{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,17]],"date-time":"2026-09-17T14:01:51Z","timestamp":1789653711689,"version":"4.0.0"},"reference-count":33,"publisher":"American Chemical Society (ACS)","issue":"37","license":[{"start":{"date-parts":[[2026,9,4]],"date-time":"2026-09-04T00:00:00Z","timestamp":1788480000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001700","name":"Ministry of Education, Culture, Sports, Science and Technology","doi-asserted-by":"publisher","award":["JPMXS0118067246"],"award-info":[{"award-number":["JPMXS0118067246"]}],"id":[{"id":"10.13039\/501100001700","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001691","name":"Japan Society for the Promotion of Science","doi-asserted-by":"publisher","award":["23H00503"],"award-info":[{"award-number":["23H00503"]}],"id":[{"id":"10.13039\/501100001691","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002241","name":"Japan Science and Technology Agency","doi-asserted-by":"publisher","award":["JP- MJPF2013"],"award-info":[{"award-number":["JP- MJPF2013"]}],"id":[{"id":"10.13039\/501100002241","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Oda pharmaceutical Co.Ltd and Os? Lab"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026,9,17]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>Torsion sign flips are fundamental discrete events in protein backbone dynamics, yet their geometric triggers remain poorly understood. While traditionally associated with singular critical points, we show that these transitions are primarily driven by local geometric instability, quantified by the Laplacian of a curvature-derived support field, \u0394S. Through a large-scale analysis of over 1.3 million residue positions from 3,000 PDB structures, we demonstrate a robust physical law: flip events are significantly depleted in Laplacian-zero (locally balanced) regions and exhibit progressively higher enrichment as the instability magnitude |\u0394S| increases. This supports an instability-associated statistical interpretation in which geometric imbalance is correlated with an increased propensity for torsion inversions in the analyzed static structural data set. We further identify a \u201ctopological locking\u201d effect, where looplike constraints systematically suppress flips, particularly in high-instability regimes. Multivariate modeling confirms that \u0394S provides predictive information inaccessible to standard local descriptors (curvature and torsion). Our results establish a physically interpretable framework linking discrete differential geometry to stochastic backbone dynamics, revealing how local geometric imbalance and global structural constraints are jointly associated with torsion sign-flip propensity in experimentally determined static protein structures.<\/jats:p>","DOI":"10.1021\/acs.jpcb.6c03120","type":"journal-article","created":{"date-parts":[[2026,9,5]],"date-time":"2026-09-05T01:02:19Z","timestamp":1788570139000},"page":"9406-9417","source":"Crossref","is-referenced-by-count":0,"title":["Instability-Driven\nTorsion Sign Flips Revealed by\nthe Laplacian Structure of Curvature Support Fields in Protein Backbones"],"prefix":"10.1021","volume":"130","author":[{"ORCID":"https:\/\/orcid.org\/0009-0002-4486-8285","authenticated-orcid":true,"given":"Jianshi","family":"Wang","sequence":"first","affiliation":[{"name":"The University of Tokyo , , Hongo 7-3-1 , , ,","place":["Bunkyo-ku, Tokyo, Japan, 113-8656"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yukio","family":"Ohsawa","sequence":"additional","affiliation":[{"name":"The University of Tokyo , , Hongo 7-3-1 , , ,","place":["Bunkyo-ku, Tokyo, Japan, 113-8656"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"316","published-online":{"date-parts":[[2026,9,4]]},"reference":[{"key":"2026091708470496800_cit1","doi-asserted-by":"publisher","first-page":"646","DOI":"10.1038\/nsb0902-646","article-title":"Molecular dynamics\nsimulations of biomolecules","volume":"9","author":"Karplus","year":"2002","journal-title":"Nat. Struct. Biol."},{"key":"2026091708470496800_cit2","doi-asserted-by":"publisher","first-page":"341","DOI":"10.1126\/science.1187409","article-title":"Atomic-level characterization of\nthe structural dynamics of proteins","volume":"330","author":"Shaw","year":"2010","journal-title":"Science"},{"key":"2026091708470496800_cit3","doi-asserted-by":"publisher","first-page":"429","DOI":"10.1146\/annurev-biophys-042910-155245","article-title":"Biomolecular\nsimulation: a computational microscope for molecular biology","volume":"41","author":"Dror","year":"2012","journal-title":"Annu. Rev. Biophys."},{"key":"2026091708470496800_cit4","doi-asserted-by":"publisher","first-page":"517","DOI":"10.1126\/science.1208351","article-title":"How fast-folding\nproteins fold","volume":"334","author":"Lindorff-Larsen","year":"2011","journal-title":"Science"},{"key":"2026091708470496800_cit5","doi-asserted-by":"publisher","first-page":"964","DOI":"10.1038\/nature06522","article-title":"Dynamic personalities\nof proteins","volume":"450","author":"Henzler-Wildman","year":"2007","journal-title":"Nature"},{"key":"2026091708470496800_cit6","doi-asserted-by":"publisher","first-page":"289","DOI":"10.1146\/annurev.biophys.37.092707.153558","article-title":"The Protein Folding\nProblem","volume":"37","author":"Dill","year":"2008","journal-title":"Annu. Rev. Biophys."},{"key":"2026091708470496800_cit7","doi-asserted-by":"publisher","first-page":"505","DOI":"10.1016\/S0006-3495(01)76033-X","article-title":"Anisotropy of fluctuation\ndynamics of proteins with an elastic network\nmodel","volume":"80","author":"Atilgan","year":"2001","journal-title":"Biophys. J."},{"key":"2026091708470496800_cit8","doi-asserted-by":"publisher","first-page":"1463","DOI":"10.1021\/cr900095e","article-title":"Normal\nmode analysis of biomolecular structures: functional mechanisms of\nmembrane proteins","volume":"110","author":"Bahar","year":"2010","journal-title":"Chem. Rev."},{"key":"2026091708470496800_cit9","doi-asserted-by":"publisher","first-page":"417","DOI":"10.1002\/(SICI)1097-0134(19981115)33:3&lt;417::AID-PROT10&gt;3.0.CO;2-8","article-title":"Analysis of\ndomain motions by approximate normal mode calculations","volume":"33","author":"Hinsen","year":"1998","journal-title":"Proteins"},{"key":"2026091708470496800_cit10","doi-asserted-by":"publisher","first-page":"583","DOI":"10.1038\/s41586-021-03819-2","article-title":"Highly accurate protein\nstructure prediction with AlphaFold","volume":"596","author":"Jumper","year":"2021","journal-title":"Nature"},{"key":"2026091708470496800_cit11","doi-asserted-by":"publisher","first-page":"195","DOI":"10.1021\/cr60270a003","article-title":"Theoretical\nand experimental studies of conformations of polypeptides","volume":"71","author":"Scheraga","year":"1971","journal-title":"Chem. Rev."},{"key":"2026091708470496800_cit12","doi-asserted-by":"publisher","first-page":"5138","DOI":"10.1021\/bi00668a030","article-title":"Status of empirical methods for the prediction of protein\nbackbone topography","volume":"15","author":"Maxfield","year":"1976","journal-title":"Biochemistry"},{"key":"2026091708470496800_cit13","doi-asserted-by":"publisher","first-page":"418","DOI":"10.1002\/prot.22357","article-title":"Description and recognition\nof regular and distorted secondary structures in proteins using the\nautomated protein structure analysis method","volume":"76","author":"Ranganathan","year":"2009","journal-title":"Proteins"},{"key":"2026091708470496800_cit14","doi-asserted-by":"publisher","first-page":"024406","DOI":"10.1103\/PhysRevE.111.024406","article-title":"Local topology and\nperestroikas in protein structure and folding dynamics","volume":"111","author":"Begun","year":"2025","journal-title":"Phys. Rev. E"},{"key":"2026091708470496800_cit15","doi-asserted-by":"publisher","DOI":"10.1093\/oso\/9780195140187.001.0001","volume-title":"Nonequilibrium Statistical\nMechanics","author":"Zwanzig","year":"2001"},{"key":"2026091708470496800_cit16","first-page":"447","volume-title":"Stochastic Methods:\nA Handbook for the Natural and Social Sciences","author":"Gardiner","year":"2009","edition":"4th"},{"key":"2026091708470496800_cit17","doi-asserted-by":"publisher","DOI":"10.1016\/B978-0-444-52965-7.X5000-4","volume-title":"Stochastic\nProcesses in Physics and Chemistry","author":"van Kampen","year":"2007","edition":"3rd"},{"key":"2026091708470496800_cit18","doi-asserted-by":"publisher","first-page":"300","DOI":"10.1063\/1.1749657","article-title":"Statistical\nmechanics of fluid mixtures","volume":"3","author":"Kirkwood","year":"1935","journal-title":"J. Chem. Phys."},{"key":"2026091708470496800_cit19","doi-asserted-by":"publisher","first-page":"143","DOI":"10.1080\/00018737900101365","article-title":"The nature\nof the liquid-vapour interface and other topics in the statistical\nmechanics of non-uniform fluids","volume":"28","author":"Evans","year":"1979","journal-title":"Adv. Phys."},{"key":"2026091708470496800_cit20","doi-asserted-by":"publisher","first-page":"045317","DOI":"10.1063\/5.0315788","article-title":"A continuum support\nfield theory with mass conservation\nfor micro-scale structural rearrangement","volume":"16","author":"Wang","year":"2026","journal-title":"AIP\nAdv."},{"key":"2026091708470496800_cit21","doi-asserted-by":"publisher","first-page":"10","DOI":"10.1038\/s44341-026-00040-y","article-title":"Density-Driven Support Fields for Topological Stability\nin Protein Structures","volume":"3","author":"Wang","year":"2026","journal-title":"Npj Biol. Phys. Mech."},{"key":"2026091708470496800_cit22","doi-asserted-by":"publisher","first-page":"42","DOI":"10.1038\/s44385-025-00045-7","article-title":"Support field\nneural representation learner framework for learning stability landscapes\nin molecular geometry","volume":"2","author":"Wang","year":"2025","journal-title":"Npj Biomed. Innov."},{"key":"2026091708470496800_cit23","doi-asserted-by":"publisher","first-page":"111802","DOI":"10.1103\/PhysRevLett.130.111802","article-title":"Phase Structure\nof Electroweak Vacuum\nin a Strong Magnetic Field: The Lattice Results","volume":"130","author":"Chernodub","year":"2023","journal-title":"Phys. Rev. Lett."},{"key":"2026091708470496800_cit24","doi-asserted-by":"publisher","first-page":"17249","DOI":"10.1038\/s41598-025-01410-7","article-title":"TCoCPIn reveals topological characteristics of chemical\nprotein interaction networks for novel feature discovery","volume":"15","author":"Wang","year":"2025","journal-title":"Sci. Rep."},{"key":"2026091708470496800_cit25","doi-asserted-by":"publisher","DOI":"10.1016\/C2010-0-66723-X","volume-title":"Theory of Simple Liquids:\nWith Applications to Soft Matter","author":"Hansen","year":"2013","edition":"4th"},{"key":"2026091708470496800_cit26","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4614-6980-3","volume-title":"Stochastic Tools in\nMathematics and Science","author":"Chorin","year":"2013","edition":"3rd"},{"key":"2026091708470496800_cit27","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-61544-3","volume-title":"The Fokker\u2013Planck\nEquation: Methods of Solution and Applications","author":"Risken","year":"1996","edition":"2nd"},{"key":"2026091708470496800_cit28","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1137\/S0036141096303359","article-title":"The variational formulation\nof the\nFokker\u2013Planck equation","volume":"29","author":"Jordan","year":"1998","journal-title":"SIAM J. Math.\nAnal."},{"key":"2026091708470496800_cit29","doi-asserted-by":"publisher","first-page":"3939","DOI":"10.1021\/acs.jpcb.4c07910","article-title":"Effect of a Knot on the Thermal Stability\nof Protein MJ0366: Insights into Molecular Dynamics and Monte Carlo\nSimulations","volume":"129","author":"Begun","year":"2025","journal-title":"J. Phys. Chem. B"},{"key":"2026091708470496800_cit30","doi-asserted-by":"publisher","first-page":"3050","DOI":"10.1073\/pnas.71.8.3050","article-title":"Classical\nstatistical mechanics of constraints","volume":"71","author":"Fixman","year":"1974","journal-title":"Proc.\nNatl. Acad. Sci. U.S.A."},{"key":"2026091708470496800_cit31","doi-asserted-by":"publisher","first-page":"275","DOI":"10.1016\/0010-4655(95)00053-I","article-title":"The calculation\nof the potential of mean force using computer simulations","volume":"91","author":"Roux","year":"1995","journal-title":"Comput. Phys. Commun."},{"key":"2026091708470496800_cit32","doi-asserted-by":"publisher","first-page":"257","DOI":"10.1090\/conm\/453\/08802","article-title":"Persistent homology\u2013a survey","volume":"453","author":"Edelsbrunner","year":"2008","journal-title":"Contemp.\nMath."},{"key":"2026091708470496800_cit33","doi-asserted-by":"publisher","first-page":"255","DOI":"10.1090\/S0273-0979-09-01249-X","article-title":"Topology and\ndata","volume":"46","author":"Carlsson","year":"2009","journal-title":"Bull. Am. Math. Soc."}],"container-title":["The Journal of Physical\nChemistry B"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/pubs.acs.org\/doi\/pdf\/10.1021\/acs.jpcb.6c03120","content-type":"application\/pdf","content-version":"vor","intended-application":"unspecified"},{"URL":"https:\/\/pubs.acs.org\/jpcbfk\/article-pdf\/130\/37\/9406\/68394603\/acs.jpcb.6c03120.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/pubs.acs.org\/jpcbfk\/article-pdf\/130\/37\/9406\/68394603\/acs.jpcb.6c03120.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,9,17]],"date-time":"2026-09-17T13:03:28Z","timestamp":1789650208000},"score":1,"resource":{"primary":{"URL":"https:\/\/pubs.acs.org\/jpcbfk\/article\/130\/37\/9406\/5421816\/Instability-Driven-Torsion-Sign-Flips-Revealed-by"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,9,4]]},"references-count":33,"journal-issue":{"issue":"37","published-online":{"date-parts":[[2026,9,4]]},"published-print":{"date-parts":[[2026,9,17]]}},"URL":"https:\/\/doi.org\/10.1021\/acs.jpcb.6c03120","relation":{},"ISSN":["1520-6106","1520-5207"],"issn-type":[{"value":"1520-6106","type":"print"},{"value":"1520-5207","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,9,4]]}}}