Menzerath-Altmann's Law of Syntax in RNA Accretion History

RNA evolves by adding substructural parts to growing molecules. Molecular accretion history can be dissected with phylogenetic methods that exploit structural and functional evidence. Here, we explore the statistical behaviors of lengths of double-stranded and single-stranded segments of growing tRNA, 5S rRNA, RNase P RNA, and rRNA molecules. The reconstruction of character state changes along branches of phylogenetic trees of molecules and trees of substructures revealed strong pushes towards an economy of scale. In addition, statistically significant negative correlations and strong associations between the average lengths of helical double-stranded stems and their time of origin (age) were identified with the Pearson's correlation and Spearman's rho methods. The ages of substructures were derived directly from published rooted trees of substructures. A similar negative correlation was detected in unpaired segments of rRNA but not for the other molecules studied. These results suggest a principle of diminishing returns in RNA accretion history. We show this principle follows a tendency of substructural parts to decrease their size when molecular systems enlarge that follows the Menzerath-Altmann's law of language in full generality and without interference from the details of molecular growth.