Topology and Dynamics of Transcriptome (Dys)Regulation - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue International Journal of Molecular Sciences Année : 2024

Topology and Dynamics of Transcriptome (Dys)Regulation

Résumé

RNA transcripts play a crucial role as witnesses of gene expression health. Identifying disruptive short sequences in RNA transcription and regulation is essential for potentially treating diseases. Let us delve into the mathematical intricacies of these sequences. We have previously devised a mathematical approach for defining a “healthy” sequence. This sequence is characterized by having at most four distinct nucleotides (denoted as $nt$ ≤ 4). It serves as the generator of a group denoted as $fp$ . The desired properties of this sequence are as follows: $fp$ should be close to a free group of rank $nt$−1 , it must be aperiodic, and $fp$ should not have isolated singularities within its $SL_2\mathbb{C}$ character variety (specifically within the corresponding Groebner basis). Now, let us explore the concept of singularities. There are cubic surfaces associated with the character variety of a four-punctured sphere denoted as S$^4_2$. When we encounter these singularities, we find ourselves dealing with some algebraic solutions of a dynamical second-order differential (and transcendental) equation known as the Painlevé VI Equation. In certain cases, S$^4_2$ degenerates, in the sense that two punctures collapse, resulting in a “wild” dynamics governed by the Painlevé equations of an index lower than VI. In our paper, we provide examples of these fascinating mathematical structures within the context of miRNAs. Specifically, we find a clear relationship between decorated character varieties of Painlevé equations and the character variety calculated from the seed of oncomirs. These findings should find many applications including cancer research and the investigation of neurodegenative diseases
Fichier principal
Vignette du fichier
3a72639d-94da-4b5d-941b-7974fc828a82-author.pdf (1.87 Mo) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-04693035 , version 1 (10-09-2024)

Identifiants

Citer

Michel Planat, David Chester. Topology and Dynamics of Transcriptome (Dys)Regulation. International Journal of Molecular Sciences, 2024, 25 (9), pp.4971. ⟨10.3390/ijms25094971⟩. ⟨hal-04693035⟩
0 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Mastodon Facebook X LinkedIn More