{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,14]],"date-time":"2026-03-14T02:21:55Z","timestamp":1773454915498,"version":"3.50.1"},"reference-count":34,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2023,2,2]],"date-time":"2023-02-02T00:00:00Z","timestamp":1675296000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Stony Brook University\u2019s OVPR"},{"name":"IEDM COVID-19"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>Coarse-grained (CG) modeling has defined a well-established approach to accessing greater space and time scales inaccessible to the computationally expensive all-atomic (AA) molecular dynamics (MD) simulations. Popular methods of CG follow a bottom-up architecture to match properties of fine-grained or experimental data whose development is a daunting challenge for requiring the derivation of a new set of parameters in potential calculation. We proposed a novel physics-informed machine learning (PIML) framework for a CG model and applied it, as a verification, for modeling the SARS-CoV-2 spike glycoprotein. The PIML in the proposed framework employs a force-matching scheme with which we determined the force-field parameters. Our PIML framework defines its trainable parameters as the CG force-field parameters and predicts the instantaneous forces on each CG bead, learning the force field parameters to best match the predicted forces with the reference forces. Using the learned interaction parameters, CGMD validation simulations reach the microsecond time scale with stability, at a simulation speed 40,000 times faster than the conventional AAMD. Compared with the traditional iterative approach, our framework matches the AA reference structure with better accuracy. The improved efficiency enhances the timeliness of research and development in producing long-term simulations of SARS-CoV-2 and opens avenues to help illuminate protein mechanisms and predict its environmental changes.<\/jats:p>","DOI":"10.3390\/computation11020024","type":"journal-article","created":{"date-parts":[[2023,2,3]],"date-time":"2023-02-03T02:05:28Z","timestamp":1675389928000},"page":"24","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Coarse-Grained Modeling of the SARS-CoV-2 Spike Glycoprotein by Physics-Informed Machine Learning"],"prefix":"10.3390","volume":"11","author":[{"given":"David","family":"Liang","sequence":"first","affiliation":[{"name":"Department of Chemistry, University of Chicago, Chicago, IL 60637, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3923-6267","authenticated-orcid":false,"given":"Ziji","family":"Zhang","sequence":"additional","affiliation":[{"name":"Departments of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, NY 11790, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Miriam","family":"Rafailovich","sequence":"additional","affiliation":[{"name":"Materials Science and Chemical Engineering, Stony Brook University, Stony Brook, NY 11790, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Marcia","family":"Simon","sequence":"additional","affiliation":[{"name":"Oral Biology and Pathology, Stony Brook University, Stony Brook, NY 11790, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5224-3958","authenticated-orcid":false,"given":"Yuefan","family":"Deng","sequence":"additional","affiliation":[{"name":"Departments of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, NY 11790, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9539-1136","authenticated-orcid":false,"given":"Peng","family":"Zhang","sequence":"additional","affiliation":[{"name":"Departments of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, NY 11790, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,2,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"224104","DOI":"10.1063\/1.4880555","article-title":"Derivation of coarse-grained potentials via multistate iterative Boltzmann inversion","volume":"140","author":"Moore","year":"2014","journal-title":"J. Chem. Phys."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"680983","DOI":"10.3389\/fphy.2021.680983","article-title":"Coarse-Grained Modeling of Coronavirus Spike Proteins and ACE2 Receptors","volume":"9","author":"Leong","year":"2021","journal-title":"Front. Phys."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1097","DOI":"10.1016\/j.bpj.2020.10.048","article-title":"A multiscale coarse-grained model of the SARS-CoV-2 virion","volume":"120","author":"Yu","year":"2021","journal-title":"Biophys. J."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"134105","DOI":"10.1063\/1.2038787","article-title":"Multiscale coarse graining of liquid-state systems","volume":"123","author":"Izvekov","year":"2005","journal-title":"J. Chem. Phys."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"2469","DOI":"10.1021\/jp044629q","article-title":"A Multiscale Coarse-Graining Method for Biomolecular Systems","volume":"109","author":"Izvekov","year":"2005","journal-title":"J. Phys. Chem. B"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Voth, G.A. (2009). Coarse-Graining of Condensed Phase and Biomolecular Systems, CRC Press.","DOI":"10.1201\/9781420059564"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Liang, D., Zhang, Z., Rafailovich, M., Simon, M., Deng, Y., and Zhang, P. (2021). Beyond the Scales: A physics-informed machine learning approach for more efficient modeling of SARS-CoV-2 spike glycoprotein. Res. Sq.","DOI":"10.21203\/rs.3.rs-1011812\/v1"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"101895","DOI":"10.1016\/j.compmedimag.2021.101895","article-title":"Rapid analysis of streaming platelet images by semi-unsupervised learning","volume":"89","author":"Zhang","year":"2021","journal-title":"Comput. Med. Imaging Graph."},{"key":"ref_9","unstructured":"Zhang, Z., Zhang, P., Han, C., Cong, G., Yang, C.-C., and Deng, Y. (2020, January 16\u201319). AI Meets HPC: Learning the Cell Motion in Biofluids. Proceedings of the Supercomputing Conference 2020 (SC20), Atlanta, GA, USA. Research Posters Track."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"812248","DOI":"10.3389\/fmolb.2021.812248","article-title":"Online Machine Learning for Accelerating Molecular Dynamics Modeling of Cells","volume":"8","author":"Zhang","year":"2022","journal-title":"Front. Mol. Biosci."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"3452","DOI":"10.1007\/s10439-021-02790-3","article-title":"In Vitro Measurements of Shear-Mediated Platelet Adhesion Kinematics as Analyzed through Machine Learning","volume":"49","author":"Sheriff","year":"2021","journal-title":"Ann. Biomed. Eng."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"533","DOI":"10.1016\/S1473-3099(20)30120-1","article-title":"An interactive web-based dashboard to track COVID-19 in real time","volume":"20","author":"Dong","year":"2020","journal-title":"Lancet Infect. Dis."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"562","DOI":"10.1038\/s41564-020-0688-y","article-title":"Functional assessment of cell entry and receptor usage for SARS-CoV-2 and other lineage B betacoronaviruses","volume":"5","author":"Letko","year":"2020","journal-title":"Nat. Microbiol."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"953064","DOI":"10.3389\/fmolb.2022.953064","article-title":"Modeling of the thermal properties of SARS-CoV-2 S-protein","volume":"9","author":"Niu","year":"2022","journal-title":"Front. Mol. Biosci."},{"key":"ref_15","unstructured":"Song, M., Zhang, P., Han, C., Zhang, Z., and Deng, Y. (2020, January 16\u201319). Long-time simulation of temperature varying conformations of COVID-19 spike glycoprotein on IBM supercomputers. Proceedings of the Supercomputing Conference 2020 (SC20), Atlanta, GA, USA. Research Posters Track."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"362","DOI":"10.1557\/s43580-021-00021-4","article-title":"Supervised machine learning approach to molecular dynamics forecast of SARS-CoV-2 spike glycoproteins at varying temperatures","volume":"6","author":"Liang","year":"2021","journal-title":"MRS Adv."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"4183","DOI":"10.1529\/biophysj.108.139733","article-title":"Systematic Multiscale Parameterization of Heterogeneous Elastic Network Models of Proteins","volume":"95","author":"Lyman","year":"2008","journal-title":"Biophys. J."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1002","DOI":"10.1038\/s41467-022-28654-5","article-title":"Cooperative multivalent receptor binding promotes exposure of the SARS-CoV-2 fusion machinery core","volume":"13","author":"Pak","year":"2022","journal-title":"Nat. Commun."},{"key":"ref_19","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":"ref_20","doi-asserted-by":"crossref","first-page":"194101","DOI":"10.1063\/5.0026133","article-title":"Coarse graining molecular dynamics with graph neural networks","volume":"153","author":"Husic","year":"2020","journal-title":"J. Chem. Phys."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"2355","DOI":"10.1021\/acs.jctc.0c01343","article-title":"TorchMD: A Deep Learning Framework for Molecular Simulations","volume":"17","author":"Doerr","year":"2021","journal-title":"J. Chem. Theory Comput."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1016\/j.cell.2020.02.058","article-title":"Structure, Function, and Antigenicity of the SARS-CoV-2 Spike Glycoprotein","volume":"181","author":"Walls","year":"2020","journal-title":"Cell"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1781","DOI":"10.1002\/jcc.20289","article-title":"Scalable molecular dynamics with NAMD","volume":"26","author":"Phillips","year":"2005","journal-title":"J. Comput. Chem."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1767","DOI":"10.1016\/j.str.2006.10.003","article-title":"Stability and Dynamics of Virus Capsids Described by Coarse-Grained Modeling","volume":"14","author":"Arkhipov","year":"2006","journal-title":"Structure"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"192","DOI":"10.1016\/j.sbi.2007.03.004","article-title":"Multiscale modeling of biomolecular systems: In serial and in parallel","volume":"17","author":"Ayton","year":"2007","journal-title":"Curr. Opin. Struct. Biol."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1624","DOI":"10.1002\/jcc.10307","article-title":"Deriving effective mesoscale potentials from atomistic simulations: Mesoscale Potentials from Atomistic Simulations","volume":"24","author":"Reith","year":"2003","journal-title":"J. Comput. Chem."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"3378","DOI":"10.1021\/ma500320n","article-title":"Simultaneous Iterative Boltzmann Inversion for Coarse-Graining of Polyurea","volume":"47","author":"Agrawal","year":"2014","journal-title":"Macromolecules"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1016\/0263-7855(96)00018-5","article-title":"VMD: Visual molecular dynamics","volume":"14","author":"Humphrey","year":"1996","journal-title":"J. Mol. Graph."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"2806","DOI":"10.1529\/biophysj.108.132563","article-title":"Four-Scale Description of Membrane Sculpting by BAR Domains","volume":"95","author":"Arkhipov","year":"2008","journal-title":"Biophys. J."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"244114","DOI":"10.1063\/1.2938860","article-title":"The multiscale coarse-graining method. I. A rigorous bridge between atomistic and coarse-grained models","volume":"128","author":"Noid","year":"2008","journal-title":"J. Chem. Phys."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"7812","DOI":"10.1021\/jp071097f","article-title":"The MARTINI Force Field: Coarse Grained Model for Biomolecular Simulations","volume":"111","author":"Marrink","year":"2007","journal-title":"J. Phys. Chem. B"},{"key":"ref_32","unstructured":"(2008). The Concise Encyclopedia of Statistics, Springer."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"4289","DOI":"10.1529\/biophysj.106.094425","article-title":"Coarse-Grained Peptide Modeling Using a Systematic Multiscale Approach","volume":"92","author":"Zhou","year":"2007","journal-title":"Biophys. J."},{"key":"ref_34","doi-asserted-by":"crossref","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","author":"Huang","year":"2013","journal-title":"J. Comput. Chem."}],"container-title":["Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2079-3197\/11\/2\/24\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T18:22:36Z","timestamp":1760120556000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2079-3197\/11\/2\/24"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,2,2]]},"references-count":34,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2023,2]]}},"alternative-id":["computation11020024"],"URL":"https:\/\/doi.org\/10.3390\/computation11020024","relation":{},"ISSN":["2079-3197"],"issn-type":[{"value":"2079-3197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,2,2]]}}}