties from the non-local contact clusters, secondary structural information and sequence length. We systematically studied the contributions of individual features to folding rate prediction. Based on the highest contributions of individual features, we trained our machine using leave one out cross-validation and tested on a testing dataset. The Pearson correlation coefficient, mean absolute difference and root mean square error between the predicted and experimental folding rates (base-10 logarithmic scale) are 0.814, 0.752 and 0.910 for two-state proteins, and 0.860, 0.687 and 0.876 for non-two-state proteins. Moreover, our method predicts whether a protein of known atomic structure folds according to two-state or non-two-state kinetics and correctly classifies 80% of the folding mechanism on a testing dataset. Finally, we evaluated the performance of our method along with the other eight existing protein folding rate prediction tools on non-overlapping benchmarking dataset. The prediction performance will also be reported and discussed.

BACKGROUND: In template-based modeling when using a single template, inter-atomic distances of an unknown protein structure are assumed to be distributed by Gaussian probability density functions, whose center peaks are located at the distances between corresponding atoms in the template structure. The width of the Gaussian distribution, the variability of a spatial restraint, is closely related to the reliability of the restraint information extracted from a template, and it should be accurately estimated for successful template-based protein structure modeling. RESULTS: To predict the variability of the spatial restraints in template-based modeling, we have devised a prediction model, Sigma-RF, by using the random forest (RF) algorithm. The benchmark results on 22 CASP9 targets show that the variability values from Sigma-RF are of higher correlations with the true distance deviation than those from Modeller. We assessed the effect of new sigma values by performing the single-domain homology modeling of 22 CASP9 targets and 24 CASP10 targets. For most of the targets tested, we could obtain more accurate 3D models from the identical alignments by using the Sigma-RF results than by using Modeller ones. CONCLUSIONS: We find that the average alignment quality of residues located between and at two aligned residues, quasi-local information, is the most contributing factor, by investigating the importance of input features used in the RF machine learning. This average alignment quality is shown to be more important than the previously identified quantity of a local information: the product of alignment qualities at two aligned residues.

MOTIVATION: Conventional Monte Carlo and molecular dynamics simulations of proteins in the canonical ensemble are of little use, because they tend to get trapped in states of energy local minima at low temperatures. One way to surmount this difficulty is to use a non-Boltzmann sampling method in which conformations are sampled upon a general weighting function instead of the conventional Boltzmann weighting function. The multiensemble sampling (MES) method is a non-Boltzmann sampling method that was originally developed to estimate free energy differences between systems with different potential energies and/or at different thermodynamic states. The method has not yet been applied to studies of complex molecular systems such as proteins. RESULTS: MES Monte Carlo simulations of small proteins have been carried out using a united-residue force field. The proteins at several temperatures from the unfolded to the folded states were simulated in a single MC run at a time and their equilibrium thermodynamic properties were calculated correctly. The distributions of sampled conformations clearly indicate that, when going through states of energy local minima, the MES simulation did not get trapped in them but escaped from them so quickly that all the relevant parts of conformation space could be sampled properly. A two-step folding process consisting of a collapse transition followed by a folding transition is observed. This study demonstrates that the use of MES alleviates the multiple-minima problem greatly. AVAILABILITY: Available on request from the authors.

United-residue models of polypeptide chains [3, 5, 19-22, 24, 31, 33] have long been of interest, because they enable one to carry out global conformational searches of proteins in real time, which in turn can facilitate ab initio protein structure predictions based solely on Anfinsen's thermodynamic hypothesis [1], according to which the native structure of a protein is a global minimum of its potential energy surface [32]. In the last few years, we developed a united-residue force field [20-22, 24], hereafter referred to as UNRES, in which a polypeptide chain is represented by a sequence of α-carbon (Cα) atoms linked by virtual bonds with attached united side chains (SC) and united peptide groups (p) located in the middle between the consecutive α-carbons (Figure 1). Only the united peptide groups and united side chains serve as interaction sites, the α-carbons serving to define the geometry.