{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T10:59:00Z","timestamp":1790852340810,"version":"4.1.0"},"reference-count":89,"publisher":"AIP Publishing","issue":"13","funder":[{"name":"Shenzhen Medical Research Fund","award":["B2404003"],"award-info":[{"award-number":["B2404003"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["T2596084"],"award-info":[{"award-number":["T2596084"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2026,10,7]]},"abstract":"<jats:p>The multipole and induced dipole (MPID) model provides a sophisticated description of electrostatics through permanent atomic multipoles up to the octupole level and point induced dipoles, but its high computational cost has limited its routine application to biomolecular simulations. Here, we present a GPU-accelerated implementation of the MPID model in OpenMM. The implementation produces energies and forces fully consistent with those obtained from CHARMM and enables routine microsecond-scale molecular dynamics simulations of explicitly solvated protein systems. Moreover, force field parameters were transferred directly from the Drude oscillator model to the MPID framework without reparameterization, yielding the MPID-2019 protein force field. Tests on five proteins show that MPID-2019 reproduces a range of NMR observables, including scalar couplings and relaxation order parameters. These results demonstrate that MPID-2019 is a valid polarizable force field that is readily applicable to protein simulations and that the effective equivalence of the induced dipole and Drude oscillator formalisms can be established at the biomolecular level.<\/jats:p>","DOI":"10.1063\/5.0345546","type":"journal-article","created":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T10:40:25Z","timestamp":1790851225000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":0,"title":["MPID polarizable force field: GPU implementation and biomolecular simulations"],"prefix":"10.1063","volume":"165","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5486-896X","authenticated-orcid":false,"given":"Qiaozhu","family":"Tan","sequence":"first","affiliation":[{"name":"College of Life Sciences, Zhejiang University 1 , Hangzhou, Zhejiang 310058,","place":["China"]},{"name":"State Key Laboratory of Gene Expression, School of Life Sciences, Westlake University 2 , Hangzhou, Zhejiang 310030,","place":["China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5921-9272","authenticated-orcid":false,"given":"Andrew C.","family":"Simmonett","sequence":"additional","affiliation":[{"name":"Laboratory of Computational Biology, National Heart, Lung, and Blood Institute, National Institutes of Health 3 , Bethesda, Maryland 20892,","place":["USA"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3586-2730","authenticated-orcid":false,"given":"Bernard R.","family":"Brooks","sequence":"additional","affiliation":[{"name":"Laboratory of Computational Biology, National Heart, Lung, and Blood Institute, National Institutes of Health 3 , Bethesda, Maryland 20892,","place":["USA"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9639-2907","authenticated-orcid":false,"given":"Jing","family":"Huang","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Gene Expression, School of Life Sciences, Westlake University 2 , Hangzhou, Zhejiang 310030,","place":["China"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"317","published-online":{"date-parts":[[2026,10,1]]},"reference":[{"key":"2026100106401933300_c1","doi-asserted-by":"publisher","first-page":"3144","DOI":"10.1021\/jz501315h","article-title":"Recent advances in polarizable force fields for macromolecules: Microsecond simulations of proteins using the classical Drude oscillator model","volume":"5","year":"2014","journal-title":"J.\u00a0Phys. Chem. Lett."},{"key":"2026100106401933300_c2","doi-asserted-by":"publisher","first-page":"779","DOI":"10.1021\/cr300461d","article-title":"Classical electrostatics for biomolecular simulations","volume":"114","year":"2014","journal-title":"Chem. Rev."},{"key":"2026100106401933300_c3","doi-asserted-by":"publisher","first-page":"9811","DOI":"10.1021\/acs.jpcb.6b06414","article-title":"Advanced potential energy surfaces for molecular simulation","volume":"120","year":"2016","journal-title":"J.\u00a0Phys. Chem. B"},{"key":"2026100106401933300_c4","doi-asserted-by":"publisher","first-page":"389","DOI":"10.1142\/S273741652202001X","article-title":"Special issue on polarizable force fields for biomolecular modelling","volume":"21","year":"2022","journal-title":"J.\u00a0Comput. Biophys. Chem."},{"key":"2026100106401933300_c5","doi-asserted-by":"publisher","first-page":"71","DOI":"10.1038\/nmeth.4067","article-title":"CHARMM36m: An improved force field for folded and intrinsically disordered proteins","volume":"14","year":"2017","journal-title":"Nat. Methods"},{"key":"2026100106401933300_c6","doi-asserted-by":"publisher","first-page":"3586","DOI":"10.1021\/jp973084f","article-title":"All-atom empirical potential for molecular modeling and dynamics studies of proteins","volume":"102","year":"1998","journal-title":"J.\u00a0Phys. Chem. B"},{"key":"2026100106401933300_c7","doi-asserted-by":"publisher","first-page":"3696","DOI":"10.1021\/acs.jctc.5b00255","article-title":"ff14SB: Improving the accuracy of protein side chain and backbone parameters from ff99SB","volume":"11","year":"2015","journal-title":"J.\u00a0Chem. Theory Comput."},{"key":"2026100106401933300_c8","doi-asserted-by":"publisher","first-page":"3499","DOI":"10.1021\/acs.jctc.5b00356","article-title":"Improved peptide and protein torsional energetics with the OPLS-AA force field","volume":"11","year":"2015","journal-title":"J.\u00a0Chem. Theory Comput."},{"key":"2026100106401933300_c9","doi-asserted-by":"publisher","first-page":"1195","DOI":"10.1016\/j.bpj.2024.03.033","article-title":"Molecular mechanisms of Na+-driven bile acid transport in human NTCP","volume":"123","year":"2024","journal-title":"Biophys. J."},{"key":"2026100106401933300_c10","doi-asserted-by":"publisher","first-page":"1405","DOI":"10.1021\/acs.biochem.4c00523","article-title":"A \u2018knob switch\u2019 model for the phosphoregulatory mechanism of KCC3 at the carboxy-terminal domain","volume":"64","year":"2025","journal-title":"Biochemistry"},{"key":"2026100106401933300_c11","doi-asserted-by":"publisher","first-page":"991","DOI":"10.1016\/j.bpj.2014.06.038","article-title":"Induction of peptide bond dipoles drives cooperative helix formation in the (AAQAA)3 peptide","volume":"107","year":"2014","journal-title":"Biophys. J."},{"key":"2026100106401933300_c12","doi-asserted-by":"publisher","first-page":"E7495","DOI":"10.1073\/pnas.1805049115","article-title":"Many-body effect determines the selectivity for Ca2+ and Mg2+ in proteins","volume":"115","year":"2018","journal-title":"Proc. Natl. Acad. Sci. U. S. A."},{"key":"2026100106401933300_c13","doi-asserted-by":"publisher","first-page":"212","DOI":"10.1021\/jz5024543","article-title":"Differential impact of the monovalent ions Li+, Na+, K+, and Rb+ on DNA conformational properties","volume":"6","year":"2015","journal-title":"J.\u00a0Phys. Chem. Lett."},{"key":"2026100106401933300_c14","doi-asserted-by":"publisher","first-page":"1087","DOI":"10.1007\/s10822-018-0147-5","article-title":"Absolute binding free energies for the SAMPL6 cucurbit [8] uril host-guest challenge via the AMOEBA polarizable force field","volume":"32","year":"2018","journal-title":"J.\u00a0Comput.-Aided Mol. Des."},{"key":"2026100106401933300_c15","doi-asserted-by":"publisher","first-page":"2549","DOI":"10.1021\/jp910674d","article-title":"Current status of the AMOEBA polarizable force field","volume":"114","year":"2010","journal-title":"J.\u00a0Phys. Chem. B"},{"key":"2026100106401933300_c16","doi-asserted-by":"publisher","first-page":"4046","DOI":"10.1021\/ct4003702","article-title":"Polarizable atomic multipole-based AMOEBA force field for proteins","volume":"9","year":"2013","journal-title":"J.\u00a0Chem. Theory Comput."},{"key":"2026100106401933300_c17","doi-asserted-by":"publisher","first-page":"3143","DOI":"10.1021\/ct200304d","article-title":"Polarizable atomic multipole-based molecular mechanics for organic molecules","volume":"7","year":"2011","journal-title":"J.\u00a0Chem. Theory Comput."},{"key":"2026100106401933300_c18","doi-asserted-by":"publisher","first-page":"2084","DOI":"10.1021\/acs.jctc.7b01169","article-title":"AMOEBA polarizable atomic multipole force field for nucleic acids","volume":"14","year":"2018","journal-title":"J.\u00a0Chem. Theory Comput."},{"key":"2026100106401933300_c19","doi-asserted-by":"publisher","first-page":"4122","DOI":"10.1021\/acs.jctc.9b00261","article-title":"AMOEBA+ classical potential for modeling molecular interactions","volume":"15","year":"2019","journal-title":"J.\u00a0Chem. Theory Comput."},{"key":"2026100106401933300_c20","doi-asserted-by":"publisher","first-page":"4983","DOI":"10.1021\/acs.chemrev.5b00505","article-title":"An empirical polarizable force field based on the classical Drude oscillator model: Development history and recent applications","volume":"116","year":"2016","journal-title":"Chem. Rev."},{"key":"2026100106401933300_c21","doi-asserted-by":"publisher","first-page":"5430","DOI":"10.1021\/ct400781b","article-title":"Polarizable force field for peptides and proteins based on the classical Drude oscillator","volume":"9","year":"2013","journal-title":"J.\u00a0Chem. Theory Comput."},{"key":"2026100106401933300_c22","doi-asserted-by":"publisher","first-page":"3221","DOI":"10.1021\/acs.jctc.0c00057","article-title":"Further optimization and validation of the classical Drude polarizable protein force field","volume":"16","year":"2020","journal-title":"J.\u00a0Chem. Theory Comput."},{"key":"2026100106401933300_c23","doi-asserted-by":"publisher","first-page":"1219","DOI":"10.1002\/jcc.23611","article-title":"All-atom polarizable force field for DNA based on the classical Drude oscillator model","volume":"35","year":"2014","journal-title":"J.\u00a0Comput. Chem."},{"key":"2026100106401933300_c24","doi-asserted-by":"publisher","first-page":"9142","DOI":"10.1021\/jp402860e","article-title":"A polarizable force field of dipalmitoylphosphatidylcholine based on the classical Drude model for molecular dynamics simulations of lipids","volume":"117","year":"2013","journal-title":"J.\u00a0Phys. Chem. B"},{"key":"2026100106401933300_c25","doi-asserted-by":"publisher","first-page":"724","DOI":"10.1002\/bip.22286","article-title":"Polarizable empirical force field for acyclic polyalcohols based on the classical Drude oscillator","volume":"99","year":"2013","journal-title":"Biopolymers"},{"key":"2026100106401933300_c26","doi-asserted-by":"publisher","first-page":"161702","DOI":"10.1063\/1.4984113","article-title":"Mapping the Drude polarizable force field onto a multipole and induced dipole model","volume":"147","year":"2017","journal-title":"J.\u00a0Chem. Phys."},{"key":"2026100106401933300_c27","year":"2017"},{"key":"2026100106401933300_c28","doi-asserted-by":"publisher","first-page":"1682","DOI":"10.1002\/jcc.25339","article-title":"Molecular dynamics simulations using the Drude polarizable force field on GPUs with OpenMM: Implementation, validation, and benchmarks","volume":"39","year":"2018","journal-title":"J.\u00a0Comput. Chem."},{"key":"2026100106401933300_c29","doi-asserted-by":"publisher","first-page":"956","DOI":"10.1039\/c7sc04531j","article-title":"Tinker-HP: A massively parallel molecular dynamics package for multiscale simulations of large complex systems with advanced point dipole polarizable force fields","volume":"9","year":"2018","journal-title":"Chem. Sci."},{"key":"2026100106401933300_c30","doi-asserted-by":"publisher","first-page":"9976","DOI":"10.1021\/acs.jpcb.4c04100","article-title":"CHARMM at 45: Enhancements in accessibility, functionality, and speed","volume":"128","year":"2024","journal-title":"J.\u00a0Phys. Chem. B"},{"key":"2026100106401933300_c31","doi-asserted-by":"publisher","first-page":"e1005659","DOI":"10.1371\/journal.pcbi.1005659","article-title":"OpenMM 7: Rapid development of high performance algorithms for molecular dynamics","volume":"13","year":"2017","journal-title":"PLoS Comput. Biol."},{"key":"2026100106401933300_c32","doi-asserted-by":"publisher","first-page":"109","DOI":"10.1021\/acs.jpcb.3c06662","article-title":"OpenMM 8: Molecular dynamics simulation with machine learning potentials","volume":"128","year":"2023","journal-title":"J.\u00a0Phys. Chem. B"},{"key":"2026100106401933300_c33","doi-asserted-by":"publisher","first-page":"616","DOI":"10.1021\/acs.jpclett.3c03158","article-title":"DP\/MM: A hybrid model for zinc-protein interactions in molecular dynamics","volume":"15","year":"2024","journal-title":"J.\u00a0Phys. Chem. Lett."},{"key":"2026100106401933300_c34","doi-asserted-by":"publisher","first-page":"1448","DOI":"10.3390\/ijms25031448","article-title":"Implementation and validation of an OpenMM plugin for the deep potential representation of potential energy","volume":"25","year":"2024","journal-title":"Int. J. Mol. Sci."},{"key":"2026100106401933300_c35","doi-asserted-by":"publisher","first-page":"164101","DOI":"10.1063\/1.4964866","article-title":"An empirical extrapolation scheme for efficient treatment of induced dipoles","volume":"145","year":"2016","journal-title":"J.\u00a0Chem. Phys."},{"key":"2026100106401933300_c36","doi-asserted-by":"publisher","first-page":"341","DOI":"10.1016\/0301-0104(81)85176-2","article-title":"Molecular polarizabilities calculated with a modified dipole interaction","volume":"59","year":"1981","journal-title":"Chem. Phys."},{"key":"2026100106401933300_c37","doi-asserted-by":"publisher","first-page":"774","DOI":"10.1021\/ct900576a","article-title":"Simulating monovalent and divalent ions in aqueous solution using a Drude polarizable force field","volume":"6","year":"2010","journal-title":"J.\u00a0Chem. Theory Comput."},{"key":"2026100106401933300_c38","doi-asserted-by":"publisher","first-page":"9401","DOI":"10.1021\/jp510560k","article-title":"Representation of ion-protein interactions using the Drude polarizable force-field","volume":"119","year":"2015","journal-title":"J.\u00a0Phys. Chem. B"},{"key":"2026100106401933300_c39","doi-asserted-by":"publisher","first-page":"5728","DOI":"10.1063\/1.449880","article-title":"Direct inversion in the iterative subspace (DIIS) optimization of open-shell, excited-state, and small multiconfiguration SCF wave functions","volume":"84","year":"1986","journal-title":"J.\u00a0Chem. Phys."},{"key":"2026100106401933300_c40","doi-asserted-by":"publisher","first-page":"439","DOI":"10.1002\/jcc.26067","article-title":"Improved modeling of cation-\u03c0 and anion-ring interactions using the Drude polarizable empirical force field for proteins","volume":"41","year":"2020","journal-title":"J.\u00a0Comput. Chem."},{"key":"2026100106401933300_c41","doi-asserted-by":"publisher","first-page":"531","DOI":"10.1016\/0022-2836(87)90679-6","article-title":"Structure of ubiquitin refined at 1.8\u00a0\u00c5 resolution","volume":"194","year":"1987","journal-title":"J.\u00a0Mol. Biol."},{"key":"2026100106401933300_c42","doi-asserted-by":"publisher","first-page":"5119","DOI":"10.1073\/pnas.91.11.5119","article-title":"Crystal structure of CspA, the major cold shock protein of Escherichia coli","volume":"91","year":"1994","journal-title":"Proc. Natl. Acad. Sci. U. S. A."},{"key":"2026100106401933300_c43","doi-asserted-by":"publisher","first-page":"14362","DOI":"10.1021\/jp075531p","article-title":"Crystal polymorphism of protein GB1 examined by solid-state NMR spectroscopy and X-ray diffraction","volume":"111","year":"2007","journal-title":"J.\u00a0Phys. Chem. B"},{"key":"2026100106401933300_c44","doi-asserted-by":"publisher","first-page":"849","DOI":"10.1016\/j.str.2004.03.017","article-title":"Crystal structures of apocalmodulin and an apocalmodulin\/SK potassium channel gating domain complex","volume":"12","year":"2004","journal-title":"Structure"},{"key":"2026100106401933300_c45","doi-asserted-by":"publisher","first-page":"4253","DOI":"10.1016\/s0021-9258(19)50654-8","article-title":"Refinement of the structure of recombinant rat intestinal fatty acid-binding apoprotein at 1.2-A resolution","volume":"267","year":"1992","journal-title":"J.\u00a0Biol. Chem."},{"key":"2026100106401933300_c46","doi-asserted-by":"publisher","first-page":"034508","DOI":"10.1063\/1.4774577","article-title":"Six-site polarizable model of water based on the classical Drude oscillator","volume":"138","year":"2013","journal-title":"J.\u00a0Chem. Phys."},{"key":"2026100106401933300_c47","doi-asserted-by":"publisher","first-page":"5185","DOI":"10.1063\/1.1598191","article-title":"A simple polarizable model of water based on classical Drude oscillators","volume":"119","year":"2003","journal-title":"J.\u00a0Chem. Phys."},{"key":"2026100106401933300_c48","doi-asserted-by":"publisher","first-page":"245","DOI":"10.1016\/j.cplett.2005.10.135","article-title":"A polarizable model of water for molecular dynamics simulations of biomolecules","volume":"418","year":"2006","journal-title":"Chem. Phys. Lett."},{"key":"2026100106401933300_c49","doi-asserted-by":"publisher","first-page":"1016","DOI":"10.1021\/acs.jpclett.4c03451","article-title":"Computationally efficient polarizable md simulations: A simple water model for the classical Drude oscillator polarizable force field","volume":"16","year":"2025","journal-title":"J.\u00a0Phys. Chem. Lett."},{"key":"2026100106401933300_c50","doi-asserted-by":"publisher","first-page":"10034","DOI":"10.1021\/acs.jctc.4c00966","article-title":"Revised 4-point water model for the classical Drude oscillator polarizable force field: SWM4-HLJ","volume":"20","year":"2024","journal-title":"J.\u00a0Chem. Theory Comput."},{"key":"2026100106401933300_c51","doi-asserted-by":"publisher","first-page":"10089","DOI":"10.1063\/1.464397","article-title":"Particle mesh Ewald: An N\u00b7log(N) method for Ewald sums in large systems","volume":"98","year":"1993","journal-title":"J.\u00a0Chem. Phys."},{"key":"2026100106401933300_c52","doi-asserted-by":"publisher","first-page":"5737","DOI":"10.1021\/acs.jctc.5b00726","article-title":"Direct-space corrections enable fast and accurate Lorentz\u2013Berthelot combination rule Lennard\u2013Jones lattice summation","volume":"11","year":"2015","journal-title":"J.\u00a0Chem. Theory Comput."},{"key":"2026100106401933300_c53","first-page":"240","article-title":"Multiscale dynamics of macromolecules using normal mode Langevin","volume-title":"Biocomputing","year":"2010"},{"key":"2026100106401933300_c54","doi-asserted-by":"publisher","first-page":"288","DOI":"10.1016\/j.cplett.2003.12.039","article-title":"Molecular dynamics simulations of water and biomolecules with a Monte Carlo constant pressure algorithm","volume":"384","year":"2004","journal-title":"Chem. Phys. Lett."},{"key":"2026100106401933300_c55","doi-asserted-by":"publisher","first-page":"1311","DOI":"10.1080\/00268977700102571","article-title":"Algorithms for macromolecular dynamics and constraint dynamics","volume":"34","year":"1977","journal-title":"Mol. Phys."},{"key":"2026100106401933300_c56","doi-asserted-by":"publisher","first-page":"1545","DOI":"10.1002\/jcc.21287","article-title":"CHARMM: The biomolecular simulation program","volume":"30","year":"2009","journal-title":"J.\u00a0Comput. Chem."},{"key":"2026100106401933300_c57","doi-asserted-by":"publisher","first-page":"L07","DOI":"10.1529\/biophysj.108.132696","article-title":"Are current molecular dynamics force fields too helical?","volume":"95","year":"2008","journal-title":"Biophys. J."},{"key":"2026100106401933300_c58","doi-asserted-by":"publisher","first-page":"11","DOI":"10.1063\/1.1729860","article-title":"Contact electron-spin coupling of nuclear magnetic moments","volume":"30","year":"1959","journal-title":"J.\u00a0Chem. Phys."},{"key":"2026100106401933300_c59","doi-asserted-by":"publisher","first-page":"1179","DOI":"10.1021\/ja0660406","article-title":"Structure and dynamics of the homologous series of alanine peptides: A joint molecular dynamics\/NMR study","volume":"129","year":"2007","journal-title":"J.\u00a0Am. Chem. Soc."},{"key":"2026100106401933300_c60","doi-asserted-by":"publisher","first-page":"3257","DOI":"10.1021\/ct300400x","article-title":"Optimization of the additive CHARMM all-atom protein force field targeting improved sampling of the backbone \u03d5, \u03c8 and side-chain \u03c71 and \u03c72 dihedral angles","volume":"8","year":"2012","journal-title":"J.\u00a0Chem. Theory Comput."},{"key":"2026100106401933300_c61","doi-asserted-by":"publisher","first-page":"6360","DOI":"10.1021\/ja970067v","article-title":"Determination of \u03d5 and \u03c71 angles in proteins from 13C\u201313C three-bond J couplings measured by three-dimensional heteronuclear NMR. How planar is the peptide bond?","volume":"119","year":"1997","journal-title":"J.\u00a0Am. Chem. Soc."},{"key":"2026100106401933300_c62","doi-asserted-by":"publisher","first-page":"6232","DOI":"10.1021\/ja049049l","article-title":"Protein backbone 1H(N)\u201313C\u03b1 and 15N\u201313C\u03b1 residual dipolar and J couplings: New constraints for NMR structure determination","volume":"126","year":"2004","journal-title":"J.\u00a0Am. Chem. Soc."},{"key":"2026100106401933300_c63","doi-asserted-by":"publisher","first-page":"6268","DOI":"10.1021\/ja9928834","article-title":"Determination of \u03c8 torsion angle restraints from 3\u00a0J (C\u03b1, C\u03b1) and 3\u00a0J (C\u03b1, HN) coupling constants in proteins","volume":"122","year":"2000","journal-title":"J.\u00a0Am. Chem. Soc."},{"key":"2026100106401933300_c64","doi-asserted-by":"publisher","first-page":"1601","DOI":"10.1021\/ja983945d","article-title":"Direct observation of hydrogen bonds in proteins by interresidue 3h J NC\u2032 scalar couplings","volume":"121","year":"1999","journal-title":"J.\u00a0Am. Chem. Soc."},{"key":"2026100106401933300_c65","doi-asserted-by":"publisher","first-page":"6275","DOI":"10.1021\/ja9909024","article-title":"Correlation between 3h J NC\u2032 and hydrogen bond length in proteins","volume":"121","year":"1999","journal-title":"J.\u00a0Am. Chem. Soc."},{"key":"2026100106401933300_c66","doi-asserted-by":"publisher","first-page":"4158","DOI":"10.1021\/ja012674v","article-title":"Structural dependencies of interresidue scalar coupling (h3) J NC\u2032 and donor (1)H chemical shifts in the hydrogen bonding regions of proteins","volume":"124","year":"2002","journal-title":"J.\u00a0Am. Chem. Soc."},{"key":"2026100106401933300_c67","doi-asserted-by":"publisher","first-page":"2135","DOI":"10.1002\/jcc.23354","article-title":"CHARMM36 all-atom additive protein force field: Validation based on comparison to NMR data","volume":"34","year":"2013","journal-title":"J.\u00a0Comput. Chem."},{"key":"2026100106401933300_c68","doi-asserted-by":"publisher","first-page":"185","DOI":"10.1016\/j.jmb.2005.03.001","article-title":"What contributions to protein side-chain dynamics are probed by NMR experiments? A molecular dynamics simulation analysis","volume":"349","year":"2005","journal-title":"J.\u00a0Mol. Biol."},{"key":"2026100106401933300_c69","doi-asserted-by":"publisher","first-page":"425","DOI":"10.1038\/nsb798","article-title":"Designing a 20-residue protein","volume":"9","year":"2002","journal-title":"Nat. Struct. Biol."},{"key":"2026100106401933300_c70","doi-asserted-by":"publisher","first-page":"1877","DOI":"10.1021\/cr040433a","article-title":"Conformation of the backbone in unfolded proteins","volume":"106","year":"2006","journal-title":"Chem. Rev."},{"key":"2026100106401933300_c71","doi-asserted-by":"publisher","first-page":"1045","DOI":"10.1016\/j.bpj.2012.07.042","article-title":"Inclusion of many-body effects in the additive CHARMM protein CMAP potential results in enhanced cooperativity of \u03b1-helix and \u03b2-hairpin formation","volume":"103","year":"2012","journal-title":"Biophys. J."},{"key":"2026100106401933300_c72","doi-asserted-by":"publisher","first-page":"99","DOI":"10.1038\/s42004-021-00537-8","article-title":"Validating the CHARMM36m protein force field with LJ-PME reveals altered hydrogen bonding dynamics under elevated pressures","volume":"4","year":"2021","journal-title":"Commun. Chem."},{"key":"2026100106401933300_c73","doi-asserted-by":"publisher","first-page":"12562","DOI":"10.1021\/ja00155a020","article-title":"Rotational diffusion anisotropy of human ubiquitin from 15N NMR relaxation","volume":"117","year":"1995","journal-title":"J.\u00a0Am. Chem. Soc."},{"key":"2026100106401933300_c74","doi-asserted-by":"publisher","first-page":"2278","DOI":"10.1021\/bi962018l","article-title":"Ligand binding alters the backbone mobility of intestinal fatty acid-binding protein as monitored by 15N NMR relaxation and 1H exchange","volume":"36","year":"1997","journal-title":"Biochemistry"},{"key":"2026100106401933300_c75","doi-asserted-by":"publisher","first-page":"6836","DOI":"10.1021\/ja9812610","article-title":"Validation of protein structure from anisotropic carbonyl chemical shifts in a dilute liquid crystalline phase","volume":"120","year":"1998","journal-title":"J.\u00a0Am. Chem. Soc."},{"key":"2026100106401933300_c76","doi-asserted-by":"publisher","first-page":"10881","DOI":"10.1021\/bi980269j","article-title":"Solution NMR structure and backbone dynamics of the major cold-shock protein (CspA) from Escherichia coli: Evidence for conformational dynamics in the single-stranded RNA-binding site","volume":"37","year":"1998","journal-title":"Biochemistry"},{"key":"2026100106401933300_c77","doi-asserted-by":"publisher","first-page":"1053","DOI":"10.1038\/nsmb.2355","article-title":"Spatial elucidation of motion in proteins by ensemble-based structure calculation using exact NOEs","volume":"19","year":"2012","journal-title":"Nat. Struct. Mol. Biol."},{"key":"2026100106401933300_c78","doi-asserted-by":"publisher","first-page":"909","DOI":"10.1021\/ja107847d","article-title":"Dynamics of lysine side-chain amino groups in a protein studied by heteronuclear 1H\u201315N NMR spectroscopy","volume":"133","year":"2011","journal-title":"J.\u00a0Am. Chem. Soc."},{"key":"2026100106401933300_c79","doi-asserted-by":"publisher","first-page":"9192","DOI":"10.1021\/ja202219n","article-title":"Signature of mobile hydrogen bonding of lysine side chains from long-range 15N\u201313C scalar J-couplings and computation","volume":"133","year":"2011","journal-title":"J.\u00a0Am. Chem. Soc."},{"key":"2026100106401933300_c80","doi-asserted-by":"publisher","first-page":"4674","DOI":"10.1021\/ja808223p","article-title":"Characterization of salt bridges to lysines in the protein G B1 domain","volume":"131","year":"2009","journal-title":"J.\u00a0Am. Chem. Soc."},{"key":"2026100106401933300_c81","doi-asserted-by":"publisher","first-page":"e4967","DOI":"10.7717\/peerj.4967","article-title":"How well do force fields capture the strength of salt bridges in proteins?","volume":"6","year":"2018","journal-title":"PeerJ"},{"key":"2026100106401933300_c82","doi-asserted-by":"publisher","first-page":"40","DOI":"10.1016\/j.sbi.2017.10.008","article-title":"Force field development and simulations of intrinsically disordered proteins","volume":"48","year":"2018","journal-title":"Curr. Opin. Struct. Biol."},{"key":"2026100106401933300_c83","doi-asserted-by":"publisher","first-page":"115737","DOI":"10.1016\/j.isci.2026.115737","article-title":"The intrinsic disorder challenge for AlphaFold: A case study of G3BP1 and pathogenic peptide","volume":"29","year":"2026","journal-title":"iScience"},{"key":"2026100106401933300_c84","doi-asserted-by":"publisher","first-page":"1138","DOI":"10.1016\/j.str.2025.05.013","article-title":"The continuous evolution of biomolecular force fields","volume":"33","year":"2025","journal-title":"Structure"},{"key":"2026100106401933300_c85","doi-asserted-by":"publisher","first-page":"2162","DOI":"10.1016\/j.str.2013.09.014","article-title":"Phosphorylation drives a dynamic switch in serine\/arginine-rich proteins","volume":"21","year":"2013","journal-title":"Structure"},{"key":"2026100106401933300_c86","doi-asserted-by":"publisher","first-page":"214108","DOI":"10.1063\/5.0128780","article-title":"A transferrable range-separated force field for water: Combining the power of both physically-motivated models and machine learning techniques","volume":"157","year":"2022","journal-title":"J.\u00a0Chem. Phys."},{"key":"2026100106401933300_c87","doi-asserted-by":"publisher","first-page":"1293","DOI":"10.1021\/acs.jctc.3c01171","article-title":"A fast, convenient, polarizable electrostatic model for molecular dynamics","volume":"20","year":"2024","journal-title":"J.\u00a0Chem. Theory Comput."},{"key":"2026100106401933300_c88","doi-asserted-by":"publisher","first-page":"6964","DOI":"10.1021\/acs.jctc.5c00603","article-title":"A simple, polarizable, rigid, 3-point water model using the direct polarization approximation","volume":"21","year":"2025","journal-title":"J.\u00a0Chem. Theory Comput."},{"key":"2026100106401933300_c89","doi-asserted-by":"publisher","first-page":"3543","DOI":"10.1021\/acs.jctc.5c02167","article-title":"Induced dipole calculation with E(3)-equivariant neural networks and multipole field perturbation","volume":"22","year":"2026","journal-title":"J.\u00a0Chem. Theory Comput."}],"container-title":["The Journal of Chemical Physics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/pubs.aip.org\/aip\/jcp\/article-pdf\/doi\/10.1063\/5.0345546\/21156293\/134101_1_5.0345546.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/pubs.aip.org\/aip\/jcp\/article-pdf\/doi\/10.1063\/5.0345546\/21156293\/134101_1_5.0345546.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T10:40:26Z","timestamp":1790851226000},"score":1,"resource":{"primary":{"URL":"https:\/\/pubs.aip.org\/jcp\/article\/165\/13\/134101\/3405494\/MPID-polarizable-force-field-GPU-implementation"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,10,1]]},"references-count":89,"journal-issue":{"issue":"13","published-print":{"date-parts":[[2026,10,7]]}},"URL":"https:\/\/doi.org\/10.1063\/5.0345546","relation":{},"ISSN":["0021-9606","1089-7690"],"issn-type":[{"value":"0021-9606","type":"print"},{"value":"1089-7690","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2026,10,7]]},"published":{"date-parts":[[2026,10,1]]},"article-number":"134101"}}