Thermodynamic rules that link RNA sequences to secondary structure are well established, but the link between secondary structure and three-dimensional global conformation remains poorly understood. We constructed comprehensive three-dimensional maps depicting the orientation of A-form helices across RNA junctions in the Protein Data Bank and rationalized our findings with modeling and nuclear magnetic resonance spectroscopy. We show that the secondary structures of junctions encode readily computable topological constraints that accurately predict the three-dimensional orientation of helices across all two-way junctions. Our results suggest that RNA global conformation is largely defined by topological constraints encoded at the secondary structural level and that tertiary contacts and intermolecular interactions serve to stabilize specific conformers within the topologically allowed ensemble.

More than 50% of RNA secondary structure is estimated to be A-form helices, which are linked together by various junctions. Here we describe a protocol for computing three interhelical Euler angles describing the relative orientation of helices across RNA junctions. 5' and 3' helices, H1 and H2, respectively, are assigned based on the junction topology. A reference canonical helix is constructed using an appropriate molecular builder software consisting of two continuous idealized A-form helices (iH1 and iH2) with helix axis oriented along the molecular Z-direction running toward the positive direction from iH1 to iH2. The phosphate groups and the carbon and oxygen atoms of the sugars are used to superimpose helix H1 of a target interhelical junction onto the corresponding iH1 of the reference helix. A copy of iH2 is then superimposed onto the resulting H2 helix to generate iH2'. A rotation matrix R is computed, which rotates iH2' into iH2 and expresses the rotation parameters in terms of three Euler angles α(h), β(h) and γ(h). The angles are processed to resolve a twofold degeneracy and to select an overall rotation around the axis of the reference helix. The three interhelical Euler angles define clockwise rotations around the 5' (-γ(h)) and 3' (α(h)) helices and an interhelical bend angle (β(h)). The angles can be depicted graphically to provide a 'Ramachandran'-type view of RNA global structure that can be used to identify unusual conformations as well as to understand variations due to changes in sequence, junction topology and other parameters.

Recent studies have shown that topological constraints encoded at the RNA secondary structure level involving basic steric and stereochemical forces can significantly restrict the orientations sampled by helices across two-way RNA junctions. Here, we formulate these topological constraints in greater quantitative detail and use this topological framework to rationalize long-standing but poorly understood observations regarding the basic behavior of RNA two-way junctions. Notably, we show that the asymmetric nature of the A-form helix and the finite length of a bulge provide a physical basis for the experimentally observed directionality and bulge-length amplitude dependence of bulge induced inter-helical bends. We also find that the topologically allowed space can be modulated by variations in sequence, particularly with the addition of non-canonical GU base pairs at the junction, and, surprisingly, by the length of the 5′ and 3′ helices. A survey of two-way RNA junctions in the protein data bank confirms that junction residues have a strong preference to adopt looped-in, non-canonically base-paired conformations, providing a route for extending our bulge-directed framework to internal loop motifs and implying a simplified link between secondary and tertiary structure. Finally, our results uncover a new simple mechanism for coupling junction-induced topological constraints with tertiary interactions.

We present a protocol for determining the relative orientation and dynamics of A-form helices in 13 C/ 15 N isotopically enriched RNA samples using NMR residual dipolar couplings (RDCs). Non-terminal Watson-Crick base pairs in helical stems are experimentally identified using NOE and trans-hydrogen bond connectivity and modeled using the idealized A-form helix geometry. RDCs measured in the partially aligned RNA are used to compute order tensors describing average alignment of each helix relative to the applied magnetic field. The order tensors are translated into Euler angles defining the average relative orientation of helices and order parameters describing the amplitude and asymmetry of interhelix motions. The protocol does not require complete resonance assignments and therefore can be implemented rapidly to RNAs much larger than those for which complete high-resolution NMR structure determination is feasible. The protocol is particularly valuable for exploring adaptive changes in RNA conformation that occur in response to biologically relevant signals. Following resonance assignments, the procedure is expected to take no more than 2 weeks of acquisition and data analysis time.

Summary Accompanying recent advances in determining RNA secondary structure is the growing appreciation for the importance of relatively simple topological constraints, encoded at the secondary structure level, in defining the overall architecture, folding pathways, and dynamic adaptability of RNA. A new view is emerging in which tertiary interactions do not define RNA 3D structure, but rather, help select specific conformers from an already narrow, topologically pre-defined conformational distribution. Studies are providing fundamental insights into the nature of these topological constraints, how they are encoded by the RNA secondary structure, and how they interplay with other interactions, breathing new meaning to RNA secondary structure. New approaches have been developed that take advantage of topological constraints in determining RNA backbone conformation based on secondary structure, and a limited set of other, easily accessible constraints. Topological constraints are also providing a much-needed framework for rationalizing and describing RNA dynamics and structural adaptation. Finally, studies suggest that topological constraints may play important roles steering RNA folding pathways. Here, we review recent advances in our understanding of topological constraints encoded by the RNA secondary structure.