Sigma-RF: prediction of the variability of spatial restraints in template-based modeling by random forest

Juyong Lee, Kiho Lee, InSuk Joung, Keehyoung Joo, Bernard R Brooks, Jooyoung Lee

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. 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. 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.