In the absence of experimentally determined protein structure many biological questions can be addressed using computational structural models. However, the utility of protein structural models depends on their quality. Therefore, the estimation of the quality of predicted structures is an important problem. One of the approaches to this problem is the use of knowledge-based statistical potentials. Such methods typically rely on the statistics of distances and angles of residue-residue or atom-atom interactions collected from experimentally determined structures. Here, we present VoroMQA (Voronoi tessellation-based Model Quality Assessment), a new method for the estimation of protein structure quality. Our method combines the idea of statistical potentials with the use of interatomic contact areas instead of distances. Contact areas, derived using Voronoi tessellation of protein structure, are used to describe and seamlessly integrate both explicit interactions between protein atoms and implicit interactions of protein atoms with solvent. VoroMQA produces scores at atomic, residue, and global levels, all in the fixed range from 0 to 1. The method was tested on the CASP data and compared to several other single-model quality assessment methods. VoroMQA showed strong performance in the recognition of the native structure and in the structural model selection tests, thus demonstrating the efficacy of interatomic contact areas in estimating protein structure quality. The software implementation of VoroMQA is freely available as a standalone application and as a web server at http://bioinformatics.lt/software/voromqa. Proteins 2017; 85:1131-1145. © 2017 Wiley Periodicals, Inc.

Evaluation of protein models against the native structure is essential for the development and benchmarking of protein structure prediction methods. Although a number of evaluation scores have been proposed to date, many aspects of model assessment still lack desired robustness. In this study we present CAD-score, a new evaluation function quantifying differences between physical contacts in a model and the reference structure. The new score uses the concept of residue-residue contact area difference (CAD) introduced by Abagyan and Totrov (J Mol Biol 1997; 268:678-685). Contact areas, the underlying basis of the score, are derived using the Voronoi tessellation of protein structure. The newly introduced CAD-score is a continuous function, confined within fixed limits, free of any arbitrary thresholds or parameters. The built-in logic for treatment of missing residues allows consistent ranking of models of any degree of completeness. We tested CAD-score on a large set of diverse models and compared it to GDT-TS, a widely accepted measure of model accuracy. Similarly to GDT-TS, CAD-score showed a robust performance on single-domain proteins, but displayed a stronger preference for physically more realistic models. Unlike GDT-TS, the new score revealed a balanced assessment of domain rearrangement, removing the necessity for different treatment of single-domain, multi-domain, and multi-subunit structures. Moreover, CAD-score makes it possible to assess the accuracy of inter-domain or inter-subunit interfaces directly. In addition, the approach offers an alternative to the superposition-based model clustering. The CAD-score implementation is available both as a web server and a standalone software package at http://www.ibt.lt/bioinformatics/cad-score/.

We present the results for CAPRI Round 46, the third joint CASP‐CAPRI protein assembly prediction challenge. The Round comprised a total of 20 targets including 14 homo‐oligomers and 6 heterocomplexes. Eight of the homo‐oligomer targets and one heterodimer comprised proteins that could be readily modeled using templates from the Protein Data Bank, often available for the full assembly. The remaining 11 targets comprised 5 homodimers, 3 heterodimers, and two higher‐order assemblies. These were more difficult to model, as their prediction mainly involved “ab‐initio” docking of subunit models derived from distantly related templates. A total of ~30 CAPRI groups, including 9 automatic servers, submitted on average ~2000 models per target. About 17 groups participated in the CAPRI scoring rounds, offered for most targets, submitting ~170 models per target. The prediction performance, measured by the fraction of models of acceptable quality or higher submitted across all predictors groups, was very good to excellent for the nine easy targets. Poorer performance was achieved by predictors for the 11 difficult targets, with medium and high quality models submitted for only 3 of these targets. A similar performance “gap” was displayed by scorer groups, highlighting yet again the unmet challenge of modeling the conformational changes of the protein components that occur upon binding or that must be accounted for in template‐based modeling. Our analysis also indicates that residues in binding interfaces were less well predicted in this set of targets than in previous Rounds, providing useful insights for directions of future improvements.

Methods to reliably estimate the accuracy of 3D models of proteins are both a fundamental part of most protein folding pipelines and important for reliable identification of the best models when multiple pipelines are used. Here, we describe the progress made from CASP12 to CASP13 in the field of estimation of model accuracy (EMA) as seen from the progress of the most successful methods in CASP13. We show small but clear progress, that is, several methods perform better than the best methods from CASP12 when tested on CASP13 EMA targets. Some progress is driven by applying deep learning and residue‐residue contacts to model accuracy prediction. We show that the best EMA methods select better models than the best servers in CASP13, but that there exists a great potential to improve this further. Also, according to the evaluation criteria based on local similarities, such as lDDT and CAD, it is now clear that single model accuracy methods perform relatively better than consensus‐based methods.

The Voronoi diagram of balls, corresponding to atoms of van der Waals radii, is particularly well-suited for the analysis of three-dimensional structures of biological macromolecules. However, due to the shortage of practical algorithms and the corresponding software, simpler approaches are often used instead. Here, we present a simple and robust algorithm for computing the vertices of the Voronoi diagram of balls. The vertices of Voronoi cells correspond to the centers of the empty tangent spheres defined by quadruples of balls. The algorithm is implemented as an open-source software tool, Voronota. Large-scale tests show that Voronota is a fast and reliable tool for processing both experimentally determined and computationally modeled macromolecular structures. Voronota can be easily deployed and may be used for the development of various other structure analysis tools that utilize the Voronoi diagram of balls. Voronota is available at: http://www.ibt.lt/bioinformatics/voronota.