Group Theory of Messenger RNA Metabolism and Disease

Abstract

Our recent work has focused on the application of infinite group theory and related algebraic geometric tools in the context of transcription factors and microRNAs. We were able to differentiate between "healthy" nucleotide sequences and disrupted sequences that may be associated with various diseases. In this paper, we extend our efforts to the study of messenger RNA (mRNA) metabolism, showcasing the power of our approach. We investigate (1) mRNA translation in prokaryotes and eukaryotes, (2) polyadenylation in eukaryotes, which is crucial for nuclear export, translation, stability, and splicing of mRNA, (3) microRNAs involved in RNA silencing and post-transcriptional regulation of gene expression, and (4) identification of disrupted sequences that could lead to potential illnesses. To achieve this, we used: (a) infinite (finitely generated) groups f p , with generators representing the r + 1 distinct nucleotides and a relation between them [e.g., the consensus sequence in the mRNA translation (i), the poly (A) tail in item (ii), and the microRNA seed in item (iii)]; (b) aperiodicity theory, which connects healthy groups f p to free groups F r of rank r and their profinite completion ˆr F , and (c) the representation theory of groups f p over the space-time-spin group SL 2 (C), highlighting the role of surfaces with isolated singularities in the character variety. Our approach could potentially contribute to the understanding of the molecular mechanisms underlying various diseases and help develop new diagnostic or therapeutic strategies.

Topology and Dynamics of Transcriptome (Dys)regulation

“…Chemical modifications in the environment also controls the metabolism of GE. For instance, RNA methylation with N 6 -methymadenosine (m 6 A) is documented in our recent paper [8].…”

“…Since the genome is digital with its four nucleotides A, U/T, G and C as letters, there are important short sequences as the consensus sequence of a transcription factor, a TATA box, a polyadenymation signal or a microRNA (miRNA) whose structure should obey group theory and associated character variety rules. Otherwise, a disease is in sight [6][7][8]. Chemical modifications in the environment also controls the metabolism of GE.…”

“…Schrödinger's book [9] proposes aperiodicity of living "crystals". Our papers [7,8] characterize some aperiodic DNA/RNA sequences. But in this paper we do not focus on this aspect of genome scale homeostasis.…”