Evaluating and Learning from RNA Pseudotorsional Space: Quantitative Validation of a Reduced Representation for RNA Structure

Quantitatively describing RNA structure and conformational elements remains a formidable problem. Seven standard torsion angles and the sugar pucker are necessary to characterize the conformation of an RNA nucleotide completely. Progress has been made toward understanding the discrete nature of RNA structure, but classifying simple and ubiquitous structural elements such as helices and motifs remains a difficult task. One approach for describing RNA structure in a simple, mathematically consistent, and computationally accessible manner involves the invocation of two pseudotorsions, η (C4′n-1, Pn, C4′n, Pn+1) and θ (Pn, C4′n, Pn+1, C4′n+1), which can be used to describe RNA conformation in much the same way that ϕ and ψ are used to describe backbone configuration of proteins. Here, we conduct an exploration and statistical evaluation of pseudotorsional space and of the Ramachandran-like η–θ plot. We show that, through the rigorous quantitative analysis of the η–θ plot, the pseudotorsional descriptors η and θ, together with sugar pucker, are sufficient to describe RNA backbone conformation fully in most cases. These descriptors are also shown to contain considerable information about nucleotide base conformation, revealing a previously uncharacterized interplay between backbone and base orientation. A window function analysis is used to discern statistically relevant regions of density in the η–θ scatter plot and then nucleotides in colocalized clusters in the η–θ plane are shown to have similar 3-D structures through RMSD analysis of the RNA structural constituents. We find that major clusters in the η–θ plot are few, underscoring the discrete nature of RNA backbone conformation. Like the Ramachandran plot, the η–θ plot is a valuable system for conceptualizing biomolecular conformation, it is a useful tool for analyzing RNA tertiary structures, and it is a vital component of new approaches for solving the 3-D structures of large RNA molecules and RNA assemblies.