A Branch-and-Prune algorithm for the Molecular Distance Geometry Problem
The Molecular Distance Geometry Problem consists in finding the positions in of the atoms of a molecule, given some of the inter‐atomic distances. We show that under an additional requirement on the given distances this can be transformed to a combinatorial problem. We propose a Branch‐and‐Prune alg...
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| Vydané v: | International transactions in operational research Ročník 15; číslo 1; s. 1 - 17 |
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| Hlavní autori: | , , |
| Médium: | Journal Article |
| Jazyk: | English |
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Oxford, UK
Blackwell Publishing Ltd
01.01.2008
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| ISSN: | 0969-6016, 1475-3995 |
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| Abstract | The Molecular Distance Geometry Problem consists in finding the positions in of the atoms of a molecule, given some of the inter‐atomic distances. We show that under an additional requirement on the given distances this can be transformed to a combinatorial problem. We propose a Branch‐and‐Prune algorithm for the solution of this problem and report on very promising computational results. |
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| AbstractList | The Molecular Distance Geometry Problem consists in finding the positions in of the atoms of a molecule, given some of the inter‐atomic distances. We show that under an additional requirement on the given distances this can be transformed to a combinatorial problem. We propose a Branch‐and‐Prune algorithm for the solution of this problem and report on very promising computational results. The Molecular Distance Geometry Problem consists in finding the positions in of the atoms of a molecule, given some of the inter-atomic distances. We show that under an additional requirement on the given distances this can be transformed to a combinatorial problem. We propose a Branch-and-Prune algorithm for the solution of this problem and report on very promising computational results. [PUBLICATION ABSTRACT] |
| Author | Lavor, Carlile Maculan, Nelson Liberti, Leo |
| Author_xml | – sequence: 1 givenname: Leo surname: Liberti fullname: Liberti, Leo email: LIX, Ecole Polytechnique, F-91128 Palaiseau, France liberti@lix.polytechnique.fr organization: LIX, Ecole Polytechnique, F-91128 Palaiseau, FranceE-mail: liberti@lix.polytechnique.fr – sequence: 2 givenname: Carlile surname: Lavor fullname: Lavor, Carlile email: Departamento de Matemática Aplicada (IMECC-UNICAMP), Universidade Estadual de Campinas, CP 6065, 13081-970, Campinas-SP, Brazil clavor@ime.unicam.br organization: Departamento de Matemática Aplicada (IMECC-UNICAMP), Universidade Estadual de Campinas, CP 6065, 13081-970, Campinas-SP, BrazilE-mail: clavor@ime.unicam.br – sequence: 3 givenname: Nelson surname: Maculan fullname: Maculan, Nelson email: COPPE, Universidade Federal do Rio de Janeiro (UFRJ) C.P. 68511, Rio de Janerio 21945-970, Brazil maculan@cos.ufrj.br organization: COPPE, Universidade Federal do Rio de Janeiro (UFRJ) C.P. 68511, Rio de Janerio 21945-970, BrazilE-mail: maculan@cos.ufrj.br |
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| Cites_doi | 10.1090/dimacs/023/12 10.1109/INFCOM.2004.1354686 10.1137/S1052623495283024 10.1137/0805040 10.1023/A:1008380219900 10.1002/(SICI)1096-987X(199910)20:13<1354::AID-JCC3>3.0.CO;2-N 10.1007/978-0-387-22464-0 10.1007/0-387-30528-9_14 10.1023/A:1013857218127 |
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| References | Dong, Q., Wu, Z., 2002. A linear-time algorithm for solving the molecular distance geometry problem with exact inter-atomic distances. Journal of Global Optimization 22, 365-375. Crippen, G.M., Havel, T.F., 1988. Distance Geometry and Molecular Conformation. John Wiley & Sons, New York. Moré, J.J., Wu, Z., 1997. Global continuation for distance geometry problems. SIAM Journal on Optimization 7, 814-836. Pogorelov, A., 1987. Geometry. Mir Publishers, Moscow. Klepeis, J.L., Floudas, C.A., Morikis, D., Lambris, J.D., 1999. Predicting peptide structures using NMR data and deterministic global optimization. Journal of Computational Chemistry 20, 13, 1354-1370. Moré, J.J., Wu, Z., 1999. Distance geometry optimization for protein structures. Journal of Global Optimization 15, 219-234. Hendrickson, B.A., 1995. The molecule problem: Exploiting structure in global optimization. SIAM Journal on Optimization 5, 835-857. Creighton, T.E., 1993. Proteins: Structures and Molecular Properties. W.H. Freeman and Company, New York. Wu, D., Wu, Z., Yuan, Y., to appear. Rigid versus unique determination of protein structures with geometric buildup. Optimization Letters. Phillips, A.T., Rosen, J.B., Walke, V.H., 1996. Molecular structure determination by convex underestimation of local energy minima. DIMACS Series in Discrete Mathematics and Theoretical Computer Science 23, 181-198, American Mathematical Society, Providence. Schlick, T., 2002. Molecular modelling and simulation: an interdisciplinary guide. Springer, New York. 1996; 1027 1999; 15 2002; 22 1987 2006 1999; 20 1993 2004 2002 1995; 5 1979 1997; 7 1996; 23 1988 e_1_2_7_6_1 e_1_2_7_5_1 e_1_2_7_9_1 e_1_2_7_8_1 Creighton T.E. (e_1_2_7_2_1) 1993 e_1_2_7_7_1 e_1_2_7_16_1 e_1_2_7_15_1 Crippen G.M. (e_1_2_7_3_1) 1988 e_1_2_7_12_1 e_1_2_7_11_1 Cruz I.F. (e_1_2_7_4_1) 1996 e_1_2_7_10_1 Wu D. (e_1_2_7_17_1) Phillips A.T. (e_1_2_7_13_1) 1996; 23 Pogorelov A. (e_1_2_7_14_1) 1987 |
| References_xml | – reference: Dong, Q., Wu, Z., 2002. A linear-time algorithm for solving the molecular distance geometry problem with exact inter-atomic distances. Journal of Global Optimization 22, 365-375. – reference: Pogorelov, A., 1987. Geometry. Mir Publishers, Moscow. – reference: Wu, D., Wu, Z., Yuan, Y., to appear. Rigid versus unique determination of protein structures with geometric buildup. Optimization Letters. – reference: Hendrickson, B.A., 1995. The molecule problem: Exploiting structure in global optimization. SIAM Journal on Optimization 5, 835-857. – reference: Moré, J.J., Wu, Z., 1997. Global continuation for distance geometry problems. SIAM Journal on Optimization 7, 814-836. – reference: Moré, J.J., Wu, Z., 1999. Distance geometry optimization for protein structures. Journal of Global Optimization 15, 219-234. – reference: Schlick, T., 2002. Molecular modelling and simulation: an interdisciplinary guide. Springer, New York. – reference: Crippen, G.M., Havel, T.F., 1988. Distance Geometry and Molecular Conformation. John Wiley & Sons, New York. – reference: Klepeis, J.L., Floudas, C.A., Morikis, D., Lambris, J.D., 1999. Predicting peptide structures using NMR data and deterministic global optimization. Journal of Computational Chemistry 20, 13, 1354-1370. – reference: Phillips, A.T., Rosen, J.B., Walke, V.H., 1996. Molecular structure determination by convex underestimation of local energy minima. DIMACS Series in Discrete Mathematics and Theoretical Computer Science 23, 181-198, American Mathematical Society, Providence. – reference: Creighton, T.E., 1993. Proteins: Structures and Molecular Properties. W.H. Freeman and Company, New York. – volume: 7 start-page: 814 year: 1997 end-page: 836 article-title: Global continuation for distance geometry problems publication-title: SIAM Journal on Optimization – volume: 22 start-page: 365 year: 2002 end-page: 375 article-title: A linear‐time algorithm for solving the molecular distance geometry problem with exact inter‐atomic distances publication-title: Journal of Global Optimization – volume: 5 start-page: 835 year: 1995 end-page: 857 article-title: The molecule problem publication-title: SIAM Journal on Optimization – year: 2002 – year: 1988 – year: 1987 – year: 2006 – volume: 1027 start-page: 162 year: 1996 end-page: 165 – year: 2004 – volume: 20 start-page: 1354 issue: 13 year: 1999 end-page: 1370 article-title: Predicting peptide structures using NMR data and deterministic global optimization publication-title: Journal of Computational Chemistry – volume: 15 start-page: 219 year: 1999 end-page: 234 article-title: Distance geometry optimization for protein structures publication-title: Journal of Global Optimization – article-title: Rigid versus unique determination of protein structures with geometric buildup publication-title: Optimization Letters – start-page: 405 year: 2006 end-page: 414 – volume: 23 start-page: 181 year: 1996 end-page: 198 article-title: Molecular structure determination by convex underestimation of local energy minima publication-title: DIMACS Series in Discrete Mathematics and Theoretical Computer Science – year: 1979 – year: 1993 – ident: e_1_2_7_10_1 – volume: 23 start-page: 181 year: 1996 ident: e_1_2_7_13_1 article-title: Molecular structure determination by convex underestimation of local energy minima publication-title: DIMACS Series in Discrete Mathematics and Theoretical Computer Science doi: 10.1090/dimacs/023/12 – volume-title: Geometry year: 1987 ident: e_1_2_7_14_1 – ident: e_1_2_7_6_1 doi: 10.1109/INFCOM.2004.1354686 – ident: e_1_2_7_11_1 doi: 10.1137/S1052623495283024 – ident: e_1_2_7_7_1 doi: 10.1137/0805040 – volume-title: Distance Geometry and Molecular Conformation year: 1988 ident: e_1_2_7_3_1 – ident: e_1_2_7_12_1 doi: 10.1023/A:1008380219900 – ident: e_1_2_7_8_1 doi: 10.1002/(SICI)1096-987X(199910)20:13<1354::AID-JCC3>3.0.CO;2-N – ident: e_1_2_7_17_1 article-title: Rigid versus unique determination of protein structures with geometric buildup publication-title: Optimization Letters – start-page: 162 volume-title: Graph Drawing, Symposium on Graph Drawing, GD ’95, Passau, Germany LNCS year: 1996 ident: e_1_2_7_4_1 – ident: e_1_2_7_16_1 doi: 10.1007/978-0-387-22464-0 – ident: e_1_2_7_9_1 doi: 10.1007/0-387-30528-9_14 – volume-title: Proteins: Structures and Molecular Properties year: 1993 ident: e_1_2_7_2_1 – ident: e_1_2_7_5_1 doi: 10.1023/A:1013857218127 – ident: e_1_2_7_15_1 |
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| Title | A Branch-and-Prune algorithm for the Molecular Distance Geometry Problem |
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