{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,6]],"date-time":"2026-10-06T15:58:32Z","timestamp":1791302312962,"version":"4.1.0"},"reference-count":39,"publisher":"American Chemical Society (ACS)","issue":"39","license":[{"start":{"date-parts":[[2026,9,18]],"date-time":"2026-09-18T00:00:00Z","timestamp":1789689600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100000038","name":"Natural Sciences and Engineering Research Council of Canada","doi-asserted-by":"publisher","award":["DGECR-2019-00087"],"award-info":[{"award-number":["DGECR-2019-00087"]}],"id":[{"id":"10.13039\/501100000038","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000038","name":"Natural Sciences and Engineering Research Council of Canada","doi-asserted-by":"publisher","award":["RGPIN 04598"],"award-info":[{"award-number":["RGPIN 04598"]}],"id":[{"id":"10.13039\/501100000038","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026,10,6]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>Protein behavior, whether evolved in nature or intentionally designed, is governed by the energetics of amino acid interactions that bridge sequence to function. As an extension of the theory of protein folding funnels, local frustration quantifies the optimality of these residue-level interactions relative to alternatives. Although this framework has existed for decades, experimental validation has remained elusive. Past deep mutational scanning datasets enable experimental assessment across nearly 8,000 positions from 178 proteins. Results provide experimental evidence for theoretical predictions regarding the relationship between local frustration and protein sequence, structure, and evolution. An evaluation of three in silico methods shows modest agreement with benchmarks (r = 0.03 to 0.26), with the predominant local frustration predictor (Protein Frustratometer) capturing under 3% of the experimental variance. A recent deep learning model, Pythia, outperformed other tools across all evaluated metrics (r = 0.42). Finally, this scale of empirical data enables an evaluation of the strengths and limitations of energetic measures themselves, inspiring a complementary Sequence Probability INverse (SPIN) framework, which characterizes optimality through a Boltzmann-weighted selection probability within an ensemble of sequences. These findings help provide experimental grounding for the theoretical principles that govern protein sequence energetics.<\/jats:p>","DOI":"10.1021\/acsomega.6c05138","type":"journal-article","created":{"date-parts":[[2026,9,18]],"date-time":"2026-09-18T19:02:09Z","timestamp":1789758129000},"page":"59271-59280","source":"Crossref","is-referenced-by-count":0,"title":["Examining Protein Residue-Level Stability Using Theory\nand Experiment"],"prefix":"10.1021","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7160-0535","authenticated-orcid":true,"given":"Andrew D.","family":"Sanders","sequence":"first","affiliation":[{"name":"The University of British Columbia , , , ,","place":["Vancouver, British Columbia, Canada, V6T 1Z4"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Rickey Y.","family":"Yada","sequence":"additional","affiliation":[{"name":"University of Alberta , , , ,","place":["Edmonton, Alberta, Canada, T6G 2R3"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4133-1020","authenticated-orcid":true,"given":"Derek R.","family":"Dee","sequence":"additional","affiliation":[{"name":"The University of British Columbia , , , ,","place":["Vancouver, British Columbia, Canada, V6T 1Z4"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"316","published-online":{"date-parts":[[2026,9,18]]},"reference":[{"key":"2026100610493251000_cit1","doi-asserted-by":"publisher","first-page":"223","DOI":"10.1126\/science.181.4096.223","article-title":"Principles\nthat govern the folding of protein chains","volume":"181","author":"Anfinsen","year":"1973","journal-title":"Science"},{"key":"2026100610493251000_cit2","article-title":"How to Fold Graciously","volume-title":"Mo\u0308ssbaun Spectroscopy in Biological Systems Proceedings","author":"Levinthal","year":"1969"},{"key":"2026100610493251000_cit3","doi-asserted-by":"publisher","first-page":"285","DOI":"10.1017\/S0033583514000092","article-title":"Frustration in Biomolecules","volume":"47","author":"Ferreiro","year":"2014","journal-title":"Q. Rev. Biophys."},{"key":"2026100610493251000_cit4","doi-asserted-by":"publisher","first-page":"452","DOI":"10.1110\/ps.9.3.452","article-title":"Entropic barriers, transition states,\nfunnels, and exponential protein\nfolding kinetics: A simple model","volume":"9","author":"Bicout","year":"2000","journal-title":"Protein Sci."},{"issue":"9","key":"2026100610493251000_cit5","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1613892114","article-title":"Evidence for the principle of minimal\nfrustration in the evolution of protein folding landscapes","volume":"114","author":"Tzul","year":"2017","journal-title":"Proc. Natl. Acad. Sci. U. S. A."},{"key":"2026100610493251000_cit6","doi-asserted-by":"publisher","DOI":"10.7554\/eLife.60895","article-title":"Gradual compaction of the nascent peptide during cotranslational\nfolding on the ribosome","volume":"9","author":"Liutkute","year":"2020","journal-title":"Elife"},{"key":"2026100610493251000_cit7","doi-asserted-by":"publisher","first-page":"6338","DOI":"10.1038\/s41467-023-41664-1","article-title":"Accurate prediction\nof protein folding mechanisms by simple structure-based\nstatistical mechanical models","volume":"14","author":"Ooka","year":"2023","journal-title":"Nat. Commun."},{"issue":"50","key":"2026100610493251000_cit8","doi-asserted-by":"publisher","first-page":"19819","DOI":"10.1073\/pnas.0709915104","article-title":"Localizing frustration\nin native proteins and protein assemblies","volume":"104","author":"Ferreiro","year":"2007","journal-title":"Proc.\nNatl. Acad. Sci. U. S. A."},{"issue":"33","key":"2026100610493251000_cit9","doi-asserted-by":"publisher","first-page":"16367","DOI":"10.1073\/pnas.1903888116","article-title":"Protein stability\nengineering insights revealed by domain-wide comprehensive mutagenesis","volume":"116","author":"Nisthal","year":"2019","journal-title":"Proc. Natl. Acad. Sci. U. S. A."},{"key":"2026100610493251000_cit10","doi-asserted-by":"publisher","first-page":"8379","DOI":"10.1038\/s41467-023-43801-2","article-title":"Local energetic frustration conservation in protein\nfamilies and superfamilies","volume":"14","author":"Freiberger","year":"2023","journal-title":"Nat. Commun."},{"issue":"10","key":"2026100610493251000_cit11","doi-asserted-by":"publisher","first-page":"3871","DOI":"10.1073\/pnas.1216597110","article-title":"SOD1 exhibits allosteric\nfrustration to facilitate\nmetal binding affinity","volume":"110","author":"Das","year":"2013","journal-title":"Proc. Natl. Acad. Sci.\nU. S. A."},{"issue":"10","key":"2026100610493251000_cit12","doi-asserted-by":"publisher","first-page":"4037","DOI":"10.1073\/pnas.1819859116","article-title":"Local frustration\naround enzyme active sites","volume":"116","author":"Freiberger","year":"2019","journal-title":"Proc. Natl. Acad.\nSci. U. S. A."},{"key":"2026100610493251000_cit13","doi-asserted-by":"publisher","DOI":"10.1002\/pro.5182","article-title":"A contact-based\nanalysis of local energetic frustration dynamics identifies key residues\nenabling RfaH fold-switch","volume":"33","author":"Gonza\u0301lez-Higueras","year":"2024","journal-title":"Protein Sci."},{"key":"2026100610493251000_cit14","doi-asserted-by":"publisher","DOI":"10.1002\/pro.4400","article-title":"Assessing\nand enhancing foldability in designed proteins","volume":"31","author":"Listov","year":"2022","journal-title":"Protein Sci."},{"key":"2026100610493251000_cit15","doi-asserted-by":"publisher","first-page":"699","DOI":"10.1007\/s00249-021-01500-0","article-title":"Evolution of frustrated\nand stabilising contacts in reconstructed ancient proteins","volume":"50","author":"Crippa","year":"2021","journal-title":"Eur. Biophys. J."},{"key":"2026100610493251000_cit16","doi-asserted-by":"publisher","first-page":"434","DOI":"10.1038\/s41586-023-06328-6","article-title":"Mega-scale experimental analysis of protein folding\nstability in biology and design","volume":"620","author":"Tsuboyama","year":"2023","journal-title":"Nature"},{"key":"2026100610493251000_cit17","doi-asserted-by":"publisher","first-page":"995","DOI":"10.1038\/s41586-024-07966-0","article-title":"The genetic architecture of protein stability","volume":"634","author":"Faure","year":"2024","journal-title":"Nature"},{"issue":"5","key":"2026100610493251000_cit18","doi-asserted-by":"publisher","first-page":"1295","DOI":"10.1016\/j.cell.2020.08.012","article-title":"Deep Mutational Scanning\nof SARS-CoV-2 Receptor\nBinding Domain Reveals Constraints on Folding and ACE2 Binding","volume":"182","author":"Starr","year":"2020","journal-title":"Cell"},{"key":"2026100610493251000_cit19","doi-asserted-by":"publisher","DOI":"10.1126\/science.abf8761","article-title":"Revealing enzyme functional architecture via high-throughput\nmicrofluidic enzyme kinetics","volume":"373","author":"Markin","year":"2021","journal-title":"Science"},{"key":"2026100610493251000_cit20","doi-asserted-by":"publisher","first-page":"643","DOI":"10.1038\/s41586-023-06954-0","article-title":"The energetic and allosteric\nlandscape for KRAS inhibition","volume":"626","author":"Weng","year":"2024","journal-title":"Nature"},{"key":"2026100610493251000_cit21","doi-asserted-by":"publisher","first-page":"885","DOI":"10.1038\/s41586-024-08370-4","article-title":"Site-saturation mutagenesis\nof 500 human protein domains","volume":"637","author":"Beltran","year":"2025","journal-title":"Nature"},{"key":"2026100610493251000_cit22","doi-asserted-by":"publisher","first-page":"5944","DOI":"10.1038\/s41467-020-19560-9","article-title":"Surveying\nbiomolecular frustration\nat atomic resolution","volume":"11","author":"Chen","year":"2020","journal-title":"Nat. Commun."},{"key":"2026100610493251000_cit23","doi-asserted-by":"publisher","first-page":"331","DOI":"10.1006\/jmbi.1993.1514","article-title":"Identification of\nthe Contact Surface of a Streptococcal\nProtein G Domain Complexed with a Human Fc Fragment","volume":"233","author":"Gronenborn","year":"1993","journal-title":"J. Mol. Biol."},{"key":"2026100610493251000_cit24","doi-asserted-by":"publisher","first-page":"W356","DOI":"10.1093\/nar\/gkw304","article-title":"Protein Frustratometer 2: a tool\nto localize energetic frustration in protein molecules, now with electrostatics","volume":"44","author":"Parra","year":"2016","journal-title":"Nucleic Acids Res."},{"key":"2026100610493251000_cit25","doi-asserted-by":"publisher","first-page":"1508","DOI":"10.1021\/acs.jcim.8b00697","article-title":"DeepDDG:\nPredicting the Stability Change of Protein Point Mutations Using Neural\nNetworks","volume":"59","author":"Cao","year":"2019","journal-title":"J. Chem. Inf. Model."},{"key":"2026100610493251000_cit26","doi-asserted-by":"publisher","first-page":"151","DOI":"10.1186\/1471-2105-12-151","article-title":"PoPMuSiC 2.1: a web\nserver for the estimation of protein stability changes upon mutation\nand sequence optimality","volume":"12","author":"Dehouck","year":"2011","journal-title":"BMC Bioinf."},{"key":"2026100610493251000_cit27","doi-asserted-by":"publisher","first-page":"100750","DOI":"10.1016\/j.xinn.2024.100750","article-title":"Structure-based self-supervised learning\nenables ultrafast protein stability prediction upon mutation","volume":"6","author":"Sun","year":"2025","journal-title":"Innovation"},{"key":"2026100610493251000_cit28","doi-asserted-by":"publisher","first-page":"3038","DOI":"10.1093\/bioinformatics\/btab176","article-title":"FrustratometeR:\nan R-package to compute local frustration in protein structures, point\nmutants and MD simulations","volume":"37","author":"Rausch","year":"2021","journal-title":"Bioinformatics"},{"key":"2026100610493251000_cit29","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":"2026100610493251000_cit30","doi-asserted-by":"publisher","first-page":"4497","DOI":"10.1021\/acs.jpcb.9b01545","article-title":"Localizing Frustration\nin Proteins Using All-Atom Energy Functions","volume":"123","author":"Chen","year":"2019","journal-title":"J. Phys. Chem. B"},{"key":"2026100610493251000_cit31","article-title":"Structural\nEquation Models with Non Normal Variables: Problems and remedies","volume-title":"Structural Equation Modeling: Concepts, Issues, and\nApplications","author":"West","year":"1995"},{"key":"2026100610493251000_cit32","doi-asserted-by":"publisher","first-page":"1303","DOI":"10.1103\/PhysRevE.50.1303","article-title":"Statistical\nmechanics of proteins with \u201cevolutionary\nselected\u201d sequences","volume":"50","author":"Ramanathan","year":"1994","journal-title":"Phys. Rev. E"},{"key":"2026100610493251000_cit33","doi-asserted-by":"publisher","first-page":"12408","DOI":"10.1073\/pnas.1413575111","article-title":"Coevolutionary\ninformation, protein folding landscapes, and the thermodynamics of\nnatural selection","volume":"111","author":"Morcos","year":"2014","journal-title":"Proc. Natl. Acad. Sci. U.\nS. A."},{"key":"2026100610493251000_cit34","volume-title":"Empirical model-building\nand response surfaces","author":"Box","year":"1987"},{"key":"2026100610493251000_cit35","doi-asserted-by":"publisher","first-page":"8611","DOI":"10.1073\/pnas.1000988107","article-title":"Insights into\nprotein folding mechanisms from large\nscale analysis of mutational effects","volume":"107","author":"Naganathan","year":"2010","journal-title":"Proc.\nNatl. Acad. Sci. U. S. A."},{"key":"2026100610493251000_cit36","doi-asserted-by":"publisher","first-page":"1139","DOI":"10.1038\/s41586-026-10328-7","article-title":"The past, present and future of de novo protein design","volume":"652","author":"Yang","year":"2026","journal-title":"Nature"},{"key":"2026100610493251000_cit37","doi-asserted-by":"publisher","first-page":"447","DOI":"10.1006\/jmbi.2000.4474","article-title":"ConSurf: an algorithmic\ntool for\nthe identification of functional regions in proteins by surface mapping\nof phylogenetic information1","volume":"307","author":"Armon","year":"2001","journal-title":"J. Mol. Biol."},{"issue":"3","key":"2026100610493251000_cit38","doi-asserted-by":"publisher","first-page":"319","DOI":"10.1002\/(SICI)1096-987X(199802)19:3&lt;319::AID-JCC6&gt;3.0.CO;2-W","article-title":"Exact and efficient\nanalytical calculation of the accessible surface\nareas and their gradients for macromolecules","volume":"19","author":"Fraczkiewicz","year":"1998","journal-title":"J. Comput. Chem."},{"key":"2026100610493251000_cit39","doi-asserted-by":"publisher","first-page":"70","DOI":"10.1002\/pro.3943","article-title":"UCSF ChimeraX: Structure\nvisualization for researchers, educators, and developers","volume":"30","author":"Pettersen","year":"2021","journal-title":"Protein Sci."}],"container-title":["ACS Omega"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/pubs.acs.org\/doi\/pdf\/10.1021\/acsomega.6c05138","content-type":"application\/pdf","content-version":"vor","intended-application":"unspecified"},{"URL":"https:\/\/pubs.acs.org\/acsodf\/article-pdf\/11\/39\/59271\/68559563\/acsomega.6c05138.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/pubs.acs.org\/acsodf\/article-pdf\/11\/39\/59271\/68559563\/acsomega.6c05138.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,10,6]],"date-time":"2026-10-06T15:30:32Z","timestamp":1791300632000},"score":1,"resource":{"primary":{"URL":"https:\/\/pubs.acs.org\/acsodf\/article\/11\/39\/59271\/5433007\/Examining-Protein-Residue-Level-Stability-Using"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,9,18]]},"references-count":39,"journal-issue":{"issue":"39","published-online":{"date-parts":[[2026,9,18]]},"published-print":{"date-parts":[[2026,10,6]]}},"URL":"https:\/\/doi.org\/10.1021\/acsomega.6c05138","relation":{},"ISSN":["2470-1343"],"issn-type":[{"value":"2470-1343","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,9,18]]}}}