Topological Structure Determination of RNA Using Small-Angle X-Ray Scattering

Abstract

Knowledge of RNA three-dimensional topological structures provides important insight into the relationship between RNA structural components and function. It is often likely that near-complete sets of biochemical and biophysical data containing structural restraints are not available, but one still wants to obtain knowledge about approximate topological folding of RNA. In this regard, general methods for determining such topological structures with minimum readily available restraints are lacking. Naked RNAs are difficult to crystallize and NMR spectroscopy is generally limited to small RNA fragments. By nature, sequence determines structure and all interactions that drive folding are self-contained within sequence. Nevertheless, there is little apparent correlation between primary sequences and three-dimensional folding unless supplemented with experimental or phylogenetic data. Thus, there is an acute need for a robust high-throughput method that can rapidly determine topological structures of RNAs guided by some experimental data. We present here a novel method (RS3D) that can assimilate the RNA secondary structure information, small-angle X-ray scattering data, and any readily available tertiary contact information to determine the topological fold of RNA. Conformations are firstly sampled at glob level where each glob represents a nucleotide. Best-ranked glob models can be further refined against solvent accessibility data, if available, and then converted to explicit all-atom coordinates for refinement against SAXS data using the Xplor-NIH program. RS3D is widely applicable to a variety of RNA folding architectures currently present in the structure database. Furthermore, we demonstrate applicability and feasibility of the program to derive low-resolution topological structures of relatively large multi-domain RNAs.

Keywords: RNA secondary and tertiary structure; RNA topological structure; hierarchical moves; small-angle X-ray scattering.

Figure 1

Strategic global and local moves implemented in RS3D. A global move (a) carries out a random translation or rotation of a single duplex or helical segment (duplexes and loops), or a complete structural motif such as a subdomain or domain. A local move (b) picks a group of globs (solid red circles with a cross) lying in a duplex, loop or junction region, and displaces them through a random translation.

Figure 2

Flowchart of RS3D and representative cases of its application for topological structure calculation. (a) Flowchart depicting various stages of structure calculations. (b) Secondary structure (left) as well as the tallies of normalized area plus χ² vs. RMSD for the MLV-PK RNA (access code: 2LC8), an example of globular folded RNA. Top 10 structures with lowest RMSD are enclosed in the cyan box, and best 10 ranked structures, based on selection criteria, are enclosed in the brown box. (c) Secondary structure (left) as well as the tallies of the normalized extendedness plus χ² vs. RMSD for the RLariat RNA (access code: 2M58), an example of an extended structure. (d) Secondary structure (left) as well as the tallies of the normalized extendedness plus χ² vs. RMSD of the SAM III RNA (access code: 3E5C), an example of a challenging case in which the criteria used to select best conformers do not converge. In all cases, RS3D was able to calculate correct overall topological folds, which are shown next to the brown box, as compared to the topological folds of the lowest RMSD structures, which are shown next to the cyan box. The database structure is shown in red. All calculations were carried out using a momentum transfer (q) cutoff at 0.3 Å⁻¹.

Figure 3

Plots of glob form factors and intensity correction factors. Left: average glob scattering form factors (F_glob) as a function of momentum transfer (q) for each nucleotide, derived from 32 different RNA structures solved by X-ray crystallography with resolution better than 3 Å. Right: mean glob correction factor (I/I_glob) and the associated standard deviation, as a function of q, calculated for 50 different RNA structures from the PDB. The size of RNAs considered for generating the above statistics ranges from 50 to 200 nucleotides.

Figure 4

Illustrations of glob and all-atom structures for RNAs calculated using RS3D. A total of 16 structures are presented, which cover the most common RNA folds, from two-way to five way junctions, in the PDB. (a–p) Superimpositions of X-ray crystal or NMR backbone structures (red) with those of the RS3D-calculated structures. PDB accession codes are (a) 2LC8, (b) 2QWY, (c) 2M58, (d) 1P5P, (e) 1Y26, (f) 2N8V, (g) 3IRW, (h) 4JF2, (i) 1GID, (j) 2QUS, (k) 3R4F, (l) 1Z43, (m) 3E5C, (n) 4MGN, (o) 3T4B, and (p) 3A3A. On the left of each panel is the superimposition of the X-ray/NMR crystal structure with the RS3D structure with the lowest RMSD at glob level, colored in red and blue, respectively. On the right of each panel is the superimposition of the top 10 RS3D structures, obtained after rendering the best 10 glob models for each RNA into all-atom representation and carrying out additional refinement using Xplor-NIH software. The top 10 RS3D structures of riboA, obtained after refinement against SAXS as well as RDC restraints are shown in the center panel of (e). All calculations were carried out using a momentum transfer (q) cutoff at 0.3 Å⁻¹.

Figure 5

Topological folds based on empirical parameters. Tallies of normalized area or extendedness plus χ² vs. RMSD for (a) HCV-IRES-II, (b) Hammerhead Ribozyme, (c) Prohead, (d) tRNA^gly, and (e) Human tRNA. The database structures are shown in red. These plots represent challenging cases in which the criteria to select best conformers do not converge. In all cases, RS3D was able to calculate correct overall topological folds, which are shown next to the brown box, as compared to the topological folds of the lowest RMSD structures, which are shown next to the cyan box. The scores (χ² + area) of the database structures are 0.93 and 0.87 for (d) and (e) respectively. Both these structures fall within top 100 of the best ranked structures in the pool. All calculations were carried out using a momentum transfer (q) cutoff at 0.3 Å⁻¹.

Figure 6

Structure improvement using additional restraints. (a) Plot of average RMSDs of the best 10 structures of the preQ1 riboswitch RNA against the number of long-range restraints, including accessible surface area (ASA), used during calculation/refinement. Topological folds of the best 10 structures aligned against the X-ray crystal structure (access code: 4JF2, red) are shown next to each corresponding RMSD. The secondary structure is shown on the top-right. (b–d) Backbone ribbon representations of (b) SAM-III, (c) tRNA^gly, and (d) P4–P6 domain of group I intron before (left) and after (right) accessible surface area refinement. The database structures are shown in red. All calculations were carried out using a momentum transfer (q) cutoff at 0.3 Å⁻¹.

Figure 7

Two-step structure calculation for multi-domain RNAs: (a) RNase P RNA and (b) Group II Intron. In each panel, from the left to right: the structure of the initial input, the intermediate after local folding, the plot of the sum of normalized χ², area and tertiary restraint scores vs. RMSD compared to the crystal structure, and the top 10 structures, best RMSD structure, and crystal structure in three different views. Each local structural element is colored similarly as in the literature [–50]. In the second step, a total of 1,000 conformers were calculated. All calculations were carried out using a momentum transfer (q) cutoff at 0.3 Å⁻¹.