NMR Protein Structure Calculation and Sphere Intersections
Nuclear Magnetic Resonance (NMR) experiments can be used to calculate 3D protein structures and geometric properties of protein molecules allow us to solve the problem iteratively using a combinatorial method, called Branch-and-Prune (BP). The main step of BP algorithm is to intersect three spheres...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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De Gruyter
2020-09-01
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| Series: | Computational and Mathematical Biophysics |
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| Online Access: | https://doi.org/10.1515/cmb-2020-0103 |
| _version_ | 1830191246566490112 |
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| author | Lavor Carlile Alves Rafael Souza Michael José Luis Aragón |
| author_facet | Lavor Carlile Alves Rafael Souza Michael José Luis Aragón |
| author_sort | Lavor Carlile |
| collection | DOAJ |
| description | Nuclear Magnetic Resonance (NMR) experiments can be used to calculate 3D protein structures and geometric properties of protein molecules allow us to solve the problem iteratively using a combinatorial method, called Branch-and-Prune (BP). The main step of BP algorithm is to intersect three spheres centered at the positions for atoms i − 3, i − 2, i − 1, with radii given by the atomic distances di−3,i, di−2,i, di−1,i, respectively, to obtain the position for atom i. Because of uncertainty in NMR data, some of the distances di−3,i should be represented as interval distances [d_i-3,i,d¯i-3,i{\underline{d}_{i - 3,i}},{\bar d_{i - 3,i}}], where d_i-3,i≤di-3,i≤d¯i-3,i{\underline{d}_{i - 3,i}} \le {d_{i - 3,i}} \le {\bar d_{i - 3,i}}. In the literature, an extension of the BP algorithm was proposed to deal with interval distances, where the idea is to sample values from [d_i-3,i,d¯i-3,i{\underline{d}_{i - 3,i}},{\bar d_{i - 3,i}}]. We present a new method, based on conformal geometric algebra, to reduce the size of [d_i-3,i,d¯i-3,i{\underline{d}_{i - 3,i}},{\bar d_{i - 3,i}}], before the sampling process. We also compare it with another approach proposed in the literature. |
| first_indexed | 2024-12-17T23:35:08Z |
| format | Article |
| id | doaj.art-b233b28479404729b4d95b1cdb06cf1a |
| institution | Directory Open Access Journal |
| issn | 2544-7297 |
| language | English |
| last_indexed | 2024-12-17T23:35:08Z |
| publishDate | 2020-09-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Computational and Mathematical Biophysics |
| spelling | doaj.art-b233b28479404729b4d95b1cdb06cf1a2022-12-21T21:28:34ZengDe GruyterComputational and Mathematical Biophysics2544-72972020-09-01818910110.1515/cmb-2020-0103cmb-2020-0103NMR Protein Structure Calculation and Sphere IntersectionsLavor Carlile0Alves Rafael1Souza Michael2José Luis Aragón3University of Campinas (IMECC-UNICAMP), 13081-970, Campinas - SP, BrazilFederal University of ABC (CMCC-UFABC), 09606-070, Sao Bernardo - SP, BrazilFederal University of Ceará (UFC), 60440-900, Fortaleza - CE, BrazilCentro de Física Aplicada y Tecnología Avanzada, Universidad Nacional Autónoma de México (UNAM), 76230, Quéretaro, MexicoNuclear Magnetic Resonance (NMR) experiments can be used to calculate 3D protein structures and geometric properties of protein molecules allow us to solve the problem iteratively using a combinatorial method, called Branch-and-Prune (BP). The main step of BP algorithm is to intersect three spheres centered at the positions for atoms i − 3, i − 2, i − 1, with radii given by the atomic distances di−3,i, di−2,i, di−1,i, respectively, to obtain the position for atom i. Because of uncertainty in NMR data, some of the distances di−3,i should be represented as interval distances [d_i-3,i,d¯i-3,i{\underline{d}_{i - 3,i}},{\bar d_{i - 3,i}}], where d_i-3,i≤di-3,i≤d¯i-3,i{\underline{d}_{i - 3,i}} \le {d_{i - 3,i}} \le {\bar d_{i - 3,i}}. In the literature, an extension of the BP algorithm was proposed to deal with interval distances, where the idea is to sample values from [d_i-3,i,d¯i-3,i{\underline{d}_{i - 3,i}},{\bar d_{i - 3,i}}]. We present a new method, based on conformal geometric algebra, to reduce the size of [d_i-3,i,d¯i-3,i{\underline{d}_{i - 3,i}},{\bar d_{i - 3,i}}], before the sampling process. We also compare it with another approach proposed in the literature.https://doi.org/10.1515/cmb-2020-0103molecular distance geometry problembranch-and-pruneconformal geometric algebranmr data51k0515a6692e10 |
| spellingShingle | Lavor Carlile Alves Rafael Souza Michael José Luis Aragón NMR Protein Structure Calculation and Sphere Intersections Computational and Mathematical Biophysics molecular distance geometry problem branch-and-prune conformal geometric algebra nmr data 51k05 15a66 92e10 |
| title | NMR Protein Structure Calculation and Sphere Intersections |
| title_full | NMR Protein Structure Calculation and Sphere Intersections |
| title_fullStr | NMR Protein Structure Calculation and Sphere Intersections |
| title_full_unstemmed | NMR Protein Structure Calculation and Sphere Intersections |
| title_short | NMR Protein Structure Calculation and Sphere Intersections |
| title_sort | nmr protein structure calculation and sphere intersections |
| topic | molecular distance geometry problem branch-and-prune conformal geometric algebra nmr data 51k05 15a66 92e10 |
| url | https://doi.org/10.1515/cmb-2020-0103 |
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