{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,12]],"date-time":"2026-08-12T04:32:00Z","timestamp":1786509120307,"version":"build-2736575974"},"reference-count":19,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2026,8,10]],"date-time":"2026-08-10T00:00:00Z","timestamp":1786320000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Genes"],"abstract":"<jats:p>Background\/Objectives: The hierarchical organization of topological associating domains (TADs) is a fundamental feature of three-dimensional genome architecture, yet its systematic characterization remains challenging due to the scale-dependent nature of conventional detection methods. Here, we applied hyperbolic embedding into a Poincar\u00e9 disc to analyze TAD hierarchies from Hi-C data. Methods: Genomic loci were projected onto the disc such that the radial coordinate encodes hierarchical depth: subTADs localize near the center, while metaTADs shift toward the periphery. The method was validated on ten cell lines, including the isogenic MCF10A\/MCF7 pair, and does not require manual parameter tuning across resolutions. Results: In the MCF10A\/MCF7 isogenic system, neoplastic transformation was associated with a redistribution of the hierarchy: the number of small TADs (levels 1\u20133) decreased by 6.7%, whereas large TADs (levels 4\u20136) increased by 4.7%, with the largest domains (level 6) showing a 33.9% increase. Comparison with standard approaches\u2014Insulation Score (IS) and Directionality Index (DI)\u2014yielded an average Jaccard index of 0.568 and F1 score of 0.718 against DI. Conclusions: Unlike IS and DI, which operate at fixed scales, the proposed approach recovers the full TAD hierarchy from a single embedding, enabling cross-resolution and cross-cell-line comparisons without parameter reoptimization. These results demonstrate that the Poincar\u00e9 disc method provides a robust, interpretable, and scale-invariant framework for detecting hierarchical chromatin rearrangements associated with cancer.<\/jats:p>","DOI":"10.3390\/genes17080932","type":"journal-article","created":{"date-parts":[[2026,8,10]],"date-time":"2026-08-10T15:10:24Z","timestamp":1786374624000},"page":"932","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Applying the Poincar\u00e9 Disc Method to Analyze the Hierarchical Structure of TADs in Hi-C Data"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7212-5230","authenticated-orcid":false,"given":"Andrey","family":"Timofeev","sequence":"first","affiliation":[{"name":"LLC \u201cAI Center for SCO+ Countries\u201d, St. Petersburg 197341, Russia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0009-9697-0194","authenticated-orcid":false,"given":"Alexander","family":"Bratchikov","sequence":"additional","affiliation":[{"name":"LLC \u201cAI Center for SCO+ Countries\u201d, St. Petersburg 197341, Russia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0009-6391-3193","authenticated-orcid":false,"given":"Alexander","family":"Anufriev","sequence":"additional","affiliation":[{"name":"LLC \u201cAI Center for SCO+ Countries\u201d, St. Petersburg 197341, Russia"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,8,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"240","DOI":"10.1038\/nature14450","article-title":"Condensin-driven remodelling of X chromosome topology during dosage compensation","volume":"523","author":"Crane","year":"2015","journal-title":"Nature"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"376","DOI":"10.1038\/nature11082","article-title":"Topological domains in mammalian genomes identified by analysis of chromatin interactions","volume":"485","author":"Dixon","year":"2012","journal-title":"Nature"},{"key":"ref_3","unstructured":"Nickel, M., and Kiela, D. 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