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Within the framework of the protein model quality assessment problem, we demonstrate that the proposed spherical convolution method significantly improves the quality of model assessment compared to the standard message-passing approach. It is also comparable to state-of-the-art methods, as we demonstrate on critical assessment of structure prediction benchmarks. The proposed technique operates only on geometric features of protein 3D models. This makes it universal and applicable to any other geometric-learning task where the graph structure allows constructing local coordinate systems. The method is available at <jats:ext-link xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" ext-link-type=\"uri\" xlink:href=\"https:\/\/team.inria.fr\/nano-d\/software\/s-gcn\/\" xlink:type=\"simple\">https:\/\/team.inria.fr\/nano-d\/software\/s-gcn\/<\/jats:ext-link>.<\/jats:p>","DOI":"10.1088\/2632-2153\/abf856","type":"journal-article","created":{"date-parts":[[2021,4,16]],"date-time":"2021-04-16T02:06:44Z","timestamp":1618538804000},"page":"045005","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":16,"title":["Spherical convolutions on molecular graphs for protein model quality assessment"],"prefix":"10.1088","volume":"2","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6214-2827","authenticated-orcid":false,"given":"Ilia","family":"Igashov","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7330-393X","authenticated-orcid":false,"given":"Nikita","family":"Pavlichenko","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1903-7220","authenticated-orcid":false,"given":"Sergei","family":"Grudinin","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"266","published-online":{"date-parts":[[2021,7,15]]},"reference":[{"key":"mlstabf856bib1","doi-asserted-by":"publisher","first-page":"1100","DOI":"10.1002\/prot.25787","article-title":"A further leap of improvement in tertiary structure prediction in CASP13 prompts new routes for future assessments","volume":"87","author":"Abriata","year":"2019","journal-title":"Proteins: Struct. 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