{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,13]],"date-time":"2026-10-13T01:40:22Z","timestamp":1791855622306,"version":"4.3.4"},"reference-count":46,"publisher":"Oxford University Press (OUP)","issue":"6","license":[{"start":{"date-parts":[[2019,11,6]],"date-time":"2019-11-06T00:00:00Z","timestamp":1572998400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"DOI":"10.13039\/501100008252","name":"University of Udine","doi-asserted-by":"publisher","award":["PRID2017"],"award-info":[{"award-number":["PRID2017"]}],"id":[{"id":"10.13039\/501100008252","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2020,3,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:sec>\n                  <jats:title>Motivation<\/jats:title>\n                  <jats:p>Implicit solvent models play an important role in describing the thermodynamics and the dynamics of biomolecular systems. Key to an efficient use of these models is the computation of generalized Born (GB) radii, which is accomplished by algorithms based on the electrostatics of inhomogeneous dielectric media. The speed and accuracy of such computations are still an issue especially for their intensive use in classical molecular dynamics. Here, we propose an alternative approach that encodes the physics of the phenomena and the chemical structure of the molecules in model parameters which are learned from examples.<\/jats:p>\n               <\/jats:sec>\n               <jats:sec>\n                  <jats:title>Results<\/jats:title>\n                  <jats:p>GB radii have been computed using (i) a linear model and (ii) a neural network. The input is the element, the histogram of counts of neighbouring atoms, divided by atom element, within 16\u2009\u00c5. Linear models are ca. 8 times faster than the most widely used reference method and the accuracy is higher with correlation coefficient with the inverse of \u2018perfect\u2019 GB radii of 0.94 versus 0.80 of the reference method. Neural networks further improve the accuracy of the predictions with correlation coefficient with \u2018perfect\u2019 GB radii of 0.97 and ca. 20% smaller root mean square error.<\/jats:p>\n               <\/jats:sec>\n               <jats:sec>\n                  <jats:title>Availability and implementation<\/jats:title>\n                  <jats:p>We provide a C program implementing the computation using the linear model, including the coefficients appropriate for the set of Bondi radii, as Supplementary Material. We also provide a Python implementation of the neural network model with parameter and example files in the Supplementary Material as well.<\/jats:p>\n               <\/jats:sec>\n               <jats:sec>\n                  <jats:title>Supplementary information<\/jats:title>\n                  <jats:p>Supplementary data are available at Bioinformatics online.<\/jats:p>\n               <\/jats:sec>","DOI":"10.1093\/bioinformatics\/btz818","type":"journal-article","created":{"date-parts":[[2019,10,30]],"date-time":"2019-10-30T12:12:53Z","timestamp":1572437573000},"page":"1757-1764","source":"Crossref","is-referenced-by-count":9,"title":["Generalized Born radii computation using linear models and neural networks"],"prefix":"10.1093","volume":"36","author":[{"given":"Saida Saad Mohamed","family":"Mahmoud","sequence":"first","affiliation":[{"name":"Department of Mathematics, Informatics and Physics, University of Udine , Udine 33100, Italy"},{"name":"Faculty of Science, Cairo University , Giza 12613, Egypt"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Gennaro","family":"Esposito","sequence":"additional","affiliation":[{"name":"Science and Math Division , New York University at Abu Dhabi, PO Box 129188, Abu Dhabi, United Arab Emirates"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Giuseppe","family":"Serra","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Informatics and Physics, University of Udine , Udine 33100, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9862-250X","authenticated-orcid":false,"given":"Federico","family":"Fogolari","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Informatics and Physics, University of Udine , Udine 33100, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2019,11,6]]},"reference":[{"key":"2023060911591795900_btz818-B1","doi-asserted-by":"crossref","first-page":"3613","DOI":"10.1021\/ct100392h","article-title":"Reducing the secondary structure bias in the generalized born model via R6 effective radii","volume":"6","author":"Aguilar","year":"2010","journal-title":"J. Chem. Theory Comput"},{"key":"2023060911591795900_btz818-B2","doi-asserted-by":"crossref","first-page":"144105","DOI":"10.1063\/1.2987409","article-title":"Interpreting the Coulomb-field approximation for generalized-Born electrostatics using boundary-integral equation theory","volume":"129","author":"Bardhan","year":"2008","journal-title":"J. Chem. Phys"},{"key":"2023060911591795900_btz818-B3","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1146\/annurev.physchem.51.1.129","article-title":"Generalized Born models of macromolecular solvation effects","volume":"51","author":"Bashford","year":"2000","journal-title":"Annu. Rev. Phys. Chem"},{"key":"2023060911591795900_btz818-B4","doi-asserted-by":"crossref","first-page":"170901","DOI":"10.1063\/1.4966192","article-title":"Perspective: machine learning potentials for atomistic simulations","volume":"145","author":"Behler","year":"2016","journal-title":"J. Chem. Phys"},{"key":"2023060911591795900_btz818-B5","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1016\/0010-4655(95)00042-E","article-title":"GROMACS: a message-passing parallel molecular dynamics implementation","volume":"91","author":"Berendsen","year":"1995","journal-title":"Comp. Phys. Commun"},{"key":"2023060911591795900_btz818-B6","doi-asserted-by":"crossref","first-page":"441","DOI":"10.1021\/j100785a001","article-title":"van der Waals volumes and radii","volume":"68","author":"Bondi","year":"1964","journal-title":"J. Phys. Chem"},{"key":"2023060911591795900_btz818-B7","doi-asserted-by":"crossref","first-page":"1545","DOI":"10.1002\/jcc.21287","article-title":"CHARMM: the biomolecular simulation program","volume":"30","author":"Brooks","year":"2009","journal-title":"J. Comput. Chem"},{"key":"2023060911591795900_btz818-B8","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/PL00020119","article-title":"Self consistent field theory of solvent effects representation by continuum models: introduction of desolvation contribution","volume":"65","author":"Constanciel","year":"1984","journal-title":"Theor. Chim. Acta"},{"key":"2023060911591795900_btz818-B9","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1002\/(SICI)1096-987X(200003)21:4<295::AID-JCC5>3.0.CO;2-8","article-title":"Comparison of generalized Born and Poisson models: energetics and dynamics of HIV protease","volume":"21","author":"David","year":"2000","journal-title":"J. Comput. Chem"},{"key":"2023060911591795900_btz818-B10","doi-asserted-by":"crossref","first-page":"377","DOI":"10.1002\/jmr.577","article-title":"The Poisson\u2013Boltzmann equation for biomolecular electrostatics: a tool for structural biology","volume":"15","author":"Fogolari","year":"2002","journal-title":"J. Mol. Recogn"},{"key":"2023060911591795900_btz818-B11","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1016\/S0006-3495(03)74462-2","article-title":"Protocol for MM\/PBSA molecular dynamics simulations of proteins","volume":"85","author":"Fogolari","year":"2003","journal-title":"Biophys. J"},{"key":"2023060911591795900_btz818-B12","doi-asserted-by":"crossref","first-page":"S18","DOI":"10.1186\/1471-2105-13-S4-S18","article-title":"Bluues: a program for the analysis of the electrostatic properties of proteins based on generalized Born radii","volume":"13 (Suppl. 4","author":"Fogolari","year":"2012","journal-title":"BMC Bioinformatics"},{"key":"2023060911591795900_btz818-B13","doi-asserted-by":"crossref","first-page":"054112","DOI":"10.1063\/1.4789537","article-title":"Generalized Born forces: surface integral formulation","volume":"138","author":"Fogolari","year":"2013","journal-title":"J. Chem. Phys"},{"key":"2023060911591795900_btz818-B14","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1007\/978-3-319-12211-3_7","volume-title":"Computational Electrostatics for Biological Applications: Geometric and Numerical Approaches to the Description of Electrostatic Interaction between Macromolecules","author":"Fogolari","year":"2015"},{"key":"2023060911591795900_btz818-B15","doi-asserted-by":"crossref","first-page":"11","DOI":"10.3389\/fmolb.2018.00011","article-title":"Free energy, enthalpy and entropy from implicit solvent end-point simulations","volume":"5","author":"Fogolari","year":"2018","journal-title":"Front. Mol. Biosci"},{"key":"2023060911591795900_btz818-B16","doi-asserted-by":"crossref","first-page":"10983","DOI":"10.1021\/jp982533o","article-title":"Generalized Born model based on a surface integral formulation","volume":"102","author":"Ghosh","year":"1998","journal-title":"J. Phys. Chem. B"},{"key":"2023060911591795900_btz818-B17","doi-asserted-by":"crossref","first-page":"1081","DOI":"10.1002\/jcc.540160904","article-title":"Molecular dynamics simulation with a continuum electrostatic model of the solvent","volume":"16","author":"Gilson","year":"1995","journal-title":"J. Comput. Chem"},{"key":"2023060911591795900_btz818-B18","doi-asserted-by":"crossref","first-page":"4817","DOI":"10.1063\/1.1595641","article-title":"Deficiency of the Coulomb-field approximation in the generalized Born model: an improved formula for Born radii evaluation","volume":"119","author":"Grycuk","year":"2003","journal-title":"J. Chem. Phys"},{"key":"2023060911591795900_btz818-B19","doi-asserted-by":"crossref","first-page":"701","DOI":"10.1002\/jcc.20832","article-title":"FACTS: fast analytical continuum treatment of solvation","volume":"29","author":"Haberthur","year":"2008","journal-title":"J. Comput. Chem"},{"key":"2023060911591795900_btz818-B20","doi-asserted-by":"crossref","first-page":"122","DOI":"10.1016\/0009-2614(95)01082-K","article-title":"Pairwise solute descreening of solute charges from a dielectric medium","volume":"246","author":"Hawkins","year":"1995","journal-title":"Chem. Phys. Lett"},{"key":"2023060911591795900_btz818-B21","doi-asserted-by":"crossref","first-page":"19824","DOI":"10.1021\/jp961710n","article-title":"Parametrized models of aqueous free energies of solvation based on pairwise descreening of solute atomic charges from a dielectric medium","volume":"100","author":"Hawkins","year":"1996","journal-title":"J. Phys. Chem"},{"key":"2023060911591795900_btz818-B23","doi-asserted-by":"crossref","first-page":"1656","DOI":"10.1021\/acs.jctc.7b00886","article-title":"Accuracy comparison of generalized Born models in the calculation of electrostatic binding free energies","volume":"14","author":"Izadi","year":"2018","journal-title":"J. Chem. Theory Comput"},{"key":"2023060911591795900_btz818-B24","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1006\/jcph.1999.6201","article-title":"NAMD2: greater scalability for parallel molecular dynamics","volume":"151","author":"Kale","year":"1999","journal-title":"J. Comp. Phys"},{"key":"2023060911591795900_btz818-B25","doi-asserted-by":"crossref","first-page":"437","DOI":"10.1002\/prot.10286","article-title":"Structure validation by C\u03b1 geometry: \u03d5,\u03c8 and C\u03b2 deviation","volume":"50","author":"Lovell","year":"2003","journal-title":"Proteins"},{"key":"2023060911591795900_btz818-B26","doi-asserted-by":"crossref","first-page":"185101","DOI":"10.1063\/1.2783847","article-title":"Analysis of integral expressions for effective Born radii","volume":"127","author":"Mongan","year":"2007","journal-title":"J. Chem. Phys"},{"key":"2023060911591795900_btz818-B27","doi-asserted-by":"crossref","first-page":"156","DOI":"10.1021\/ct600085e","article-title":"Generalized Born model with a simple robust molecular volume correction","volume":"3","author":"Mongan","year":"2007","journal-title":"J. Chem. Theory Comput"},{"key":"2023060911591795900_btz818-B28","doi-asserted-by":"crossref","first-page":"207","DOI":"10.32614\/RJ-2017-009","article-title":"imputeTS: time series missing value imputation in R","volume":"9","author":"Moritz","year":"2017","journal-title":"R J"},{"key":"2023060911591795900_btz818-B29","first-page":"807","author":"Nair","year":"2010"},{"key":"2023060911591795900_btz818-B30","doi-asserted-by":"crossref","first-page":"13959","DOI":"10.1021\/ja5032776","article-title":"Folding simulations for proteins with diverse topologies are accessible in days with a single physics-based force field and implicit solvent","volume":"136","author":"Nguyen","year":"2014","journal-title":"J. Am. Chem. Soc"},{"key":"2023060911591795900_btz818-B31","doi-asserted-by":"crossref","first-page":"361","DOI":"10.1080\/08927029208022491","article-title":"Molecular dynamics simulations in heterogeneous dielectrics and Debye-Huckel media: application to the protein bovine pancreatic trypsin inhibitor","volume":"8","author":"Niedermeier","year":"1992","journal-title":"Mol. Simul"},{"key":"2023060911591795900_btz818-B32","doi-asserted-by":"crossref","first-page":"1297","DOI":"10.1002\/jcc.10126","article-title":"Effective Born radii in the generalized Born approximation: the importance of being perfect","volume":"23","author":"Onufriev","year":"2002","journal-title":"J. Comput. Chem"},{"key":"2023060911591795900_btz818-B33","doi-asserted-by":"crossref","first-page":"383","DOI":"10.1002\/prot.20033","article-title":"Exploring protein native states and large-scale conformational changes with a modified generalized Born model","volume":"55","author":"Onufriev","year":"2004","journal-title":"Proteins Struct. Funct. Genet"},{"key":"2023060911591795900_btz818-B34","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1146\/annurev-biophys-052118-115325","article-title":"Generalized Born implicit solvent models for biomolecules","volume":"48","author":"Onufriev","year":"2019","journal-title":"Annu. Rev. Biophys"},{"key":"2023060911591795900_btz818-B35","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1007\/3-540-49430-8_3","volume-title":"Neural Networks: Tricks of the Trade","author":"Prechelt","year":"1998"},{"key":"2023060911591795900_btz818-B36","doi-asserted-by":"crossref","first-page":"3005","DOI":"10.1021\/jp961992r","article-title":"The GB\/SA continuum model for solvation. a fast analytical method for the calculation of approximate Born radii","volume":"101","author":"Qiu","year":"1997","journal-title":"J. Phys. Chem"},{"key":"2023060911591795900_btz818-B37","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1002\/(SICI)1097-0282(199603)38:3<305::AID-BIP4>3.0.CO;2-Y","article-title":"Reduced surface: an efficient way to compute molecular surfaces","volume":"38","author":"Sanner","year":"1996","journal-title":"Biopolymers"},{"key":"2023060911591795900_btz818-B38","doi-asserted-by":"crossref","first-page":"454","DOI":"10.1002\/jcc.540120407","article-title":"Incorporating solvent and ion screening into molecular dynamics using the finite-difference Poisson\u2013Boltzmann method","volume":"12","author":"Sharp","year":"1991","journal-title":"J. Comput. Chem"},{"key":"2023060911591795900_btz818-B39","first-page":"1264","article-title":"Analysis of different activation functions using back propagation neural networks","volume":"47","author":"Sibi","year":"2013","journal-title":"J. Theor. Appl. Inform. Technol"},{"key":"2023060911591795900_btz818-B40","doi-asserted-by":"crossref","first-page":"6127","DOI":"10.1021\/ja00172a038","article-title":"Semianalytical treatment of solvation for molecular mechanics and dynamics","volume":"112","author":"Still","year":"1990","journal-title":"J. Am. Chem. Soc"},{"key":"2023060911591795900_btz818-B41","doi-asserted-by":"crossref","first-page":"484","DOI":"10.1021\/ct049834o","article-title":"Optimized radii for Poisson\u2013Boltzmann calculations with the AMBER force field","volume":"1","author":"Swanson","year":"2005","journal-title":"J. Chem. Theory Comput"},{"key":"2023060911591795900_btz818-B42","doi-asserted-by":"crossref","first-page":"170","DOI":"10.1021\/ct600216k","article-title":"Optimizing the Poisson dielectric boundary with explicit solvent forces and energies: lessons learned with atom-centered dielectric functions","volume":"3","author":"Swanson","year":"2007","journal-title":"J. Chem. Theory Comput"},{"key":"2023060911591795900_btz818-B43","doi-asserted-by":"crossref","first-page":"3055","DOI":"10.1021\/jp066284c","article-title":"GBr6: a parametrization free, accurate, analytical generalized Born method","volume":"111","author":"Tjong","year":"2007","journal-title":"J. Phys. Chem"},{"key":"2023060911591795900_btz818-B44","doi-asserted-by":"crossref","first-page":"1701","DOI":"10.1002\/jcc.20291","article-title":"Gromacs: fast, flexible, and free","volume":"26","author":"Van Der Spoel","year":"2005","journal-title":"J. Comput. Chem"},{"key":"2023060911591795900_btz818-B45","doi-asserted-by":"crossref","first-page":"755","DOI":"10.1021\/acscentsci.8b00913","article-title":"Machine learning of coarse-grained molecular dynamics force fields","volume":"5","author":"Wang","year":"2019","journal-title":"ACS Cent. Sci"},{"key":"2023060911591795900_btz818-B46","volume-title":"A History of the Theories of Aether and Electricity: From the Age of Descartes to the Close of the Nineteenth Century.","author":"Whittaker","year":"1910"},{"key":"2023060911591795900_btz818-B47","doi-asserted-by":"crossref","first-page":"034101","DOI":"10.1063\/1.5027645","article-title":"DeePCG: constructing coarse-grained models via deep neural networks","volume":"149","author":"Zhang","year":"2018","journal-title":"J. Chem. Phys"}],"container-title":["Bioinformatics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/academic.oup.com\/bioinformatics\/article-pdf\/36\/6\/1757\/50553695\/bioinformatics_36_6_1757.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/bioinformatics\/article-pdf\/36\/6\/1757\/50553695\/bioinformatics_36_6_1757.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,6,9]],"date-time":"2023-06-09T12:02:24Z","timestamp":1686312144000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/bioinformatics\/article\/36\/6\/1757\/5613804"}},"subtitle":[],"editor":[{"given":"Lenore","family":"Cowen","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"editor"}]}],"short-title":[],"issued":{"date-parts":[[2019,11,6]]},"references-count":46,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2020,3,1]]}},"URL":"https:\/\/doi.org\/10.1093\/bioinformatics\/btz818","relation":{},"ISSN":["1367-4803","1367-4811"],"issn-type":[{"value":"1367-4803","type":"print"},{"value":"1367-4811","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2020,3,15]]},"published":{"date-parts":[[2019,11,6]]}}}