Numerical integration techniques for curved-element discretizations of molecule-solvent interfaces
urface formulations of biophysical modeling problems offer attractive theoretical and computational properties. Numerical simulations based on these formulations usually begin with discretization of the surface under consideration; often, the surface is curved, possessing complicated structure and p...
| Main Authors: | , , , , , |
|---|---|
| Other Authors: | |
| Format: | Article |
| Language: | en_US |
| Published: |
American Institute of Physics (AIP)
2012
|
| Online Access: | http://hdl.handle.net/1721.1/70039 https://orcid.org/0000-0002-3320-3969 https://orcid.org/0000-0003-1080-4005 |
| _version_ | 1826197068228591616 |
|---|---|
| author | Bardhan, Jaydeep P. Altman, Michael D. Willis, David J. Lippow, Shaun M. Tidor, Bruce White, Jacob K. |
| author2 | Massachusetts Institute of Technology. Department of Chemical Engineering |
| author_facet | Massachusetts Institute of Technology. Department of Chemical Engineering Bardhan, Jaydeep P. Altman, Michael D. Willis, David J. Lippow, Shaun M. Tidor, Bruce White, Jacob K. |
| author_sort | Bardhan, Jaydeep P. |
| collection | MIT |
| description | urface formulations of biophysical modeling problems offer attractive theoretical and computational properties. Numerical simulations based on these formulations usually begin with discretization of the surface under consideration; often, the surface is curved, possessing complicated structure and possibly singularities. Numerical simulations commonly are based on approximate, rather than exact, discretizations of these surfaces. To assess the strength of the dependence of simulation accuracy on the fidelity of surface representation, here methods were developed to model several important surface formulations using exact surface discretizations. Following and refining Zauhar’s work [J. Comput.-Aided Mol. Des. 9, 149 (1995) ], two classes of curved elements were defined that can exactly discretize the van der Waals, solvent-accessible, and solvent-excluded (molecular) surfaces. Numerical integration techniques are presented that can accurately evaluate nonsingular and singular integrals over these curved surfaces. After validating the exactness of the surface discretizations and demonstrating the correctness of the presented integration methods, a set of calculations are presented that compare the accuracy of approximate, planar-triangle-based discretizations and exact, curved-element-based simulations of surface-generalized-Born (sGB), surface-continuum van der Waals (scvdW), and boundary-element method (BEM) electrostatics problems. Results demonstrate that continuum electrostatic calculations with BEM using curved elements, piecewise-constant basis functions, and centroid collocation are nearly ten times more accurate than planar-triangle BEM for basis sets of comparable size. The sGB and scvdW calculations give exceptional accuracy even for the coarsest obtainable discretized surfaces. The extra accuracy is attributed to the exact representation of the solute-solvent interface; in contrast, commonly used planar-triangle discretizations can only offer improved approximations with increasing discretization and associated increases in computational resources. The results clearly demonstrate that the methods for approximate integration on an exact geometry are far more accurate than exact integration on an approximate geometry. A MATLAB implementation of the presented integration methods and sample data files containing curved-element discretizations of several small molecules are available online as supplemental material. |
| first_indexed | 2024-09-23T10:42:19Z |
| format | Article |
| id | mit-1721.1/70039 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T10:42:19Z |
| publishDate | 2012 |
| publisher | American Institute of Physics (AIP) |
| record_format | dspace |
| spelling | mit-1721.1/700392022-09-30T22:23:19Z Numerical integration techniques for curved-element discretizations of molecule-solvent interfaces Bardhan, Jaydeep P. Altman, Michael D. Willis, David J. Lippow, Shaun M. Tidor, Bruce White, Jacob K. Massachusetts Institute of Technology. Department of Chemical Engineering Massachusetts Institute of Technology. Department of Chemistry Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Tidor, Bruce Bardhan, Jaydeep P. Altman, Michael D. Willis, David J. Lippow, Shaun M. Tidor, Bruce White, Jacob K. urface formulations of biophysical modeling problems offer attractive theoretical and computational properties. Numerical simulations based on these formulations usually begin with discretization of the surface under consideration; often, the surface is curved, possessing complicated structure and possibly singularities. Numerical simulations commonly are based on approximate, rather than exact, discretizations of these surfaces. To assess the strength of the dependence of simulation accuracy on the fidelity of surface representation, here methods were developed to model several important surface formulations using exact surface discretizations. Following and refining Zauhar’s work [J. Comput.-Aided Mol. Des. 9, 149 (1995) ], two classes of curved elements were defined that can exactly discretize the van der Waals, solvent-accessible, and solvent-excluded (molecular) surfaces. Numerical integration techniques are presented that can accurately evaluate nonsingular and singular integrals over these curved surfaces. After validating the exactness of the surface discretizations and demonstrating the correctness of the presented integration methods, a set of calculations are presented that compare the accuracy of approximate, planar-triangle-based discretizations and exact, curved-element-based simulations of surface-generalized-Born (sGB), surface-continuum van der Waals (scvdW), and boundary-element method (BEM) electrostatics problems. Results demonstrate that continuum electrostatic calculations with BEM using curved elements, piecewise-constant basis functions, and centroid collocation are nearly ten times more accurate than planar-triangle BEM for basis sets of comparable size. The sGB and scvdW calculations give exceptional accuracy even for the coarsest obtainable discretized surfaces. The extra accuracy is attributed to the exact representation of the solute-solvent interface; in contrast, commonly used planar-triangle discretizations can only offer improved approximations with increasing discretization and associated increases in computational resources. The results clearly demonstrate that the methods for approximate integration on an exact geometry are far more accurate than exact integration on an approximate geometry. A MATLAB implementation of the presented integration methods and sample data files containing curved-element discretizations of several small molecules are available online as supplemental material. National Institutes of Health (U.S.) (GM065418) National Institutes of Health (U.S.) (CA096504) Singapore-MIT Alliance National Science Foundation (U.S.) Natural Sciences and Engineering Research Council of Canada (NSERC) 2012-04-13T20:23:22Z 2012-04-13T20:23:22Z 2007-07 2006-09 Article http://purl.org/eprint/type/JournalArticle 0021-9606 1089-7690 http://hdl.handle.net/1721.1/70039 Bardhan, Jaydeep P. et al. “Numerical Integration Techniques for Curved-element Discretizations of Molecule-solvent Interfaces.” The Journal of Chemical Physics 127.1 (2007): 014701. Web. 13 Apr. 2012. © 2007 American Institute of Physics https://orcid.org/0000-0002-3320-3969 https://orcid.org/0000-0003-1080-4005 en_US http://dx.doi.org/10.1063/1.2743423 Journal of Chemical Physics Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf American Institute of Physics (AIP) American Institute of Physics |
| spellingShingle | Bardhan, Jaydeep P. Altman, Michael D. Willis, David J. Lippow, Shaun M. Tidor, Bruce White, Jacob K. Numerical integration techniques for curved-element discretizations of molecule-solvent interfaces |
| title | Numerical integration techniques for curved-element discretizations of molecule-solvent interfaces |
| title_full | Numerical integration techniques for curved-element discretizations of molecule-solvent interfaces |
| title_fullStr | Numerical integration techniques for curved-element discretizations of molecule-solvent interfaces |
| title_full_unstemmed | Numerical integration techniques for curved-element discretizations of molecule-solvent interfaces |
| title_short | Numerical integration techniques for curved-element discretizations of molecule-solvent interfaces |
| title_sort | numerical integration techniques for curved element discretizations of molecule solvent interfaces |
| url | http://hdl.handle.net/1721.1/70039 https://orcid.org/0000-0002-3320-3969 https://orcid.org/0000-0003-1080-4005 |
| work_keys_str_mv | AT bardhanjaydeepp numericalintegrationtechniquesforcurvedelementdiscretizationsofmoleculesolventinterfaces AT altmanmichaeld numericalintegrationtechniquesforcurvedelementdiscretizationsofmoleculesolventinterfaces AT willisdavidj numericalintegrationtechniquesforcurvedelementdiscretizationsofmoleculesolventinterfaces AT lippowshaunm numericalintegrationtechniquesforcurvedelementdiscretizationsofmoleculesolventinterfaces AT tidorbruce numericalintegrationtechniquesforcurvedelementdiscretizationsofmoleculesolventinterfaces AT whitejacobk numericalintegrationtechniquesforcurvedelementdiscretizationsofmoleculesolventinterfaces |