The pseudotorsional space of RNA

Abstract

The characterization of the conformational landscape of the RNA backbone is rather complex due to the ability of RNA to assume a large variety of conformations. These backbone conformations can be depicted by pseudotorsional angles linking RNA backbone atoms, from which Ramachandran-like plots can be built. We explore here different definitions of these pseudotorsional angles, finding that the most accurate ones are the traditional η (eta) and θ (theta) angles, which represent the relative position of RNA backbone atoms P and C4'. We explore the distribution of η - θ in known experimental structures, comparing the pseudotorsional space generated with structures determined exclusively by one experimental technique. We found that the complete picture only appears when combining data from different sources. The maps provide a quite comprehensive representation of the RNA accessible space, which can be used in RNA-structural predictions. Finally, our results highlight that protein interactions lead to significant changes in the population of the η - θ space, pointing toward the role of induced-fit mechanisms in protein-RNA recognition.

Keywords: bioinformatics; computational chemistry; conformations; data mining; structure.

FIGURE 1.

Structural representation of the pseudotorsional angles of RNA. (A) Definition of the η (eta: C4′_{i − 1}, P_i, C4′_i, P_{i + 1}) and the θ (theta: P_i, C4′_i, P_{i + 1}, C4′_{i + 1}) angles. (B) Definition of the η′ (eta′: C1′_{i − 1}, P_i, C1′_i, P_{i + 1}) and the θ′ (theta′: P_i, C1′_i, P_{i + 1}, C1′_{i + 1}) angles. (C) Definition of the η″ (eta″: SRF_{i − 1}, P_i, SRF_i, P_{i + 1}) and the θ″ (theta″: P_i, SRF_i, P_{i + 1}, SRF_{i + 1}) angles, where SRF stands for standard reference frame as implemented in DSSR (Lu et al. 2015).

FIGURE 2.

(A) η − θ from the complete-data set for nonhelical nucleotides with sugar conformation in North. Density contours of $\overline{\rho }+X\cdot \sigma$ (X = 1, 2, or 4; dark red, violet, and dark blue, respectively) highlight regions of the plots with a significant population of nucleotides. Cluster or HDRs previously identified by Pyle and coworkers are labeled in red, while new clusters found in this work appear in dark green. Black dashed lines delimit the region occupied by canonical helical A-form. (B) Same as (A) for nucleotides in South configuration. (C) Representative structure for each new cluster found. (D) Example of the stacking analysis for cluster I North. ρ and z components of the R-vector (Bottaro et al. 2014) between the given nucleobase and its 5′ (green) and 3′ (pink) neighboring nucleobases are shown. The inner space between ellipses and dotted lines shows the region in which stacking occurs. (E) Same as (D) for cluster I South. (F) Interaction energy between the given nucleobase and its 5′ (green) and 3′ (pink) neighboring for cluster I North. (G) Direct interaction energy between the 5′ and 3′ nucleobases (one to three interactions) for cluster I North. (H) Same as (F) for cluster I South. (I) Same as (G) for cluster I South.

FIGURE 3.

Distributions of real dihedral angles in the nucleotides i − 1 (panels on the left), i (mid-panels), and i + 1 (panels on the right), as a function of the pseudodihedral angle eta (η) in the central nucleotide i. Panels show: α (black), β (red), γ (blue), δ (green), ε (yellow), ζ (orange), ξ (gray), and the puckering phase (brown).

FIGURE 4.

η − θ conformational space as detected by each experimental technique. Results are divided into North (panels on the left) or South (panels on the right) sugar conformations. Density contours of $\overline{\rho }+X\cdot \sigma$ (X = 1, 2, or 4; dark red, violet, and dark blue, respectively) highlight regions of the plots with a significant population of nucleotides. Black dashed lines delimit the region occupied by canonical helical A-form (those structures are removed from the analyses as described in the Materials and Methods section). Cluster numbers are identified in red or dark green when they were not seen in the complete-data set depicted in Figure 2. (A) Densities and cluster analysis of the xray-subset for central nucleotides with sugars in North. (B) Same as (A) for South conformations. (C,D) are the same as (A) and (B) for the em-subset. (E,F) are the same as (A) and (B) for the nmr-subset.

FIGURE 5.

η − θ conformational space described by the naked-subset and protein-subset. Results are divided into nonhelical North (panels on the left) or South (panels on the right) sugar conformations. Density contours of $\overline{\rho }+X\cdot \sigma$ (X = 1, 2, or 4; dark red, violet, and dark blue, respectively) highlight regions of the plots with a significant population of nucleotides. Black dashed lines delimit the region occupied by canonical helical A-form (those structures are removed from the analyses as described in the Materials and Methods section). Cluster numbers are identified in red or dark green when they were not seen in the complete-data set depicted in Figure 2. (A) Densities and cluster analysis of the naked-subset for central nucleotides with sugars in North. (B) Same as (A) for South conformations. (C,D) are the same as (A) and (B) for the protein-subset.

FIGURE 6.

η − θ conformational space described by the monovalent-subset and divalent-subset. Results are divided into nonhelical North (panels on the left) or South (panels on the right) sugar conformations. Density contours of $\overline{\rho }+X\cdot \sigma$ (X = 1, 2, or 4; dark red, violet, and dark blue, respectively) highlight regions of the plots with a significant population of nucleotides. Black dashed lines delimit the region occupied by canonical helical A-form (those structures are removed from the analyses as described in the Materials and Methods section). (A) Densities and cluster analysis of the both types of cations together (monovalent in pink dots and divalent in turquoise) over the clusters obtained for the complete-data set. (B) Clusters obtained by using only the monovalent-subset. (C) Idem than (B) using the divalent-subset.

FIGURE 7.

η − θ conformational space of the complete-data set. Results are divided into nonhelical North (top-panels) or South (bottom-panels) sugar conformations. Density contours of $\overline{\rho }+X\cdot \sigma$ (X = 1, 2, or 4; dark red, violet, and dark blue, respectively) highlight regions of the plots with a significant population of nucleotides. Black dashed lines delimit the region occupied by canonical helical A-form (those structures are removed from the analyses as described in the Materials and Methods section). Cluster numbers are identified in black in the left panels. (A) The panel on the left shows densities and sequence logo-plots of the complete-data set for sugars in North. The panel on the right shows the corresponding dot-plot with adenine (green), uracil (red), guanine (yellow), and cytosine (blue). (B) Same as (A) for South conformations.