Mathematical analysis and calculation of molecular surfaces
In this article we derive a complete characterization of the Solvent Excluded Surface (SES) for molecular systems including a complete characterization of singularities of the surface. The theory is based on an implicit representation of the SES, which, in turn, is based on the signed distance funct...
Uloženo v:
| Vydáno v: | Journal of computational physics Ročník 322; s. 760 - 782 |
|---|---|
| Hlavní autoři: | , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Elsevier Inc
01.10.2016
Elsevier |
| Témata: | |
| ISSN: | 0021-9991, 1090-2716 |
| On-line přístup: | Získat plný text |
| Tagy: |
Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
|
| Abstract | In this article we derive a complete characterization of the Solvent Excluded Surface (SES) for molecular systems including a complete characterization of singularities of the surface. The theory is based on an implicit representation of the SES, which, in turn, is based on the signed distance function to the Solvent Accessible Surface (SAS). All proofs are constructive so that the theory allows for efficient algorithms in order to compute the area of the SES and the volume of the SES-cavity, or to visualize the surface. Further, we propose to refine the notion of SAS and SES in order to take inner holes in a solute molecule into account or not. |
|---|---|
| AbstractList | In this article we derive a complete characterization of the Solvent Excluded Surface (SES) for molecular systems including a complete characterization of singularities of the surface. The theory is based on an implicit representation of the SES, which, in turn, is based on the signed distance function to the Solvent Accessible Surface (SAS). All proofs are constructive so that the theory allows for efficient algorithms in order to compute the area of the SES and the volume of the SES-cavity, or to visualize the surface. Further, we propose to refine the notion of SAS and SES in order to take inner holes in a solute molecule into account or not. In this article we derive a complete characterization of the Solvent Excluded Surface (SES) for molecular systems including a complete characterization of singularities of the surface. The proofs are constructive so that the theory allows for efficient algorithms in order to compute the area of the SES and the volume of the SES-cavity, or to visualize the surface. Further, we propose to refine the notion of SAS and SES in order to take inner holes in a solute molecule into account or not. |
| Author | Stamm, Benjamin Quan, Chaoyu |
| Author_xml | – sequence: 1 givenname: Chaoyu surname: Quan fullname: Quan, Chaoyu organization: Sorbonne Universités, UPMC Univ. Paris 06, UMR 7598, Laboratoire Jacques-Louis Lions, F-75005, Paris, France – sequence: 2 givenname: Benjamin surname: Stamm fullname: Stamm, Benjamin email: best@mathcces.rwth-aachen.de organization: Center for Computational Engineering Science, RWTH Aachen University, Aachen, Germany |
| BackLink | https://hal.sorbonne-universite.fr/hal-01205580$$DView record in HAL |
| BookMark | eNp9kDtPwzAQxy1UJNrCB2DLypBw5zycqFNVAUUqYoHZcpyz6ihNKjut1G-PS2FhYLrn7x7_GZv0Q0-M3SMkCFg8tkmr9wkPbgIiARBXbIpQQcwFFhM2BeAYV1WFN2zmfQsAZZ6VU7Z4U-OWdmq0WnWR6lV38tYHp4lCQh-6UBn6aDDRbujoHLvIH5xRmvwtuzaq83T3Y-fs8_npY7WON-8vr6vlJtZZBmNcZViLrCiMojwNF3DRGEo1pUVeCl5nGjGlEkrK6iZHVZWmMoZDowqlsQZM5-zhMnerOrl3dqfcSQ7KyvVyI885QA55XsKRh15x6dVu8N6RkdqO3z-MTtlOIsizXrKVQS951kuCkEGvQOIf8nfVf8ziwlB4_2jJSa8t9Zoa60iPshnsP_QX89qEjQ |
| CitedBy_id | crossref_primary_10_1002_open_202400172 crossref_primary_10_1002_qua_25669 crossref_primary_10_1002_qua_25695 crossref_primary_10_1016_j_jmgm_2016_11_008 crossref_primary_10_1002_qua_25685 crossref_primary_10_1137_24M1717087 crossref_primary_10_1002_jcc_26191 crossref_primary_10_1016_j_memsci_2025_124622 crossref_primary_10_1109_TVCG_2024_3380100 crossref_primary_10_1002_jcc_26139 crossref_primary_10_1137_18M119553X crossref_primary_10_1007_s00371_020_01967_6 crossref_primary_10_1007_s10092_024_00587_z crossref_primary_10_1137_20M1342872 crossref_primary_10_1007_s10444_020_09765_3 |
| Cites_doi | 10.1021/ja00051a040 10.1107/S0021889883010985 10.1016/0022-2836(71)90324-X 10.1137/0216006 10.1021/ct400280b 10.1186/s12859-015-0531-2 10.1007/BF01901190 10.1016/j.cpc.2004.08.002 10.1021/cr9904009 10.1063/1.4816767 10.1002/(SICI)1096-987X(19981130)19:15<1758::AID-JCC8>3.0.CO;2-M 10.1145/2049662.2049665 10.1002/nme.1620372103 10.1146/annurev.bb.06.060177.001055 10.1016/0022-2836(84)90231-6 10.1090/S0002-9947-1945-0013786-6 10.1002/(SICI)1097-0282(199603)38:3<305::AID-BIP4>3.0.CO;2-Y |
| ContentType | Journal Article |
| Copyright | 2016 Elsevier Inc. Distributed under a Creative Commons Attribution 4.0 International License |
| Copyright_xml | – notice: 2016 Elsevier Inc. – notice: Distributed under a Creative Commons Attribution 4.0 International License |
| DBID | AAYXX CITATION 1XC VOOES |
| DOI | 10.1016/j.jcp.2016.07.007 |
| DatabaseName | CrossRef Hyper Article en Ligne (HAL) Hyper Article en Ligne (HAL) (Open Access) |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Applied Sciences Mathematics |
| EISSN | 1090-2716 |
| EndPage | 782 |
| ExternalDocumentID | oai:HAL:hal-01205580v2 10_1016_j_jcp_2016_07_007 S0021999116302868 |
| GroupedDBID | --K --M -~X .~1 0R~ 1B1 1RT 1~. 1~5 4.4 457 4G. 5GY 5VS 6OB 7-5 71M 8P~ 9JN AABNK AACTN AAEDT AAEDW AAIAV AAIKJ AAKOC AALRI AAOAW AAQFI AAXUO AAYFN ABBOA ABFRF ABJNI ABMAC ABNEU ABYKQ ACBEA ACDAQ ACFVG ACGFO ACGFS ACNCT ACRLP ACZNC ADBBV ADEZE AEBSH AEFWE AEKER AENEX AFKWA AFTJW AGHFR AGUBO AGYEJ AHHHB AHZHX AIALX AIEXJ AIKHN AITUG AIVDX AJBFU AJOXV ALMA_UNASSIGNED_HOLDINGS AMFUW AMRAJ AOUOD AXJTR BKOJK BLXMC CS3 DM4 DU5 EBS EFBJH EFLBG EJD EO8 EO9 EP2 EP3 F5P FDB FEDTE FIRID FNPLU FYGXN G-Q GBLVA GBOLZ HLZ HVGLF IHE J1W K-O KOM LG5 LX9 LZ4 M37 M41 MO0 N9A O-L O9- OAUVE OGIMB OZT P-8 P-9 P2P PC. Q38 RIG RNS ROL RPZ SDF SDG SDP SES SPC SPCBC SPD SSQ SSV SSZ T5K TN5 UPT YQT ZMT ZU3 ~02 ~G- 29K 6TJ 8WZ 9DU A6W AAQXK AATTM AAXKI AAYWO AAYXX ABFNM ABWVN ABXDB ACLOT ACNNM ACRPL ACVFH ADCNI ADFGL ADIYS ADJOM ADMUD ADNMO AEIPS AEUPX AFFNX AFJKZ AFPUW AGQPQ AIGII AIIUN AKBMS AKRWK AKYEP ANKPU APXCP ASPBG AVWKF AZFZN BBWZM CAG CITATION COF D-I EFKBS FGOYB G-2 HME HMV HZ~ NDZJH R2- SBC SEW SHN SPG T9H UQL WUQ ZY4 ~HD 1XC VOOES |
| ID | FETCH-LOGICAL-c440t-941b7466fae5399127dfe3ce365872b4c113e808e4bd51a98f9ff20da6ac1b013 |
| ISICitedReferencesCount | 27 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000381585100038&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 0021-9991 |
| IngestDate | Sat Nov 29 15:00:13 EST 2025 Tue Nov 18 22:38:24 EST 2025 Sat Nov 29 03:10:14 EST 2025 Fri Feb 23 02:17:17 EST 2024 |
| IsDoiOpenAccess | true |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Keywords | Mathematical description Molecular surface Constructive algorithm Solvent excluded surface Solvation models solvent excluded surface mathematical description constructive algorithm solvation models |
| Language | English |
| License | Distributed under a Creative Commons Attribution 4.0 International License: http://creativecommons.org/licenses/by/4.0 |
| LinkModel | OpenURL |
| MergedId | FETCHMERGED-LOGICAL-c440t-941b7466fae5399127dfe3ce365872b4c113e808e4bd51a98f9ff20da6ac1b013 |
| ORCID | 0000-0003-3246-8989 0000-0003-3375-483X |
| OpenAccessLink | https://hal.sorbonne-universite.fr/hal-01205580 |
| PageCount | 23 |
| ParticipantIDs | hal_primary_oai_HAL_hal_01205580v2 crossref_citationtrail_10_1016_j_jcp_2016_07_007 crossref_primary_10_1016_j_jcp_2016_07_007 elsevier_sciencedirect_doi_10_1016_j_jcp_2016_07_007 |
| PublicationCentury | 2000 |
| PublicationDate | 2016-10-01 2016-10-00 |
| PublicationDateYYYYMMDD | 2016-10-01 |
| PublicationDate_xml | – month: 10 year: 2016 text: 2016-10-01 day: 01 |
| PublicationDecade | 2010 |
| PublicationTitle | Journal of computational physics |
| PublicationYear | 2016 |
| Publisher | Elsevier Inc Elsevier |
| Publisher_xml | – name: Elsevier Inc – name: Elsevier |
| References | Richmond (br0190) 1984; 178 Cancès, Maday, Stamm (br0040) 2013; 139 Avis, Bhattacharya, Imai (br0020) 1988; 3 Kauker, Krone, Panagiotidis, Reina, Ertl (br0120) 2013 Wikipedia, Spherical cap, Wikipedia, the free encyclopedia, 2016. Online; accessed 25-February-2016. Drysdale (br0090) 1979 Lee, Richards (br0130) 1971; 55 Tomasi, Mennucci, Cammi (br0210) 2005; 105 Aurenhammer (br0010) 1987; 16 Do Carmo, Do Carmo (br0080) 1976 Sanner, Olson, Spehner (br0200) 1996; 38 Cazals, Kanhere, Loriot (br0050) 2011; 38 Richards (br0180) 1977; 6 Rappé, Casewit, Colwell, Goddard, Skiff (br0170) 1992; 114 Velho, Gomes, de Figueiredo (br0220) 2002 Chen, Makhatadze (br0060) 2015; 16 Connolly (br0070) Oct. 1983; 16 Federer (br0100) 1945 Buša, Džurina, Hayryan, Hayryan, Hu, Plavka, Pokornỳ, Skřivánek, Wu (br0030) 2005; 165 George, Seveno (br0110) 1994; 37 Parulek, Viola (br0150) 2012 Pomelli, Tomasi. Defpol (br0160) 1998; 19 Lipparini, Stamm, Cancès, Maday, Mennucci (br0140) 2013; 9 George (10.1016/j.jcp.2016.07.007_br0110) 1994; 37 Buša (10.1016/j.jcp.2016.07.007_br0030) 2005; 165 Sanner (10.1016/j.jcp.2016.07.007_br0200) 1996; 38 Cazals (10.1016/j.jcp.2016.07.007_br0050) 2011; 38 Federer (10.1016/j.jcp.2016.07.007_br0100) 1945 Tomasi (10.1016/j.jcp.2016.07.007_br0210) 2005; 105 10.1016/j.jcp.2016.07.007_br0230 Drysdale (10.1016/j.jcp.2016.07.007_br0090) 1979 Connolly (10.1016/j.jcp.2016.07.007_br0070) 1983; 16 Pomelli (10.1016/j.jcp.2016.07.007_br0160) 1998; 19 Kauker (10.1016/j.jcp.2016.07.007_br0120) 2013 Rappé (10.1016/j.jcp.2016.07.007_br0170) 1992; 114 Do Carmo (10.1016/j.jcp.2016.07.007_br0080) 1976 Lee (10.1016/j.jcp.2016.07.007_br0130) 1971; 55 Parulek (10.1016/j.jcp.2016.07.007_br0150) 2012 Richards (10.1016/j.jcp.2016.07.007_br0180) 1977; 6 Velho (10.1016/j.jcp.2016.07.007_br0220) 2002 Aurenhammer (10.1016/j.jcp.2016.07.007_br0010) 1987; 16 Cancès (10.1016/j.jcp.2016.07.007_br0040) 2013; 139 Chen (10.1016/j.jcp.2016.07.007_br0060) 2015; 16 Richmond (10.1016/j.jcp.2016.07.007_br0190) 1984; 178 Avis (10.1016/j.jcp.2016.07.007_br0020) 1988; 3 Lipparini (10.1016/j.jcp.2016.07.007_br0140) 2013; 9 |
| References_xml | – start-page: 33 year: 2013 end-page: 40 ident: br0120 article-title: Rendering molecular surfaces using order-independent transparency publication-title: Proceedings of the 13th Eurographics Symposium on Parallel Graphics and Visualization – volume: 37 start-page: 3605 year: 1994 end-page: 3619 ident: br0110 article-title: The advancing-front mesh generation method revisited publication-title: Int. J. Numer. Methods Eng. – volume: 38 start-page: 3 year: 2011 ident: br0050 article-title: Computing the volume of a union of balls: a certified algorithm publication-title: ACM Trans. Math. Softw. – volume: 114 start-page: 10024 year: 1992 end-page: 10035 ident: br0170 article-title: Uff, a full periodic table force field for molecular mechanics and molecular dynamics simulations publication-title: J. Am. Chem. Soc. – volume: 6 start-page: 151 year: 1977 end-page: 176 ident: br0180 article-title: Areas, volumes, packing and protein structure publication-title: Annu. Rev. Biophys. Bioeng. – volume: 3 start-page: 323 year: 1988 end-page: 328 ident: br0020 article-title: Computing the volume of the union of spheres publication-title: Vis. Comput. – volume: 9 start-page: 3637 year: 2013 end-page: 3648 ident: br0140 article-title: Fast domain decomposition algorithm for continuum solvation models: energy and first derivatives publication-title: J. Chem. Theory Comput. – volume: 16 start-page: 548 year: Oct. 1983 end-page: 558 ident: br0070 article-title: Analytical molecular surface calculation publication-title: J. Appl. Crystallogr. – year: 1976 ident: br0080 article-title: Differential Geometry of Curves and Surfaces, vol. 2 – year: 1979 ident: br0090 article-title: Generalized Voronoi diagrams and geometric searching – volume: 16 start-page: 101 year: 2015 ident: br0060 article-title: ProteinVolume: calculating molecular van der Waals and void volumes in proteins publication-title: BMC Bioinform. – volume: 139 year: 2013 ident: br0040 article-title: Domain decomposition for implicit solvation models publication-title: J. Chem. Phys. – start-page: 217 year: 2012 end-page: 224 ident: br0150 article-title: Implicit representation of molecular surfaces publication-title: Pacific Visualization Symposium – volume: 16 start-page: 78 year: 1987 end-page: 96 ident: br0010 article-title: Power diagrams: properties, algorithms and applications publication-title: SIAM J. Comput. – volume: 55 year: 1971 ident: br0130 article-title: The interpretation of protein structures: estimation of static accessibility publication-title: J. Mol. Biol. – volume: 38 start-page: 305 year: 1996 end-page: 320 ident: br0200 article-title: Reduced surface: an efficient way to compute molecular surfaces publication-title: Biopolymers – start-page: 44 year: 1945 end-page: 76 ident: br0100 article-title: The Gauss–Green theorem publication-title: Trans. Am. Math. Soc. – reference: Wikipedia, Spherical cap, Wikipedia, the free encyclopedia, 2016. Online; accessed 25-February-2016. – volume: 105 start-page: 2999 year: 2005 end-page: 3094 ident: br0210 article-title: Quantum mechanical continuum solvation models publication-title: Chem. Rev. – volume: 19 start-page: 1758 year: 1998 end-page: 1776 ident: br0160 article-title: New procedure to build molecular surfaces and its use in continuum solvation methods publication-title: J. Comput. Chem. – year: 2002 ident: br0220 article-title: Implicit Objects in Computer Graphics – volume: 165 start-page: 59 year: 2005 end-page: 96 ident: br0030 article-title: ARVO: a Fortran package for computing the solvent accessible surface area and the excluded volume of overlapping spheres via analytic equations publication-title: Comput. Phys. Commun. – volume: 178 start-page: 63 year: 1984 end-page: 89 ident: br0190 article-title: Solvent accessible surface area and excluded volume in proteins: analytical equations for overlapping spheres and implications for the hydrophobic effect publication-title: J. Mol. Biol. – start-page: 33 year: 2013 ident: 10.1016/j.jcp.2016.07.007_br0120 article-title: Rendering molecular surfaces using order-independent transparency – year: 1976 ident: 10.1016/j.jcp.2016.07.007_br0080 – volume: 114 start-page: 10024 issue: 25 year: 1992 ident: 10.1016/j.jcp.2016.07.007_br0170 article-title: Uff, a full periodic table force field for molecular mechanics and molecular dynamics simulations publication-title: J. Am. Chem. Soc. doi: 10.1021/ja00051a040 – volume: 16 start-page: 548 issue: 5 year: 1983 ident: 10.1016/j.jcp.2016.07.007_br0070 article-title: Analytical molecular surface calculation publication-title: J. Appl. Crystallogr. doi: 10.1107/S0021889883010985 – volume: 55 issue: 3 year: 1971 ident: 10.1016/j.jcp.2016.07.007_br0130 article-title: The interpretation of protein structures: estimation of static accessibility publication-title: J. Mol. Biol. doi: 10.1016/0022-2836(71)90324-X – volume: 16 start-page: 78 issue: 1 year: 1987 ident: 10.1016/j.jcp.2016.07.007_br0010 article-title: Power diagrams: properties, algorithms and applications publication-title: SIAM J. Comput. doi: 10.1137/0216006 – volume: 9 start-page: 3637 issue: 8 year: 2013 ident: 10.1016/j.jcp.2016.07.007_br0140 article-title: Fast domain decomposition algorithm for continuum solvation models: energy and first derivatives publication-title: J. Chem. Theory Comput. doi: 10.1021/ct400280b – volume: 16 start-page: 101 issue: 1 year: 2015 ident: 10.1016/j.jcp.2016.07.007_br0060 article-title: ProteinVolume: calculating molecular van der Waals and void volumes in proteins publication-title: BMC Bioinform. doi: 10.1186/s12859-015-0531-2 – volume: 3 start-page: 323 issue: 6 year: 1988 ident: 10.1016/j.jcp.2016.07.007_br0020 article-title: Computing the volume of the union of spheres publication-title: Vis. Comput. doi: 10.1007/BF01901190 – year: 1979 ident: 10.1016/j.jcp.2016.07.007_br0090 – volume: 165 start-page: 59 issue: 1 year: 2005 ident: 10.1016/j.jcp.2016.07.007_br0030 article-title: ARVO: a Fortran package for computing the solvent accessible surface area and the excluded volume of overlapping spheres via analytic equations publication-title: Comput. Phys. Commun. doi: 10.1016/j.cpc.2004.08.002 – ident: 10.1016/j.jcp.2016.07.007_br0230 – volume: 105 start-page: 2999 issue: 8 year: 2005 ident: 10.1016/j.jcp.2016.07.007_br0210 article-title: Quantum mechanical continuum solvation models publication-title: Chem. Rev. doi: 10.1021/cr9904009 – volume: 139 issue: 5 year: 2013 ident: 10.1016/j.jcp.2016.07.007_br0040 article-title: Domain decomposition for implicit solvation models publication-title: J. Chem. Phys. doi: 10.1063/1.4816767 – year: 2002 ident: 10.1016/j.jcp.2016.07.007_br0220 – volume: 19 start-page: 1758 issue: 15 year: 1998 ident: 10.1016/j.jcp.2016.07.007_br0160 article-title: New procedure to build molecular surfaces and its use in continuum solvation methods publication-title: J. Comput. Chem. doi: 10.1002/(SICI)1096-987X(19981130)19:15<1758::AID-JCC8>3.0.CO;2-M – volume: 38 start-page: 3 issue: 1 year: 2011 ident: 10.1016/j.jcp.2016.07.007_br0050 article-title: Computing the volume of a union of balls: a certified algorithm publication-title: ACM Trans. Math. Softw. doi: 10.1145/2049662.2049665 – volume: 37 start-page: 3605 issue: 21 year: 1994 ident: 10.1016/j.jcp.2016.07.007_br0110 article-title: The advancing-front mesh generation method revisited publication-title: Int. J. Numer. Methods Eng. doi: 10.1002/nme.1620372103 – volume: 6 start-page: 151 year: 1977 ident: 10.1016/j.jcp.2016.07.007_br0180 article-title: Areas, volumes, packing and protein structure publication-title: Annu. Rev. Biophys. Bioeng. doi: 10.1146/annurev.bb.06.060177.001055 – start-page: 217 year: 2012 ident: 10.1016/j.jcp.2016.07.007_br0150 article-title: Implicit representation of molecular surfaces – volume: 178 start-page: 63 issue: 1 year: 1984 ident: 10.1016/j.jcp.2016.07.007_br0190 article-title: Solvent accessible surface area and excluded volume in proteins: analytical equations for overlapping spheres and implications for the hydrophobic effect publication-title: J. Mol. Biol. doi: 10.1016/0022-2836(84)90231-6 – start-page: 44 year: 1945 ident: 10.1016/j.jcp.2016.07.007_br0100 article-title: The Gauss–Green theorem publication-title: Trans. Am. Math. Soc. doi: 10.1090/S0002-9947-1945-0013786-6 – volume: 38 start-page: 305 issue: 3 year: 1996 ident: 10.1016/j.jcp.2016.07.007_br0200 article-title: Reduced surface: an efficient way to compute molecular surfaces publication-title: Biopolymers doi: 10.1002/(SICI)1097-0282(199603)38:3<305::AID-BIP4>3.0.CO;2-Y |
| SSID | ssj0008548 |
| Score | 2.3698072 |
| Snippet | In this article we derive a complete characterization of the Solvent Excluded Surface (SES) for molecular systems including a complete characterization of... |
| SourceID | hal crossref elsevier |
| SourceType | Open Access Repository Enrichment Source Index Database Publisher |
| StartPage | 760 |
| SubjectTerms | Chemical Sciences Constructive algorithm Mathematical description Mathematical Physics Mathematics Molecular surface or physical chemistry Solvation models Solvent excluded surface Theoretical and |
| Title | Mathematical analysis and calculation of molecular surfaces |
| URI | https://dx.doi.org/10.1016/j.jcp.2016.07.007 https://hal.sorbonne-universite.fr/hal-01205580 |
| Volume | 322 |
| WOSCitedRecordID | wos000381585100038&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVESC databaseName: Elsevier SD Freedom Collection Journals 2021 customDbUrl: eissn: 1090-2716 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0008548 issn: 0021-9991 databaseCode: AIEXJ dateStart: 19950101 isFulltext: true titleUrlDefault: https://www.sciencedirect.com providerName: Elsevier |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1daxQxFA229cEXrV9YbcsgPilTkkxmkuDTtrRUqUWhwr4NmUyCLu1s2Y9S_703n7aVFhV8GYawk11yssmZm3vPQeiNtaqjVWdLi_uqZFqoUliuS6mcC4FqjLXeteSIHx-L8Vh-jh6bc28nwIdBXF7K8_8KNbQB2K509i_gzp1CA9wD6HAF2OH6R8B_ykKsXgYgao748jV1qqNblz9WT8647-bLmXWpWbcwVe2dH1LUMMRCMhX_slTp3H76Y5kDNgt15mfarhkm6izKe8foAmlynloMeaWyl2tZmSGvQwabrR0TVk4scUl5KJxMS2sVao7j4siDc0DcZ3kwHfptCQ_RhMnORDs5URK0VYMz7g1lbHfQ7FQUCHBKoEmNWEFrlNcSFre10Yf98ce8JYuahS05_u50vO0T_W580W0EZeVbCrV76nGyjh5GJIpRwPoxumeGJ-hRfH8o4uo8f4reX4W-SNDDTV9cgb6Y2iJDXyTon6GvB_sne4dlNMcoNWN4UUpGOs6axirjxIUJ5b01lTYVUEpOO6YJqYzAwrCur4mSwkprKe5VozRxwe_naHWYDuYFKoilQJU4xgrYaFXRDveN7ZnBxmoOr-8bCKcRaXVUjncGJqdtShGctDCIrRvEFrt8Br6B3uZHzoNsyl0fZmmY28j7Ap9rYU7c9dhrgCR373TSD0dHrWtzFeF1LfAFfflvfb9CD379GzbR6mK2NFvovr5YfJ_PtuP0-gnRwofK |
| linkProvider | Elsevier |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Mathematical+analysis+and+calculation+of+molecular+surfaces&rft.jtitle=Journal+of+computational+physics&rft.au=Quan%2C+Chaoyu&rft.au=Stamm%2C+Benjamin&rft.date=2016-10-01&rft.pub=Elsevier+Inc&rft.issn=0021-9991&rft.eissn=1090-2716&rft.volume=322&rft.spage=760&rft.epage=782&rft_id=info:doi/10.1016%2Fj.jcp.2016.07.007&rft.externalDocID=S0021999116302868 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0021-9991&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0021-9991&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0021-9991&client=summon |