Mathematical model of a short translatable G-quadruplex and an assessment of its relevance to misfolding-induced proteostasis

G-quadruplexes can form in protein coding and non-coding segments such as the untranslated regions and introns of the mRNA transcript of several genes. This implies that amino acid forms of the G-quadruplex may have important consequences for protein homeostasis and the diseases caused by their alterations thereof. However, the absence of a suitable model and multitude of predicted physical forms has precluded a comprehensive enumeration and analysis of potential translatable G-quadruplexes. In this manuscript a mathematical model of a short translatable G-quadruplex (TG4) in the protein coding segment of the mRNA of a hypothetical gene is presented. Several novel indices (α, β) are formulated and utilized to categorize and select codons along with the amino acids that they code for. A generic algorithm is then iteratively deployed which computes the entire complement of peptide members that TG4 corresponds to, i.e., PTG4~TG4. The presence, distribution and relevance of this peptidome to protein sequence is investigated by comparing it with disorder promoting short linear motifs. In frame termination codon, co-occurrence, homology and distribution of overlapping/shared amino acids suggests that TG4 (~PTG4) may facilitate misfolding-induced proteostasis. The findings presented rigorously argue for the existence of a unique and potentially clinically relevant peptidome of a short translatable G-quadruplex that could be used as a diagnostic- or prognostic-screen of certain proteopathies.