{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T22:49:51Z","timestamp":1773269391392,"version":"3.50.1"},"reference-count":49,"publisher":"Oxford University Press (OUP)","issue":"7","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2008,4,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>Motivation: We introduce a new method for designating the location of residues in folded protein structures based on the recursive convex hull (RCH) of a point set of atomic coordinates. The RCH can be calculated with an efficient and parameterless algorithm.<\/jats:p>\n               <jats:p>Results: We show that residue RCH class contains information complementary to widely studied measures such as solvent accessibility (SA), residue depth (RD) and to the distance of residues from the centroid of the chain, the residues\u2019 exposure (Exp). RCH is more conserved for related structures across folds and correlates better with changes in thermal stability of mutants than the other measures. Further, we assess the predictability of these measures using three types of machine-learning technique: decision trees (C4.5), Naive Bayes and Learning Classifier Systems (LCS) showing that RCH is more easily predicted than the other measures. As an exemplar application of predicted RCH class (in combination with other measures), we show that RCH is potentially helpful in improving prediction of residue contact numbers (CN).<\/jats:p>\n               <jats:p>Contact: \u00a0nxk@cs.nott.ac.uk<\/jats:p>\n               <jats:p>Supplementary Information: For Supplementary data please refer to Datasets: www.infobiotic.net\/datasets, RCH Prediction Servers: www.infobiotic.net<\/jats:p>","DOI":"10.1093\/bioinformatics\/btn050","type":"journal-article","created":{"date-parts":[[2008,2,6]],"date-time":"2008-02-06T01:25:52Z","timestamp":1202261152000},"page":"916-923","source":"Crossref","is-referenced-by-count":37,"title":["Prediction of recursive convex hull class assignments for protein residues"],"prefix":"10.1093","volume":"24","author":[{"given":"Michael","family":"Stout","sequence":"first","affiliation":[{"name":"1 Automated Scheduling, Optimization and Planning research group, School of Computer Science, 2Multi-disciplinary Centre for Integrative Biology, School of Biosciences and 3School of Chemistry, University of Nottingham, UK"}]},{"given":"Jaume","family":"Bacardit","sequence":"additional","affiliation":[{"name":"1 Automated Scheduling, Optimization and Planning research group, School of Computer Science, 2Multi-disciplinary Centre for Integrative Biology, School of Biosciences and 3School of Chemistry, University of Nottingham, UK"},{"name":"1 Automated Scheduling, Optimization and Planning research group, School of Computer Science, 2Multi-disciplinary Centre for Integrative Biology, School of Biosciences and 3School of Chemistry, University of Nottingham, UK"}]},{"given":"Jonathan D.","family":"Hirst","sequence":"additional","affiliation":[{"name":"1 Automated Scheduling, Optimization and Planning research group, School of Computer Science, 2Multi-disciplinary Centre for Integrative Biology, School of Biosciences and 3School of Chemistry, University of Nottingham, UK"}]},{"given":"Natalio","family":"Krasnogor","sequence":"additional","affiliation":[{"name":"1 Automated Scheduling, Optimization and Planning research group, School of Computer Science, 2Multi-disciplinary Centre for Integrative Biology, School of Biosciences and 3School of Chemistry, University of Nottingham, UK"}]}],"member":"286","published-online":{"date-parts":[[2008,2,5]]},"reference":[{"key":"2023020209532701300_B1","article-title":"Coordination number predication using learning classifier systems: Performance and interpretability","author":"Bacardit","year":"2004"},{"key":"2023020209532701300_B2","doi-asserted-by":"crossref","DOI":"10.1145\/1276958.1277033","article-title":"Automated alphabet reduction method with evolutionary algorithms for protein structure prediction","volume-title":"GECCO '07: Proceedings of the 9th annual conference on Genetic and evolutionary computation","author":"Bacardit","year":"2007"},{"key":"2023020209532701300_B3","article-title":"Pittsburgh Genetics-Based Machine Learning in the Data mining era: Representations, generalization, and run-time","author":"Bacardit","year":"2004"},{"key":"2023020209532701300_B4","doi-asserted-by":"crossref","first-page":"162","DOI":"10.1016\/0263-7855(94)80082-0","article-title":"\u201cIso-depth contour map\u201d of a molecular surface","volume":"12","author":"Badel-chagnon","year":"1994","journal-title":"J. Mol. Graph"},{"key":"2023020209532701300_B5","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1109\/5254.999217","article-title":"A machine-learning strategy for protein analysis","volume":"17","author":"Baldi","year":"2002","journal-title":"IEEE Intel. Sys"},{"key":"2023020209532701300_B6","doi-asserted-by":"crossref","first-page":"469","DOI":"10.1145\/235815.235821","article-title":"The quickhull algorithm for convex hulls","volume":"22","author":"Barber","year":"1996","journal-title":"ACM Trans. Math. Software"},{"issue":"Database issue","key":"2023020209532701300_B7","doi-asserted-by":"crossref","first-page":"D120","DOI":"10.1093\/nar\/gkh082","article-title":"Protherm, version 4.0: thermodynamic database for proteins and mutants","volume":"32","author":"Bava","year":"2004","journal-title":"Nucl. Acids Res"},{"key":"2023020209532701300_B8","doi-asserted-by":"crossref","first-page":"309","DOI":"10.1016\/j.jmb.2005.06.047","article-title":"Looking at enzymes from the inside out: the proximity of catalytic residues to the molecular centroid can be used for detection of active sites and enzyme-ligand interfaces","volume":"351","author":"Ben-shimon","year":"2005","journal-title":"J. Mol. Biol"},{"key":"2023020209532701300_B9","doi-asserted-by":"crossref","first-page":"724","DOI":"10.1016\/S0969-2126(99)80097-5","article-title":"Residue depth: a novel parameter for the analysis of protein structure and stability","volume":"7","author":"Chakravarty","year":"1999","journal-title":"Structure"},{"key":"2023020209532701300_B10","doi-asserted-by":"crossref","first-page":"353","DOI":"10.1142\/S021972000700276X","article-title":"Cavity scaling: automated refinement of cavity-aware motifs in protein function prediction","volume":"5","author":"Chen","year":"2007","journal-title":"J. Bioinform. Comput. Biol"},{"key":"2023020209532701300_B11","doi-asserted-by":"crossref","first-page":"441","DOI":"10.1016\/j.jmb.2006.07.022","article-title":"Travel depth, a new shape descriptor for macromolecules: application to ligand binding","volume":"362","author":"Coleman","year":"2006","journal-title":"J. Mol. Biol"},{"key":"2023020209532701300_B12","article-title":"Elements of Information Theory (Wiley Series in Telecommunications and Signal Processing)","author":"Cover","year":"2006"},{"key":"2023020209532701300_B13","doi-asserted-by":"crossref","first-page":"838","DOI":"10.1002\/prot.21298","article-title":"Achieving 80% ten-fold cross-validated accuracy for secondary structure prediction by large-scale training","volume":"66","author":"Dor","year":"2007","journal-title":"Proteins"},{"key":"2023020209532701300_B14","doi-asserted-by":"crossref","DOI":"10.1002\/9780470092620","article-title":"Protein Bioinformatics: An Algorithmic Approach to Sequence and Structure Analysis","author":"Eidhammer","year":"2003"},{"key":"2023020209532701300_B15","doi-asserted-by":"crossref","first-page":"838","DOI":"10.1002\/prot.21298","article-title":"Achieving 80% ten-fold cross-validated accuracy for secondary structure prediction by large-scale training","volume":"66","author":"Dor","year":"2007","journal-title":"Proteins"},{"key":"2023020209532701300_B16","doi-asserted-by":"crossref","DOI":"10.1002\/9780470092620","volume-title":"Protein Bioinformatics","author":"Eidhammer","year":"2003"},{"key":"2023020209532701300_B17","doi-asserted-by":"crossref","first-page":"621","DOI":"10.1002\/jcc.20370","article-title":"A consensus procedure improving solvent accessibility prediction","volume":"27","author":"Gianese","year":"2006","journal-title":"J. Comput. Chem"},{"key":"2023020209532701300_B18","doi-asserted-by":"crossref","first-page":"286","DOI":"10.1093\/nar\/27.1.286","article-title":"Protherm: thermodynamic database for proteins and mutants","volume":"27","author":"Gromiha","year":"1999","journal-title":"Nucl. Acids Res"},{"key":"2023020209532701300_B19","doi-asserted-by":"crossref","first-page":"38","DOI":"10.1002\/prot.20379","article-title":"An amino acid has two sides: a new 2d measure provides a different view of solvent exposure","volume":"59","author":"Hamelryck","year":"2005","journal-title":"Proteins"},{"key":"2023020209532701300_B20","volume-title":"Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control and Artificial Intelligence","author":"Holland","year":"1975"},{"key":"2023020209532701300_B21","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1016\/B978-0-12-737550-2.50020-8","article-title":"Cognitive systems based on adaptive algorithms","volume-title":"Pattern directed Inference Systems","author":"Holland","year":"1978"},{"key":"2023020209532701300_B22","doi-asserted-by":"crossref","first-page":"706","DOI":"10.1016\/j.jmb.2005.09.081","article-title":"Characterizing conserved structural contacts by pair-wise relative contacts and relative packing groups","volume":"354","author":"Holmes","year":"2005","journal-title":"J. Mol. Biol"},{"key":"2023020209532701300_B23","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":"2023020209532701300_B24","first-page":"338","article-title":"Estimating continuous distributions in Bayesia classifiers","volume-title":"In Proceedings of the Eleventh Conference on Uncertainty in Artificial Intelligence","author":"John","year":"1995"},{"key":"2023020209532701300_B25","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1006\/jmbi.1999.3091","article-title":"Protein secondary structure prediction based on position-specific scoring matrices","volume":"292","author":"Jones","year":"1999","journal-title":"J. Mol. Biol"},{"key":"2023020209532701300_B26","doi-asserted-by":"crossref","first-page":"516","DOI":"10.1002\/prot.21283","article-title":"Detection of pockets on protein surfaces using small and large probe spheres to find putative ligand binding sites","volume":"68","author":"Kawabata","year":"2007","journal-title":"Proteins"},{"key":"2023020209532701300_B27","doi-asserted-by":"crossref","first-page":"158","DOI":"10.1002\/prot.20300","article-title":"Predicting absolute contact numbers of native protein structure from amino acid sequence","volume":"58","author":"Kinjo","year":"2005","journal-title":"Proteins"},{"key":"2023020209532701300_B28","first-page":"1137","article-title":"A study of cross-validation and bootstrap for accuracy estimation and model selection","author":"Kohavi","year":"1995"},{"issue":"Database issue","key":"2023020209532701300_B29","doi-asserted-by":"crossref","first-page":"D204","DOI":"10.1093\/nar\/gkj103","article-title":"Protherm and pronit: thermodynamic databases for proteins and protein-nucleic acid interactions","volume":"34","author":"Kumar","year":"2006","journal-title":"Nucl. Acids Res"},{"key":"2023020209532701300_B30","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1016\/0022-2836(71)90324-X","article-title":"The interpretation of protein structures: estimation of static accessibility","volume":"55","author":"Lee","year":"1971","journal-title":"J. Mol. Biol"},{"key":"2023020209532701300_B31","doi-asserted-by":"crossref","first-page":"5082","DOI":"10.1021\/jo052659z","article-title":"Shapes of antibody binding sites: qualitative and quantitative analyses based on a geomorphic classification scheme","volume":"71","author":"Lee","year":"2006","journal-title":"J Org Chem"},{"key":"2023020209532701300_B32","doi-asserted-by":"crossref","first-page":"751","DOI":"10.1016\/S0006-3495(01)75739-6","article-title":"Are proteins well-packed?","volume":"81","author":"Liang","year":"2001","journal-title":"Biophys. J"},{"key":"2023020209532701300_B33","doi-asserted-by":"crossref","first-page":"489","DOI":"10.1016\/S0097-8485(00)00113-3","article-title":"Three-dimensional quantitative structure-activity relationship for several bioactive peptides searched by a convex hull-comparative molecular field analysis approach","volume":"25","author":"Lin","year":"2001","journal-title":"Comput. Chem"},{"key":"2023020209532701300_B34","doi-asserted-by":"crossref","first-page":"476","DOI":"10.1016\/S0167-4838(98)00261-1","article-title":"A comparative molecular field analysis study on several bioactive peptides using the alignment rules derived from identification of commonly exposed groups","volume":"1429","author":"Lin","year":"1999","journal-title":"Biochim Biophys Acta"},{"key":"2023020209532701300_B35","doi-asserted-by":"crossref","first-page":"636","DOI":"10.1002\/prot.21459","article-title":"Fold recognition by concurrent use of solvent accessibility and residue depth","volume":"68","author":"Liu","year":"2007","journal-title":"Proteins"},{"key":"2023020209532701300_B36","doi-asserted-by":"crossref","first-page":"552","DOI":"10.1109\/ICIP.1995.537694","article-title":"Segmentation of molecular surfaces based on their convex hull","volume-title":"ICIP 95: Proceedings of the 1995 International Conference on Image Processing","author":"Meier","year":"1995"},{"key":"2023020209532701300_B37","article-title":"Simultaneous Statistical Inference (Springer Series in Statistics)","author":"Miller","year":"1981"},{"key":"2023020209532701300_B38","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1093\/nar\/29.1.219","article-title":"Pdb-reprdb: a database of representative protein chains from the protein data bank (pdb)","volume":"29","author":"Noguchi","year":"2001","journal-title":"Nucl. Acids Res"},{"key":"2023020209532701300_B39","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1093\/bioinformatics\/19.2.313","article-title":"Dpx: for the analysis of the protein core","volume":"19","author":"Pintar","year":"2003","journal-title":"Bioinformatics"},{"key":"2023020209532701300_B40","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1145\/359423.359430","article-title":"Convex hulls of finite sets of points in two and three dimensions","volume":"20","author":"Preparata","year":"1977","journal-title":"Commun. ACM"},{"key":"2023020209532701300_B41","volume-title":"C4.5: Programs for Machine Learning","author":"Quinlan","year":"1992"},{"key":"2023020209532701300_B42","doi-asserted-by":"crossref","first-page":"216","DOI":"10.1002\/prot.340200303","article-title":"Conservation and prediction of solvent accessibility in protein families","volume":"20","author":"Rost","year":"1994","journal-title":"Proteins"},{"key":"2023020209532701300_B43","doi-asserted-by":"crossref","first-page":"56","DOI":"10.1002\/prot.340090107","article-title":"Database of homology-derived protein structures and the structural meaning of sequence alignment","volume":"9","author":"Sander","year":"1991","journal-title":"Proteins"},{"key":"2023020209532701300_B44","article-title":"Prediction of topological contacts in proteins using learning classifier systems","author":"Stout","year":"2008","journal-title":"Soft Computing"},{"key":"2023020209532701300_B45","doi-asserted-by":"crossref","first-page":"1267","DOI":"10.1093\/bioinformatics\/bth493","article-title":"Sabmark\u2013a benchmark for sequence alignment that covers the entire known fold space","volume":"21","author":"Van Walle","year":"2005","journal-title":"Bioinformatics"},{"issue":"Web Server issue","key":"2023020209532701300_B46","doi-asserted-by":"crossref","first-page":"W252","DOI":"10.1093\/nar\/gki362","article-title":"Cx, dpx and pride: Www servers for the analysis and comparison of protein 3d structures","volume":"33","author":"Vlahovicek","year":"2005","journal-title":"Nucl. Acids Res"},{"key":"2023020209532701300_B47","doi-asserted-by":"crossref","DOI":"10.1007\/11750321_48","article-title":"Automatic classification of protein structures based on convex hull representation by integrated neural network","author":"Wang","year":"2006"},{"key":"2023020209532701300_B48","article-title":"Data Mining: Practical Machine Learning Tools and Techniques","volume-title":"Second Edition: (The Morgan Kaufmann Series in Data Management Systems)","author":"Witten","year":"2005"},{"key":"2023020209532701300_B49","doi-asserted-by":"crossref","first-page":"476","DOI":"10.1002\/prot.20435","article-title":"Protein secondary structure prediction with dihedral angles","volume":"59","author":"Wood","year":"2005","journal-title":"Proteins"}],"container-title":["Bioinformatics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/academic.oup.com\/bioinformatics\/article-pdf\/24\/7\/916\/49047876\/bioinformatics_24_7_916.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/bioinformatics\/article-pdf\/24\/7\/916\/49047876\/bioinformatics_24_7_916.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,2,2]],"date-time":"2023-02-02T11:09:36Z","timestamp":1675336176000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/bioinformatics\/article\/24\/7\/916\/296166"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,2,5]]},"references-count":49,"journal-issue":{"issue":"7","published-print":{"date-parts":[[2008,4,1]]}},"URL":"https:\/\/doi.org\/10.1093\/bioinformatics\/btn050","relation":{},"ISSN":["1367-4811","1367-4803"],"issn-type":[{"value":"1367-4811","type":"electronic"},{"value":"1367-4803","type":"print"}],"subject":[],"published-other":{"date-parts":[[2008,4,1]]},"published":{"date-parts":[[2008,2,5]]}}}