The backbone conformation of an individual nucleotide in an RNA molecule can be described by six torsions (α, β, γ, δ, ε, ζ). We have developed an alternative shorthand description of nucleotide structure in which each nucleotide is spanned by two pseudobonds: one from P to C4′ and one from C4′ to P of the following nucleotide (Duarte & Pyle, JMB 1998. Olson, Biopolymers 1975. Malathi & Yathindra, J Biomolec Struct Dyn 1985). These pseudobonds form two virtual dihedral angles: η (C4′_n-1-P_n-C4′_n-P_n+1) and θ (P_n-C4′_n-P_n+1-C4′_n+1).

The resulting pseudotorsions (η and θ) simplify the conformational space of RNA to two dimensions, which can be easily plotted on an η-θ plot. This plot allows RNA structure to be visualized in the same way as peptide conformation is displayed on a Ramachandran plot, as the location of a nucleotide on an η-θ plot corresponds closely with its conformational state. Even when the nucleoside base is considered, the relationship between the pseudotorsions and structural RMSD is far stronger than the relationship between the standard torsions and RMSD. Additionally, when an η-θ plot is constructed from a large database of RNA structures, clusters quickly emerge. These clusters represent similar nucleotides with common conformations that can be formally defined and quantified (Wadley et al, JMB 2007).

The pseudotorsions provide a mathematically discrete way to describe RNA substructure and serve numerous practical applications. They provide a robust tool for finding examples of known motifs through the building of RNA "worms," which are strings of (η,θ) coordinates for sequential nucleotides. Each motif has a unique worm signature, and a database of structures can be rapidly searched for all examples of any given worm (Duarte et al, NAR 2003). This concept can be further extended to identify and define novel motifs. By searching for worms that are frequently repeated in a database of structures, a list of novel RNA substructures can automatically be compiled. This approach has been used to identify a number of new motifs, such as the π-turn, the ω-turn, the α-loop, and the C2′-endo mediated flipped adenosine (Wadley & Pyle, NAR 2004). The pseudotorsions can also be used to quickly and automatically compare multiple molecular conformations by calculating the difference in their (η,θ) coordinates. For example, two alternate ribosomal crystal structures can be compared to immediately locate nucleotides affected by a bound mRNA or antibiotic (Duarte et al, NAR 2003). In addition, pseudotorsional analyses can also be combined with standard torsional measurements. For example, η and θ aided in the development of the consensus backbone rotamer library, which defined 46 possible RNA backbone configurations (Richardson et al, RNA 2008). Due to these and other applications, the pseudotorsions have become and will continue to be a valuable tool for the inspection and characterization of RNA structure.