Evaluation of ensemble quality. Comparisons in ensemble quality, as measured by MAMMOTH MaxSub (black, best in set; gray, average of set) are shown for 3D-Pair alignments between query native structure and parents from detection method, alignments from detection method (3D-Jury, FFAS03 or PSI-BLAST), and progressive stages in modeling.

Selection from backbone optimized ensembles. Scheme is the same as that used in Figure 5, with additional average quality scores for models selected from ensembles after addition of long loops (‘+ Long Loops’, in magenta) and full-length backbone optimization (‘+ Backbone Optimization’, in green). Also shown are the quality of the initial template of the selected model for the long loop model (‘+ Long Loops (IT)’, in turquoise) and the initial template for the backbone optimized model (‘+ Backbone Optimization (IT)’, in yellow).

Inputs to K*Sync alignment method. K*Sync combines sequence information with structural information to produce an alignment by dynamic programming. The inputs and weights on terms may be varied. The default alignment uses secondary structure predicted by PSIPRED and sequence comparison by the inner product of the residue substitution frequency profiles. In the diagram, ‘+’ indicates a bonus, ‘−’ a penalty, ‘<=>’ an alignment between two positions with the given characteristic.

Evaluation of K*Sync default alignments. Average accuracy and completeness of alignments for targets in SCOP1.38 test set with respect to a structure–structure alignment (CE) are shown for profile–sequence alignment (PSSM, in dashed gray), profile–profile alignment (Inner Product, in solid gray), the combination of profile–profile and structural information (K*Sync, in solid black), and another structure–structure alignment method (Dali, in dashed black). Targets are grouped into 5% identity bins (based on the CE alignment). Note that the Dali alignment diverges from the CE alignment as the pairs become more remote, owing to our strict alignment equivalence requirement.

Sampling of near best possible alignments. Histogram of number of targets with a member of the K*Sync ensemble with a model close in quality to the model derived from the 3D-Pair alignment of the query native structure to the structure of the best parent (that provides the most coordinates similar to the query). Horizontal axis represents the difference in the MAMMOTH MaxSub score of the 3D-Pair model and the best model in the ensemble (with values indicating the upper bound for the bin), and y-axis is the number of targets that are within that upper bound.

Scoring of alignment ensembles. The similarity to the query native structure of each model in the initial template-only ensemble (before loop modeling) with respect to a selection score, with (a) the hydrophobic burial score, (b) the full-atom energy and (c) the consensus score. An example target in each of the three difficulty regimes (3D-Jury, FFAS03 and PSI-BLAST) is shown, in the same scheme as Figure 6. Targets are: 3D-Jury regime, 20906 (1uocA); FFAS03 regime, 20415 (1j0sA); and PSI-BLAST regime, 17597 (1iyzA). The negative of the consensus score is shown so the trend in (c) is similar to that in (a) and (b).

Comparison of strategies for selection from the ensemble. Average MAMMOTH MaxSub scores for 3D-Pair set of alignments, detection method set of alignments, K*Sync ensemble set of alignments and models selected by various measures from K*Sync ensemble both before and after loop modeling. Best in set shown in black, average of set in gray, selection of a template-only model in red, selection of a model after modeling short loops (but with a quality evaluated prior to loop modeling) in orange, and selection of a model including short loops (and with a quality evaluated with the loops present) in blue. The average of the models resulting from the K*Sync default alignment is shown as well as those selected from the ensemble using the hydrophobic burial preference (‘hφ_burial’), the side-chain centroid representation energy function (‘centroid’), the full-atom representation energy function (‘full_atom’), and the alignment consensus score (‘consensus’). Also shown is the average of the models selected using sum-of-ranks combination scores of these measures (indicated by those scores with a ‘+’ in the name).

Consensus score as a function of ensemble size. Selection by consensus score for the 3D-Jury regime targets is shown, with consensus frequencies derived from a randomized ensemble. The ensemble from which models were selected was held constant, whereas the ensemble from which the consensus frequencies were derived was varied. The size of the randomized ensemble is varied (x-axis), so that the members of smaller ensembles are subsets of the larger ensembles, with the smallest ensemble comprised solely of the K*Sync default alignment to each parent. The y-axis reports the similarity to the query native structure of the selected model, as measured by MAMMOTH MaxSub. (a) Ensembles of size up to 500 members. (b) Ensembles of size up to ∼3500 members [so (a) is a ‘close-up’ of the first part of (b)]. The power of the consensus score when the frequencies are determined separately for each parent (‘random-separate’) or with respect to the reference parent (‘random-combined’) is shown. Also shown in (b) is the power of the consensus score when determined from the filtered ensemble, both with frequencies determined separately for each parent (‘ensemble-separate’) and with respect to the reference parent (‘ensemble-combined’). The ‘ensemble-combined’ is the form of the consensus score that was actually used.

Loop modeling can improve both sampling and selection. The side-chain centroid energy score with respect the similarity of each model to the query's native structure, as measured by 1.0-MAMMOTH MaxSub (for description see Supplementary Data), both before and after modeling of short loops for targets 20888 (1q4mA) and 20415 (1j0sA). Each point represents a model, with the first parent shown with red points and up to four alternate parents with the other colors. For comparison, the quality of the model that would have resulted from the detection's alignment is shown with a vertical line with a circle on the end, with a solid line for the first parent and a dashed line for the best alternate (target 20415's first detection was the best). The vertical lines with boxes at the ends indicate the quality of the 3D-Pair alignment between the query native structure and the first parent (for both target 20888 and 20415 the first parent was the best) and approximates the upper bound. The quality of the model from the default K*Sync alignment is indicated with a blue asterisk. The native structure of each query and the lowest energy model after loop modeling are shown with colored cartoons for the template regions (with blue at the N-terminus and red at the C-terminus), and gray backbone representation for the regions that were modeled with loops in the low energy model.