{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:32:14Z","timestamp":1760243534114,"version":"build-2065373602"},"reference-count":40,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2012,2,10]],"date-time":"2012-02-10T00:00:00Z","timestamp":1328832000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>A number of measures have been used in the structural biology literature to compare the shapes or conformations of biological macromolecules. However, the issue of how to compare two ensembles of conformations has received far less attention. Herein, the problem of how to quantitatively compare two such ensembles is addressed in several different ways using concepts from probability and information theory. Ultimately, such metrics could be used in the evaluation of structure-prediction algorithms and the analysis of how conformational mobility is inhibited by bound ligands.<\/jats:p>","DOI":"10.3390\/e14020213","type":"journal-article","created":{"date-parts":[[2012,2,10]],"date-time":"2012-02-10T11:23:18Z","timestamp":1328872998000},"page":"213-232","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Quantitative Comparison of Conformational Ensembles"],"prefix":"10.3390","volume":"14","author":[{"given":"Kevin C.","family":"Wolfe","sequence":"first","affiliation":[{"name":"Department of Mechanical Engineering, Johns Hopkins University, 3400 N. Charles Street, Baltimore, MD 21218, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gregory S.","family":"Chirikjian","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, Johns Hopkins University, 3400 N. Charles Street, Baltimore, MD 21218, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2012,2,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1006\/jmbi.1993.1489","article-title":"Protein structure comparison by alignment of distance matrices","volume":"233","author":"Holm","year":"1993","journal-title":"J. Mol. Biol."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1016\/0022-2836(90)90312-A","article-title":"Use of techniques derived from graph theory to compare secondary structure motifs in proteins","volume":"212","author":"Mitchell","year":"1989","journal-title":"J. Mol. Biol."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"22","DOI":"10.1002\/(SICI)1097-0134(1999)37:3+<22::AID-PROT5>3.0.CO;2-W","article-title":"Processing and analysis of CASP3 protein structure predictions","volume":"37","author":"Zemla","year":"1999","journal-title":"Protein. Struct. Funct. Bioinform."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"338","DOI":"10.1002\/prot.20622","article-title":"Does secondary structure determine tertiary structure in proteins?","volume":"61","author":"Gong","year":"2005","journal-title":"Protein. Struct. Funct. Bioinform."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"378","DOI":"10.1002\/1097-0134(20010215)42:3<378::AID-PROT70>3.0.CO;2-3","article-title":"Protein structural alignments and functional genomics","volume":"42","author":"Irving","year":"2001","journal-title":"Proteins"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"625","DOI":"10.1093\/bioinformatics\/btg035","article-title":"MINRMS: An efficient algorithm for determining protein structure similarity using root-mean-squared-distance","volume":"19","author":"Jewett","year":"2003","journal-title":"Bioinformatics"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1545","DOI":"10.1021\/cr040423+","article-title":"G; Kapp, G.; Whitten, S.T. A statistical thermodynamic model of the protein ensemble","volume":"106","author":"Hilser","year":"2006","journal-title":"Chem. Rev."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"9903","DOI":"10.1073\/pnas.95.17.9903","article-title":"The structural distribution of cooperative interactions in proteins: Analysis of the native state ensemble","volume":"95","author":"Hilser","year":"1998","journal-title":"Proc. Nat. Acad. Sci. U. S. A."},{"key":"ref_9","first-page":"607","article-title":"Alternate states of proteins revealed by detailed energy landscape mapping","volume":"405","author":"Tyka","year":"2011","journal-title":"J. Struct. Biol."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"10505","DOI":"10.1073\/pnas.0812152106","article-title":"Global distribution of conformational states derived from redundant models in the PDB points to non-uniqueness of the protein structure","volume":"106","author":"Burra","year":"2009","journal-title":"Proc. Nat. Acad. Sci. U. S. A."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1016\/B978-0-12-381270-4.00004-4","article-title":"Modeling loop entropy","volume":"487","author":"Chirikjian","year":"2011","journal-title":"Methods Enzymol."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"6763","DOI":"10.1021\/jp011355n","article-title":"Loops in proteins can be modeled as worm-like chains","volume":"105","author":"Zhou","year":"2001","journal-title":"J. Phys. Chem. B"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Zhang, J., Lin, M., Chen, R., Wang, W., and Liang, J. (2008). Discrete state model and accurate estimation of loop entropy of RNA secondary structures. J. Chem. Phys., 128.","DOI":"10.1063\/1.2895050"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"164","DOI":"10.1002\/prot.21060","article-title":"Modeling protein conformational ensembles: From missing loops to equilibrium fluctuations","volume":"65","author":"Shehu","year":"2006","journal-title":"Protein. Struct. Funct. Bioinform."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1503","DOI":"10.1529\/biophysj.106.094409","article-title":"On the characterization of protein native state ensembles","volume":"92","author":"Shehu","year":"2007","journal-title":"Biophys. J."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"134108:1","DOI":"10.1063\/1.3574397","article-title":"Toward canonical ensemble distribution from self-guided Langevin dynamics simulation","volume":"134","author":"Wu","year":"2011","journal-title":"J. Chem. Phys."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Grosberg, A.Y., and Khokhlov, A.R. (1994). Statistical Physics of Macromolecules, American Institute of Physics.","DOI":"10.1063\/1.4823390"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"150","DOI":"10.1002\/prot.1081","article-title":"Protein flexibility predictions using graph theory","volume":"44","author":"Jacobs","year":"2001","journal-title":"Protein. Struct. Funct. Bioinform."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"4558","DOI":"10.1529\/biophysj.105.066654","article-title":"Gaussian-weighted RMSD superposition of proteins: A structural comparison for flexible proteins and predicted protein structures","volume":"90","author":"Damm","year":"2006","journal-title":"Biophys. J."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"ii","DOI":"10.1002\/prot.340230303","article-title":"A large-scale experiment to assess protein structure prediction methods","volume":"23","author":"Moult","year":"1995","journal-title":"Protein. Struct. Funct. Genet."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1002\/prot.23200","article-title":"Critical assessment of methods of protein structure prediction (CASP)\u2014Round IX","volume":"79","author":"Moult","year":"2011","journal-title":"Protein. Struct. Funct. Bioinform."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"697","DOI":"10.1002\/prot.21805","article-title":"From the Mediterranean coast to the shores of Lake Ontario: CAPRI\u2019s premiere on the American continent","volume":"69","author":"Wodak","year":"2007","journal-title":"Protein. Struct. Funct. Bioinform."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Janin, J. (2002). Welcome to CAPRI: A critical assessment of predicted interactions. Protein. Struct. Funct. Bioinform., 47.","DOI":"10.1002\/prot.10111"},{"key":"ref_24","unstructured":"Here the word \u201csimilarity\u201d is not used in the sense of basic geometry which involves rigid-body and scale transformations, but rather describes small differences in shape."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1023\/A:1026552720914","article-title":"Similarity metrics with applications in modular robot motion planning","volume":"10","author":"Chiang","year":"2001","journal-title":"Auton. Robot."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"531","DOI":"10.1109\/70.611311","article-title":"Useful metrics for modular robot motion planning","volume":"13","author":"Pamecha","year":"1997","journal-title":"IEEE Trans. Robot. Autom."},{"key":"ref_27","unstructured":"The interpretation of the \u201caction\u201d \u00b7 depends on the context. We can talk about the action on a function, g\u00b7\u03c1\u2032, or on a vector, g\u00b7x, or other objects."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1088\/1478-3975\/2\/4\/S12","article-title":"Elastic network models for understanding biomolecular machinery: From enzymes to supramolecular assemblies","volume":"2","author":"Chennubhotla","year":"2005","journal-title":"Phys. Biol."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1016\/S1093-3263(02)00143-2","article-title":"Elastic models of conformational transitions in macromolecules","volume":"21","author":"Kim","year":"2002","journal-title":"J. Mol. Graph. Model."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1002\/prot.21465","article-title":"Protein conformational transitions explored by mixed elastic network models","volume":"69","author":"Zheng","year":"2007","journal-title":"Protein. Struct. Funct. Bioinform."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"807","DOI":"10.1016\/j.jmb.2005.07.031","article-title":"Large amplitude conformational change in proteins explored with a plastic network model: Adenylate kinase","volume":"352","author":"Maragakis","year":"2005","journal-title":"J. Mol. Biol."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"505","DOI":"10.1016\/S0006-3495(01)76033-X","article-title":"Anisotropy of fluctuation dynamics of proteins with an elastic network model","volume":"80","author":"Atilgan","year":"2001","journal-title":"Biophys. J."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1016\/S1359-0278(97)00024-2","article-title":"Direct evaluation of thermal fluctuations in proteins using a single-parameter harmonic potential","volume":"2","author":"Bahar","year":"1997","journal-title":"Fold. Design"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1002\/jcc.1160","article-title":"Dynamics of large proteins through hierarchical levels of coarse-grained structures","volume":"23","author":"Doruker","year":"2002","journal-title":"J. Comput. Chem."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"302","DOI":"10.1016\/j.jsb.2004.01.005","article-title":"Global ribosome motions revealed with elastic network model","volume":"147","author":"Wang","year":"2004","journal-title":"J. Struct. Biol."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1093\/nar\/28.1.235","article-title":"The protein data bank","volume":"28","author":"Berman","year":"2000","journal-title":"Nucleic Acids Res."},{"key":"ref_37","unstructured":"CASP9 Protein Structure Prediction Center, University of California, Davis. Available online: http:\/\/predictioncenter.org\/casp9\/."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"4420","DOI":"10.1021\/bi00288a012","article-title":"Structure of the complex of Streptomyces griseus protease B and the third domain of the turkey ovomucoid inhibitor at 1.8-A resolution","volume":"22","author":"Read","year":"1983","journal-title":"Biochemistry"},{"key":"ref_39","unstructured":"RCSB Protein Data Bank. Available online: http:\/\/www.pdb.org."},{"key":"ref_40","unstructured":"Joint Center for Structural Genomics Crystal structure of a TetR family transcriptional regulator (Caur_2714) from Chloroflexus aurantiacus J-10-FL at 2.56 A resolution, PDB ID: 3NRG."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/14\/2\/213\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T21:48:50Z","timestamp":1760219330000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/14\/2\/213"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,2,10]]},"references-count":40,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2012,2]]}},"alternative-id":["e14020213"],"URL":"https:\/\/doi.org\/10.3390\/e14020213","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2012,2,10]]}}}