{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,7]],"date-time":"2025-11-07T19:01:23Z","timestamp":1762542083634},"reference-count":32,"publisher":"Oxford University Press (OUP)","issue":"15","license":[{"start":{"date-parts":[[2016,10,2]],"date-time":"2016-10-02T00:00:00Z","timestamp":1475366400000},"content-version":"vor","delay-in-days":1619,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc\/3.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2012,8,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Motivation: Superpositioning is an essential technique in structural biology that facilitates the comparison and analysis of conformational differences among topologically similar structures. Performing a superposition requires a one-to-one correspondence, or alignment, of the point sets in the different structures. However, in practice, some points are usually \u2018missing\u2019 from several structures, for example, when the alignment contains gaps. Current superposition methods deal with missing data simply by superpositioning a subset of points that are shared among all the structures. This practice is inefficient, as it ignores important data, and it fails to satisfy the common least-squares criterion. In the extreme, disregarding missing positions prohibits the calculation of a superposition altogether.<\/jats:p><jats:p>Results: Here, we present a general solution for determining an optimal superposition when some of the data are missing. We use the expectation\u2013maximization algorithm, a classic statistical technique for dealing with incomplete data, to find both maximum-likelihood solutions and the optimal least-squares solution as a special case.<\/jats:p><jats:p>Availability and implementation: The methods presented here are implemented in THESEUS 2.0, a program for superpositioning macromolecular structures. ANSI C source code and selected compiled binaries for various computing platforms are freely available under the GNU open source license from http:\/\/www.theseus3d.org.<\/jats:p><jats:p>Contact: \u00a0dtheobald@brandeis.edu<\/jats:p><jats:p>Supplementary information: \u00a0Supplementary data are available at Bioinformatics online.<\/jats:p>","DOI":"10.1093\/bioinformatics\/bts243","type":"journal-article","created":{"date-parts":[[2012,4,28]],"date-time":"2012-04-28T03:49:15Z","timestamp":1335584955000},"page":"1972-1979","source":"Crossref","is-referenced-by-count":81,"title":["Optimal simultaneous superpositioning of multiple structures with missing data"],"prefix":"10.1093","volume":"28","author":[{"given":"Douglas L.","family":"Theobald","sequence":"first","affiliation":[{"name":"Department of Biochemistry, Brandeis University, MS009, 415 South Street, Waltham, MA 02454, USA"}]},{"given":"Phillip A.","family":"Steindel","sequence":"additional","affiliation":[{"name":"Department of Biochemistry, Brandeis University, MS009, 415 South Street, Waltham, MA 02454, USA"}]}],"member":"286","published-online":{"date-parts":[[2012,4,27]]},"reference":[{"key":"2023012512455464800_B1","doi-asserted-by":"crossref","first-page":"e205","DOI":"10.1093\/bioinformatics\/btl294","article-title":"Vorolign\u2014Fast structural alignment using voronoi contacts","volume":"23","author":"Birzele","year":"2007","journal-title":"Bioinformatics"},{"key":"2023012512455464800_B2","article-title":"Structural Bioinformatics","volume-title":"Methods of Biochemical Analysis.","author":"Bourne","year":"2003"},{"key":"2023012512455464800_B3","doi-asserted-by":"crossref","first-page":"282","DOI":"10.1107\/S0567739478000522","article-title":"Stable calculation of coordinates from distance information","volume":"34","author":"Crippen","year":"1978","journal-title":"Acta Crystallogr. 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