{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:00:16Z","timestamp":1760148016555,"version":"build-2065373602"},"reference-count":46,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2023,3,21]],"date-time":"2023-03-21T00:00:00Z","timestamp":1679356800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Transcription factors (TFs) and microRNAs (miRNAs) are co-actors in genome-scale decoding and regulatory networks, often targeting common genes. To discover the symmetries and invariants of the transcription and regulation at the scale of the genome, in this paper, we introduce tools of infinite group theory and of algebraic geometry to describe both TFs and miRNAs. In TFs, the generator of the group is a DNA-binding domain while, in miRNAs, the generator is the seed of the sequence. For such a generated (infinite) group \u03c0, we compute the SL(2,C) character variety, where SL(2,C) is simultaneously a \u2018space-time\u2019 (a Lorentz group) and a \u2018quantum\u2019 (a spin) group. A noteworthy result of our approach is to recognize that optimal regulation occurs when \u03c0 looks similar to a free group Fr (r=1 to 3) in the cardinality sequence of its subgroups, a result obtained in our previous papers. A non-free group structure features a potential disease. A second noteworthy result is about the structure of the Groebner basis G of the variety. A surface with simple singularities (such as the well known Cayley cubic) within G is a signature of a potential disease even when \u03c0 looks similar to a free group Fr in its structure of subgroups. Our methods apply to groups with a generating sequence made of two to four distinct DNA\/RNA bases in {A,T\/U,G,C}. We produce a few tables of human TFs and miRNAs showing that a disease may occur when either \u03c0 is away from a free group or G contains surfaces with isolated singularities.<\/jats:p>","DOI":"10.3390\/sym15030770","type":"journal-article","created":{"date-parts":[[2023,3,21]],"date-time":"2023-03-21T06:56:48Z","timestamp":1679381808000},"page":"770","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Algebraic Morphology of DNA\u2013RNA Transcription and Regulation"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5739-546X","authenticated-orcid":false,"given":"Michel","family":"Planat","sequence":"first","affiliation":[{"name":"CNRS, Institut FEMTO-ST, Universit\u00e9 de Franche-Comt\u00e9, F-25044 Besan\u00e7on, France"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0637-1916","authenticated-orcid":false,"given":"Marcelo M.","family":"Amaral","sequence":"additional","affiliation":[{"name":"Quantum Gravity Research, Los Angeles, CA 90290, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2938-3941","authenticated-orcid":false,"given":"Klee","family":"Irwin","sequence":"additional","affiliation":[{"name":"Quantum Gravity Research, Los Angeles, CA 90290, USA"}]}],"member":"1968","published-online":{"date-parts":[[2023,3,21]]},"reference":[{"key":"ref_1","unstructured":"U\u017edavinys, A. 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