[{"date_published":"1998-10-01T00:00:00Z","article_type":"original","month":"10","language":[{"iso":"eng"}],"scopus_import":"1","publisher":"Wiley-Blackwell","date_created":"2018-12-11T12:06:25Z","type":"journal_article","day":"01","status":"public","intvolume":" 33","page":"1 - 17","publication":"Proteins: Structure, Function and Bioinformatics","issue":"1","doi":"10.1002/(SICI)1097-0134(19981001)33:1<1::AID-PROT1>3.0.CO;2-O","year":"1998","title":"Analytical shape computation of macromolecules: I. molecular area and volume through alpha shape","citation":{"ieee":"J. Liang, H. Edelsbrunner, P. Fu, P. Sudhakar, and S. Subramaniam, “Analytical shape computation of macromolecules: I. molecular area and volume through alpha shape,” Proteins: Structure, Function and Bioinformatics, vol. 33, no. 1. Wiley-Blackwell, pp. 1–17, 1998.","apa":"Liang, J., Edelsbrunner, H., Fu, P., Sudhakar, P., & Subramaniam, S. (1998). Analytical shape computation of macromolecules: I. molecular area and volume through alpha shape. Proteins: Structure, Function and Bioinformatics. Wiley-Blackwell. https://doi.org/10.1002/(SICI)1097-0134(19981001)33:1<1::AID-PROT1>3.0.CO;2-O","chicago":"Liang, Jie, Herbert Edelsbrunner, Ping Fu, Pamidighantam Sudhakar, and Shankar Subramaniam. “Analytical Shape Computation of Macromolecules: I. Molecular Area and Volume through Alpha Shape.” Proteins: Structure, Function and Bioinformatics. Wiley-Blackwell, 1998. https://doi.org/10.1002/(SICI)1097-0134(19981001)33:1<1::AID-PROT1>3.0.CO;2-O.","mla":"Liang, Jie, et al. “Analytical Shape Computation of Macromolecules: I. Molecular Area and Volume through Alpha Shape.” Proteins: Structure, Function and Bioinformatics, vol. 33, no. 1, Wiley-Blackwell, 1998, pp. 1–17, doi:10.1002/(SICI)1097-0134(19981001)33:1<1::AID-PROT1>3.0.CO;2-O.","ama":"Liang J, Edelsbrunner H, Fu P, Sudhakar P, Subramaniam S. Analytical shape computation of macromolecules: I. molecular area and volume through alpha shape. Proteins: Structure, Function and Bioinformatics. 1998;33(1):1-17. doi:10.1002/(SICI)1097-0134(19981001)33:1<1::AID-PROT1>3.0.CO;2-O","ista":"Liang J, Edelsbrunner H, Fu P, Sudhakar P, Subramaniam S. 1998. Analytical shape computation of macromolecules: I. molecular area and volume through alpha shape. Proteins: Structure, Function and Bioinformatics. 33(1), 1–17.","short":"J. Liang, H. Edelsbrunner, P. Fu, P. Sudhakar, S. Subramaniam, Proteins: Structure, Function and Bioinformatics 33 (1998) 1–17."},"publication_status":"published","author":[{"first_name":"Jie","last_name":"Liang","full_name":"Liang, Jie"},{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert"},{"full_name":"Fu, Ping","last_name":"Fu","first_name":"Ping"},{"first_name":"Pamidighantam","full_name":"Sudhakar, Pamidighantam","last_name":"Sudhakar"},{"last_name":"Subramaniam","full_name":"Subramaniam, Shankar","first_name":"Shankar"}],"abstract":[{"lang":"eng","text":"The size and shape of macromolecules such as proteins and nucleic acids play an important role in their functions. Prior efforts to quantify these properties have been based on various discretization or tessellation procedures involving analytical or numerical computations. In this article, we present an analytically exact method for computing the metric properties of macromolecules based on the alpha shape theory. This method uses the duality between alpha complex and the weighted Voronoi decomposition of a molecule. We describe the intuitive ideas and concepts behind the alpha shape theory and the algorithm for computing areas and volumes of macromolecules. We apply our method to compute areas and volumes of a number of protein systems. We also discuss several difficulties commonly encountered in molecular shape computations and outline methods to overcome these problems. (C) 1998 Wiley-Liss, Inc."}],"article_processing_charge":"No","date_updated":"2022-08-25T13:32:59Z","volume":33,"publist_id":"2112","oa_version":"None","quality_controlled":"1","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","acknowledgement":"We thank Michael Facello for the torus area formula and suggestion regarding computation of MS model from SA model. We thank Nataraj Akkiraju, Patrick Moran, and Marcus Wagner for interesting discussionson the topic of this article and for help in the generationof two- and three-dimensional illustrations. We thank NSF Meta Center Allocation for providing computational resources. The software VOLBL is available at:http://alpha.ncsa.uiuc.edu/alpha.","extern":"1","publication_identifier":{"issn":["0887-3585"]},"_id":"4011"},{"year":"1998","doi":"10.1002/(SICI)1097-0134(19981001)33:1<18::AID-PROT2>3.0.CO;2-H","title":"Analytical shape computation of macromolecules: II. Inaccessible cavities in proteins","article_processing_charge":"No","publist_id":"2113","date_updated":"2022-08-25T13:35:41Z","volume":33,"publication_identifier":{"issn":["0887-3585"]},"extern":"1","_id":"4012","quality_controlled":"1","oa_version":"None","acknowledgement":"The software for constructing weighted Delaunay complexes and the alpha shape filters was written by Ernst Mücke and Michael Facello. We thank them forcreating reliable and robust software so that wecan build on their results. The authors thank NSF Meta Center Allocation for providing computational resources. The software VOLBL is part of the standard distribution of the alpha shapes software, andis available at http://alpha.ncsa.uiuc.edu/alpha.","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","citation":{"ista":"Liang J, Edelsbrunner H, Fu P, Sudhakar P, Subramaniam S. 1998. Analytical shape computation of macromolecules: II. Inaccessible cavities in proteins. Proteins: Structure, Function and Bioinformatics. 33(1), 18–29.","short":"J. Liang, H. Edelsbrunner, P. Fu, P. Sudhakar, S. Subramaniam, Proteins: Structure, Function and Bioinformatics 33 (1998) 18–29.","ama":"Liang J, Edelsbrunner H, Fu P, Sudhakar P, Subramaniam S. Analytical shape computation of macromolecules: II. Inaccessible cavities in proteins. Proteins: Structure, Function and Bioinformatics. 1998;33(1):18-29. doi:10.1002/(SICI)1097-0134(19981001)33:1<18::AID-PROT2>3.0.CO;2-H","mla":"Liang, Jie, et al. “Analytical Shape Computation of Macromolecules: II. Inaccessible Cavities in Proteins.” Proteins: Structure, Function and Bioinformatics, vol. 33, no. 1, Wiley-Blackwell, 1998, pp. 18–29, doi:10.1002/(SICI)1097-0134(19981001)33:1<18::AID-PROT2>3.0.CO;2-H.","chicago":"Liang, Jie, Herbert Edelsbrunner, Ping Fu, Pamidighantam Sudhakar, and Shankar Subramaniam. “Analytical Shape Computation of Macromolecules: II. Inaccessible Cavities in Proteins.” Proteins: Structure, Function and Bioinformatics. Wiley-Blackwell, 1998. https://doi.org/10.1002/(SICI)1097-0134(19981001)33:1<18::AID-PROT2>3.0.CO;2-H.","ieee":"J. Liang, H. Edelsbrunner, P. Fu, P. Sudhakar, and S. Subramaniam, “Analytical shape computation of macromolecules: II. Inaccessible cavities in proteins,” Proteins: Structure, Function and Bioinformatics, vol. 33, no. 1. Wiley-Blackwell, pp. 18–29, 1998.","apa":"Liang, J., Edelsbrunner, H., Fu, P., Sudhakar, P., & Subramaniam, S. (1998). Analytical shape computation of macromolecules: II. Inaccessible cavities in proteins. Proteins: Structure, Function and Bioinformatics. Wiley-Blackwell. https://doi.org/10.1002/(SICI)1097-0134(19981001)33:1<18::AID-PROT2>3.0.CO;2-H"},"publication_status":"published","abstract":[{"text":"The structures of proteins are well-packed, yet they contain numerous cavities which play key roles in accommodating small molecules, or enabling conformational changes. From high-resolution structures it is possible to identify these cavities. We have developed a precise algorithm based on alpha shapes for measuring space-filling-based molecular models (such as van der Waals, solvent accessible, and molecular surface descriptions). We applied this method for accurate computation of the surface area and volume of cavities in several proteins. In addition, all of the atoms/residues Lining the cavities are identified, We use this method to study the structure and the stability of proteins, as well as to locate cavities that could contain structural water molecules in the proton transport pathway in the membrane protein bacteriorhodopsin.","lang":"eng"}],"author":[{"last_name":"Liang","full_name":"Liang, Jie","first_name":"Jie"},{"first_name":"Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Fu, Ping","last_name":"Fu","first_name":"Ping"},{"first_name":"Pamidighantam","full_name":"Sudhakar, Pamidighantam","last_name":"Sudhakar"},{"full_name":"Subramaniam, Shankar","last_name":"Subramaniam","first_name":"Shankar"}],"date_created":"2018-12-11T12:06:26Z","month":"10","article_type":"original","date_published":"1998-10-01T00:00:00Z","scopus_import":"1","publisher":"Wiley-Blackwell","language":[{"iso":"eng"}],"publication":"Proteins: Structure, Function and Bioinformatics","issue":"1","page":"18 - 29","day":"01","type":"journal_article","intvolume":" 33","status":"public"}]