{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T23:28:54Z","timestamp":1773271734638,"version":"3.50.1"},"reference-count":36,"publisher":"Springer Science and Business Media LLC","issue":"1","content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Algorithms Mol Biol"],"published-print":{"date-parts":[[2011,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:sec><jats:title>Background<\/jats:title><jats:p>Proteins are dynamic molecules that exhibit a wide range of motions; often these conformational changes are important for protein function. Determining biologically relevant conformational changes, or true variability, efficiently is challenging due to the noise present in structure data.<\/jats:p><\/jats:sec><jats:sec><jats:title>Results<\/jats:title><jats:p>In this paper we present a novel approach to elucidate conformational variability in structures solved using X-ray crystallography. We first infer an ensemble to represent the experimental data and then formulate the identification of truly variable members of the ensemble (as opposed to those that vary only due to noise) as a sparse estimation problem. Our results indicate that the algorithm is able to accurately distinguish genuine conformational changes from variability due to noise. We validate our predictions for structures in the Protein Data Bank by comparing with NMR experiments, as well as on synthetic data. In addition to improved performance over existing methods, the algorithm is robust to the levels of noise present in real data. In the case of Human Ubiquitin-conjugating enzyme Ubc9, variability identified by the algorithm corresponds to functionally important residues implicated by mutagenesis experiments. Our algorithm is also general enough to be integrated into state-of-the-art software tools for structure-inference.<\/jats:p><\/jats:sec>","DOI":"10.1186\/1748-7188-6-12","type":"journal-article","created":{"date-parts":[[2011,4,23]],"date-time":"2011-04-23T06:22:51Z","timestamp":1303539771000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Sparse estimation for structural variability"],"prefix":"10.1186","volume":"6","author":[{"given":"Raghavendra","family":"Hosur","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rohit","family":"Singh","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bonnie","family":"Berger","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2011,4,19]]},"reference":[{"key":"121_CR1","doi-asserted-by":"publisher","DOI":"10.1002\/0471721204","volume-title":"Structural Bioinformatics","author":"P Bourne","year":"2003","unstructured":"Bourne P, Weissig H: Structural Bioinformatics. Wiley-Liss, Inc., NJ,2003."},{"key":"121_CR2","doi-asserted-by":"publisher","first-page":"353","DOI":"10.1016\/S0076-6879(97)77020-4","volume":"277","author":"L Jensen","year":"1997","unstructured":"Jensen L: Refinement and reliability of macromolecular models based on X-ray diffraction data. Methods in Enzymology. 1997, 277: 353-366.","journal-title":"Methods in Enzymology"},{"key":"121_CR3","doi-asserted-by":"publisher","first-page":"389","DOI":"10.1016\/0076-6879(86)31050-4","volume":"131","author":"G Ringe","year":"1986","unstructured":"Ringe G, Petsko G: Study of protein dynamics by X-ray diffraction. Methods in Enzymology. 1986, 131: 389-433.","journal-title":"Methods in Enzymology"},{"key":"121_CR4","doi-asserted-by":"publisher","first-page":"2429","DOI":"10.1126\/science.291.5512.2429","volume":"291","author":"B Volkman","year":"2001","unstructured":"Volkman B, Lipson D, Wemmer D, Kern D: Two state allosteric behaviour in a single domain signalling protein. Science. 2001, 291: 2429-2433. 10.1126\/science.291.5512.2429","journal-title":"Science"},{"key":"121_CR5","doi-asserted-by":"publisher","first-page":"117","DOI":"10.1038\/nature04105","volume":"438","author":"E Eissenmesser","year":"2005","unstructured":"Eissenmesser E, Millet O, Labeikovsky W, Korzhnev D, Wolf-Watz M, Bosco D, Skalicky J, Kay L, Kern D: Intrinsic dynamics of an enzyme underlies catalysis. Nature. 2005, 438: 117-121. 10.1038\/nature04105","journal-title":"Nature"},{"key":"121_CR6","doi-asserted-by":"publisher","first-page":"1112","DOI":"10.1038\/2605","volume":"4","author":"D Koshland","year":"1998","unstructured":"Koshland D: Conformational changes: How small is big enough?. Nature Medicine. 1998, 4: 1112-1114. 10.1038\/2605","journal-title":"Nature Medicine"},{"key":"121_CR7","doi-asserted-by":"publisher","first-page":"831","DOI":"10.1016\/j.str.2004.02.031","volume":"12","author":"M DePristo","year":"2004","unstructured":"DePristo M, de Bakker P, Blundell T: Heterogeneity and Inaccuracy in Protein Structures Solved by X-ray Crystallography. Structure. 2004, 12: 831-838. 10.1016\/j.str.2004.02.031","journal-title":"Structure"},{"issue":"3","key":"121_CR8","doi-asserted-by":"publisher","first-page":"184","DOI":"10.1038\/nsmb0306-184","volume":"13","author":"N Furnham","year":"2006","unstructured":"Furnham N, Blundell T, DePristo M, Terwilliger T: Is one solution good enough. Nature Struct and Mol Biol. 2006, 13 (3): 184-185. 10.1038\/nsmb0306-184","journal-title":"Nature Struct and Mol Biol"},{"key":"121_CR9","doi-asserted-by":"publisher","first-page":"597","DOI":"10.1107\/S0907444907009791","volume":"63","author":"T Terwilliger","year":"2007","unstructured":"Terwilliger T, Grosse-Kunstleve R, Afonine P, Adams P, Moriarty N, Zwart P, Read R, Turk D, Hung LW: Interpretation of ensembles created by multiple iterative rebuilding of macromolecular models. Acta Crystallographica (D). 2007, 63: 597-610. 10.1107\/S1600536807000116","journal-title":"Acta Crystallographica (D)"},{"key":"121_CR10","doi-asserted-by":"publisher","first-page":"383","DOI":"10.1107\/S090744490800070X","volume":"64","author":"J Knight","year":"2008","unstructured":"Knight J, Zhou Z, Gallichio E, Himmel D, Friesner R, Arnold E, Levy R: Exploring Structural variability in X-ray crystallographic models using protein local optimization by torsion angle sampling. Acta Crystallographica (D). 2008, 64: 383-396. 10.1107\/S1600536807068821","journal-title":"Acta Crystallographica (D)"},{"key":"121_CR11","doi-asserted-by":"publisher","first-page":"813","DOI":"10.1089\/cmb.2007.0138","volume":"15","author":"A Nigham","year":"2008","unstructured":"Nigham A, Hsu D: Protein conformational flexibility analysis with noisy data. Journal of Computational Biology. 2008, 15: 813-828. 10.1089\/cmb.2007.0138","journal-title":"Journal of Computational Biology"},{"key":"121_CR12","first-page":"1107","volume":"D65","author":"H Bedem van den","year":"2009","unstructured":"Bedem van den H, Dhanik A, Latombe J, Deacon A: Modeling discrete heterogeneity in X-ray diffraction data by fitting multi-conformers. Acta Cryst (D). 2009, D65: 1107-1117.","journal-title":"Acta Cryst (D)"},{"key":"121_CR13","doi-asserted-by":"publisher","first-page":"337","DOI":"10.1038\/nbt.1619","volume":"28","author":"H Ji","year":"2010","unstructured":"Ji H, Liu S: Analyzing 'omics data using hierarchical models. Nature Biotechnology. 2010, 28: 337-340. 10.1038\/nbt.1619","journal-title":"Nature Biotechnology"},{"key":"121_CR14","doi-asserted-by":"publisher","first-page":"1503","DOI":"10.1529\/biophysj.106.094409","volume":"92","author":"A Shehu","year":"2007","unstructured":"Shehu A, Kavraki L, Clementi C: On the characterization of Protein Native state ensembles. Biophysical Journal. 2007, 92: 1503-1511. 10.1529\/biophysj.106.094409","journal-title":"Biophysical Journal"},{"key":"121_CR15","doi-asserted-by":"publisher","first-page":"319","DOI":"10.1107\/S0021889808001672","volume":"41","author":"S Gore","year":"2008","unstructured":"Gore S, Blundell T: Optimal side-chain packing in proteins and crystallographic refinement. J Appl Cryst. 2008, 41: 319-328. 10.1107\/S0021889808001672","journal-title":"J Appl Cryst"},{"key":"121_CR16","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1111\/j.2517-6161.1996.tb02080.x","volume":"58","author":"R Tibshirani","year":"1996","unstructured":"Tibshirani R: Regression shrinkage and selection via the Lasso. Journal of the Royal Stat Soc Series B. 1996, 58: 267-288.","journal-title":"Journal of the Royal Stat Soc Series B"},{"key":"121_CR17","doi-asserted-by":"publisher","first-page":"249","DOI":"10.1107\/S0907444999016364","volume":"56","author":"G Kleywegt","year":"2000","unstructured":"Kleywegt G: Validation of protein crystal structures. Acta Crystallographica (D). 2000, 56: 249-265.","journal-title":"Acta Crystallographica (D)"},{"key":"121_CR18","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-84858-7","volume-title":"The Elements of Statistical Learning: Data Mining, Inference and Prediction","author":"T Hastie","year":"2009","unstructured":"Hastie T, Tibshirani R, Friedman J: The Elements of Statistical Learning: Data Mining, Inference and Prediction. New York: Springer Science+Business Media, LLC,2009."},{"key":"121_CR19","doi-asserted-by":"publisher","first-page":"133","DOI":"10.1016\/0022-2836(91)90387-L","volume":"220","author":"M Gerstein","year":"1991","unstructured":"Gerstein M, Chothia C: Analysis of protein loop closure: two types of hinges produce one motion in lactate dehydrogenase. Journal of Molecular Biology. 1991, 220: 133-149. 10.1016\/0022-2836(91)90387-L","journal-title":"Journal of Molecular Biology"},{"key":"121_CR20","doi-asserted-by":"publisher","first-page":"345","DOI":"10.1002\/prot.10035","volume":"46","author":"D Vitkup","year":"2002","unstructured":"Vitkup D, Ringe D, Karplus M, Petsko G: Why Proteins R-factors are so large: a self consistent analysis. Proteins. 2002, 46: 345-354. 10.1002\/prot.10035","journal-title":"Proteins"},{"key":"121_CR21","first-page":"52","volume-title":"Pacific Symposium on Biocomputing","author":"R Singh","year":"2005","unstructured":"Singh R, Berger B: ChainTweak: Sampling from the Neighbourhood of a Protein Conformation. Pacific Symposium on Biocomputing. 2005, 52-63."},{"key":"121_CR22","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-3092-0","volume-title":"Principles of Protein X-ray Crystallography","author":"J Drenth","year":"1999","unstructured":"Drenth J: Principles of Protein X-ray Crystallography. New York: Springer-Verlag,1999."},{"key":"121_CR23","first-page":"2541","volume":"7","author":"P Zhao","year":"2006","unstructured":"Zhao P, Yu B: On Model Selection Consistency of Lasso. Journal of Machine Learning Research. 2006, 7: 2541-2563.","journal-title":"Journal of Machine Learning Research"},{"key":"121_CR24","doi-asserted-by":"publisher","first-page":"2373","DOI":"10.1214\/009053607000000460","volume":"35","author":"N Meinshausen","year":"2007","unstructured":"Meinshausen N, Rocha B, Yu B: Discussion: A tale of three cousins: Lasso, L2Boosting and Dantzig. Annals of Statistics. 2007, 35: 2373-2384. 10.1214\/009053607000000460","journal-title":"Annals of Statistics"},{"key":"121_CR25","doi-asserted-by":"publisher","first-page":"1948","DOI":"10.1107\/S0907444902016657","volume":"58","author":"P Adams","year":"2002","unstructured":"Adams P, Grosse-Kunstleve R, Hung L, Loerger T, McCoy A, Moriarty N, Read R, Sacchettini J, Sauter N, Terwilliger T: PHENIX:building new software for automated crystallographic structure determination. Acta Crystallographica (D). 2002, 58: 1948-1954.","journal-title":"Acta Crystallographica (D)"},{"key":"121_CR26","first-page":"891","volume":"54","author":"F Giraud","year":"1998","unstructured":"Giraud F, Desterro J, Naismith J: Structure of Ubiquitin-conjugating enzyme 9 displays significant differences with other ubiquitin-conjugating enzymes which may reflect its specificity for sumo rather than ubiquitin. Acta Cryst (D). 1998, 54: 891-898.","journal-title":"Acta Cryst (D)"},{"key":"121_CR27","doi-asserted-by":"publisher","first-page":"1415","DOI":"10.1021\/bi981840h","volume":"38","author":"Q Liu","year":"1999","unstructured":"Liu Q, Yuan Y, Shen B, Chen D, Chen Y: Conformational Flexibility of a Ubiquitin Conjugation Enzyme (E2). Biochemistry. 1999, 38: 1415-1425. 10.1021\/bi981840h","journal-title":"Biochemistry"},{"key":"121_CR28","doi-asserted-by":"publisher","first-page":"16979","DOI":"10.1074\/jbc.274.24.16979","volume":"274","author":"Q Liu","year":"1999","unstructured":"Liu Q, Jin C, Liao X, Shen Z, Chen D, Chen Y: The Binding Interface between an E2 (UBC9) and a Ubiquitin Homologue (UBL1). J Biol Chem. 1999, 274: 16979-16987. 10.1074\/jbc.274.24.16979","journal-title":"J Biol Chem"},{"key":"121_CR29","doi-asserted-by":"publisher","first-page":"9959","DOI":"10.1021\/bi0345283","volume":"42","author":"M Tatham","year":"2003","unstructured":"Tatham M, Kim S, Yu B, Jaffray E, Song J, Zheng J, Rodriguez M, Hay R, Chen Y: Role of N-Terminal Site of Ubc9 in SUMO-1, -2, and -3 Binding and conjugation. Biochemistry. 2003, 42: 9959-9969. 10.1021\/bi0345283","journal-title":"Biochemistry"},{"key":"121_CR30","doi-asserted-by":"publisher","first-page":"2797","DOI":"10.1038\/sj.emboj.7601711","volume":"26","author":"P Knipscheer","year":"2007","unstructured":"Knipscheer P, Dijk van W, Olsen J, Mann M, T S: Noncovalent interaction between Ubc9 and SUMO promoted SUMO chain formation. The EMBO Journal. 2007, 26: 2797-2807. 10.1038\/sj.emboj.7601711","journal-title":"The EMBO Journal"},{"key":"121_CR31","doi-asserted-by":"publisher","first-page":"21740","DOI":"10.1074\/jbc.M108418200","volume":"277","author":"D Lin","year":"2002","unstructured":"Lin D, Tatham M, Yu B, Kim S, Hay R, Chen Y: Identification of a substrate recognition site on Ubc9. Journal of Biological Chemistry. 2002, 277: 21740-21748. 10.1074\/jbc.M108418200","journal-title":"Journal of Biological Chemistry"},{"key":"121_CR32","first-page":"779","volume":"18","author":"F Li","year":"2005","unstructured":"Li F, Yang Y, Xing E: From Lasso regression to Feature vector machine. Neural Information Processing Systems (NIPS). 2005, 18: 779-786.","journal-title":"Neural Information Processing Systems (NIPS)"},{"key":"121_CR33","volume-title":"Neural Information Processing Systems (NIPS)","author":"H Xu","year":"2008","unstructured":"Xu H, Caramanis C, Mannor S: Robust Regression and Lasso. Neural Information Processing Systems (NIPS). 2008."},{"key":"121_CR34","volume-title":"Joint CCP4 and ESF-EACBM Newsletter on Protein Crystallography","author":"K Cowtan","year":"2002","unstructured":"Cowtan K: The Clipper project. Joint CCP4 and ESF-EACBM Newsletter on Protein Crystallography. 2002, 40:http:\/\/www.ccp4.ac.uk\/newsletters\/newsletter40.pdf"},{"key":"121_CR35","doi-asserted-by":"publisher","first-page":"25","DOI":"10.1007\/s10107-004-0559-y","volume":"106","author":"A Wachter","year":"2006","unstructured":"Wachter A, Biegler T: On the implementation of a primal-dual interior point filter line search algorithm for large-scale nonlinear programming. Mathematical Programming. 2006, 106: 25-57. 10.1007\/s10107-004-0559-y","journal-title":"Mathematical Programming"},{"key":"121_CR36","volume-title":"The PyMOL Molecular Graphics System","author":"W Delano","year":"2002","unstructured":"Delano W: The PyMOL Molecular Graphics System. 2002,http:\/\/www.pymol.org"}],"container-title":["Algorithms for Molecular Biology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1186\/1748-7188-6-12.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,3,5]],"date-time":"2025-03-05T06:32:25Z","timestamp":1741156345000},"score":1,"resource":{"primary":{"URL":"https:\/\/almob.biomedcentral.com\/articles\/10.1186\/1748-7188-6-12"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,4,19]]},"references-count":36,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2011,12]]}},"alternative-id":["121"],"URL":"https:\/\/doi.org\/10.1186\/1748-7188-6-12","relation":{},"ISSN":["1748-7188"],"issn-type":[{"value":"1748-7188","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,4,19]]},"assertion":[{"value":"14 October 2010","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"19 April 2011","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"19 April 2011","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"12"}}