Base pairing constraints drive structural epistasis in ribosomal RNA sequences.

It has long been accepted that the structural constraints stemming from the 3D structure of ribosomal RNA (rRNA) lead to coevolution through compensating mutations between interacting sites. State-of-the-art methods for detecting coevolving sites, however, while reaching high levels of specificity and sensitivity for Watson-Crick (WC) pairs of the helices defining the secondary structure, only scarcely reveal tertiary interactions occurring at the level of the 3D structure. In order to understand the relative failure of coevolutionary methods to detect such interactions, we analyze 2,682 interacting sites derived from high-resolution structures, which include a comprehensive data set of rRNA sequences from Archaea and Bacteria. We report a striking difference in the amount of coevolution between WC and non-WC pairs. In order to understand this pattern, we derive fitness landscapes from the geometry of base pairing interactions and construct neutral networks of substitutions for each type of interaction. These networks show that coevolution is a property of WC pairs because, unlike non-WC pairs, their landscapes exhibit fitness valleys, a single mutation in a WC pair resulting in a fitness drop. Second, we used the inferred neutral networks to estimate the level of constraint acting on each type of base pair and show that it correlates negatively with the observed rate of substitutions for all non-WC pairs. WC pairs appear as outliers, fixing more substitutions than expected according to their level of constraint. We here propose that the rate of substitution in WC pairs is due to coevolution resulting from constraints acting at intermediate levels of organization, namely the one of the helical stem with its forming WC pairs. In agreement with this hypothesis, we report a significant excess of intrahelical, inter-WC pairs coevolution compared with interhelices pairs. Altogether, these results show that detailed biochemical knowledge is required and has to be incorporated into evolutionary reasoning in order to understand the fine patterns of variation at the molecular level. They also demonstrate that coevolutionary analysis provides almost exclusively 2D information and only little 3D signal.