{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,3]],"date-time":"2026-10-03T04:52:36Z","timestamp":1791003156254,"version":"4.1.0"},"reference-count":30,"publisher":"Wiley","license":[{"start":{"date-parts":[[2026,10,2]],"date-time":"2026-10-02T00:00:00Z","timestamp":1790899200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"},{"start":{"date-parts":[[2026,10,2]],"date-time":"2026-10-02T00:00:00Z","timestamp":1790899200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Proteins"],"abstract":"<jats:title>ABSTRACT<\/jats:title>\n                  <jats:p>A central challenge in dynamic allostery is understanding how local ligand\u2010binding events selectively route and couple distant communication pathways. Here, we develop the Laplacian minor hierarchy, a parameter\u2010free mathematical framework that extracts higher\u2010order geometric invariants directly from protein contact networks. To incorporate explicit ligand interactions without computational truncation, we develop a block\u2010matrix Schur complement reduction scheme that projects pathways introduced by bound ligands directly onto an effective protein Laplacian. We apply this framework across all eight benchmark structures of the PSD95\u2010PDZ3 domain to map its evolutionary adaptation from Class I (CRIPT) to Class II (T\u20102F) ligand specificity via the G330T and H372A mutations. Evaluating doublet, triplet, and quadruplet pathway couplings shows that allosteric rewiring is governed by network\u2010level epistasis, where the surface\u2010loop mutation G330T opens communication routes that the active\u2010site mutation H372A subsequently exploits. Quadruplet correlation profiles collapse into two distinct quantitative regimes governed entirely by the pivot residue Thr332. These results indicate the potential of the Laplacian minor hierarchy as a rigorous, physically grounded framework for analyzing path organization, long\u2010range communication, and the topological basis of allosteric epistasis in proteins.<\/jats:p>","DOI":"10.1002\/prot.70188","type":"journal-article","created":{"date-parts":[[2026,10,3]],"date-time":"2026-10-03T03:57:56Z","timestamp":1790999876000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["The Geometry of Allostery: Quantifying Pathway Organization in Protein Networks"],"prefix":"10.1002","author":[{"ORCID":"https:\/\/orcid.org\/0009-0001-6901-6364","authenticated-orcid":false,"given":"Fatma Senguler","family":"Ciftci","sequence":"first","affiliation":[{"name":"Department of Chemical and Biological Engineering Koc University  Istanbul Turkey"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2496-6059","authenticated-orcid":false,"given":"Burak","family":"Erman","sequence":"additional","affiliation":[{"name":"Department of Chemical and Biological Engineering Koc University  Istanbul Turkey"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2026,10,2]]},"reference":[{"key":"e_1_2_11_2_1","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1016\/0169-7439(91)80051-Q","article-title":"Novel Graph Theoretical Approach to Heteroatoms in Quantitative Structure\u2010Activity Relationships","volume":"10","author":"Randic M.","year":"1991","journal-title":"Chemometrics and Intelligent Laboratory Systems"},{"key":"e_1_2_11_3_1","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1007\/BF01164627","article-title":"M. 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