New metrics for comparing and assessing discrepancies between RNA 3D structures and models

Abstract

To benchmark progress made in RNA three-dimensional modeling and assess newly developed techniques, reliable and meaningful comparison metrics and associated tools are necessary. Generally, the average root-mean-square deviations (RMSDs) are quoted. However, RMSD can be misleading since errors are spread over the whole molecule and do not account for the specificity of RNA base interactions. Here, we introduce two new metrics that are particularly suitable to RNAs: the deformation index and deformation profile. The deformation index is calibrated by the interaction network fidelity, which considers base-base-stacking and base-base-pairing interactions within the target structure. The deformation profile highlights dissimilarities between structures at the nucleotide scale for both intradomain and interdomain interactions. Our results show that there is little correlation between RMSD and interaction network fidelity. The deformation profile is a tool that allows for rapid assessment of the origins of discrepancies.

FIGURE 1.

Base-stacking and base-pairing nomenclature. (A) Normal vectors in pyrimidines and purines. Using a right-handed axis system, the normal vector in the pyrimidine (left) comes out of the paper plane (atom numbers counterclockwise), whereas it is reversed in the pyrimidine ring of the purine (atom numbers clockwise). (B) The four base-stacking types. Using the normal vectors (represented by arrows), we can distinguish three types of base stacking. If base A is below base B, the normal vector of A points to B, and both normal vectors point in the same direction (left), then base B is stacked upward of A (or symmetrically base A is stacked downward of B). If the normal vectors of A and B point toward each other (middle), then bases A and B stack inward. If the normal vectors flee each other (right), then bases A and B stack outward. (C) Base edges. Each base is divided into three edges: the Watson–Crick (W) edge is at the tip of the base and where the chemical groups involved in Watson–Crick base pairs interact; the Hoogsteen (H) edge is on the opposite side of the ribose; and the sugar (S) edge is on the side of the ribose. Here is a cis A–U Watson–Crick base pair, and we write W/W cis and represent it using the black dot. The fact that any edge in any base can interact with any other edge in a partner results in six different base–base interactions: W/W, W/H, W/S, H/H, H/S, and S/S. Since there are two possible relative orientations of the ribose according to the place formed by the two bases of a base pair, then this nomenclature describes 12 different base-pairing patterns. (D) The 12 base-pairing patterns, or types, and their associated symbols.

FIGURE 2.

The rat 28S rRNA loop E structure. (A) Stereoview of the crystal structure (PDB code 1Q9A). (Green) Adenosines, (yellow) cytosines, (violet) guanosines, (red) uracils. The thread through the phosphate atoms is shown using a cylinder. Each base ring is filled and highlighted by thick covalent bonds. The H-bonded bases of the characteristic loop E structure, here the G9-U10-A19 base triple, are linked with dotted lines. Note that U1 in this crystal structure is not paired with G27. The image was generated using Pymol. (B) Secondary structure annotated by MC-Annotate. (C) Secondary structure annotated by RNAview. (D) Stacking annotation.

FIGURE 3.

Distribution of (RMSD, INF) values. For each MC-Sym generated structure, the RMSD and INF values when compared with the crystal structure are plotted. The oblique line is the linear regression (P = 0.6). The horizontal line is at an INF of 0.85, and the vertical line at 2.0 Å RMSD.

FIGURE 4.

Three models of the rat 28S rRNA loop E. The models are shown colored and the crystal structure in gray (PDB code 1Q9A). (Blue) Well modeled regions (RMSD < 0.5 Å), (red) badly modeled regions (RMSD > 3.0 Å). The models were optimally aligned (all atoms but H) with the crystal structure. (A) Model with a good INF (0.88; TP 29; FP 6; FN 2) and a good RMSD (1.64 Å); DI = 1.86. (B) Model with a good INF (0.88; TP 28; FP 5; FN 3), but a bad RMSD (3.76 Å); DI = 4.30. Although the geometry of the base pairs is well conserved, the thread through the phosphate atoms is shifted. (C) Model with a bad INF (0.71; TP 21; FP 7; FN 10), but a good RMSD (2.03 Å); DI = 2.85. The thread through the phosphate atoms is well superimposed, but the base-pairing geometry is wrong. Structural features that lead to a bad INF include: (D) base-stacking parameters that differ between the crystal (yellow) and model (blue) structures, such as G9, which shows a high rise in the crystal structure when compared with the model, and A19, for which a tilt can be observed between the crystal and model structures; and (E) base-pairing parameters that differ between the crystal and model structures, such as C20, which flips (propeller twist of 180°) between the crystal and model structures.

FIGURE 5.

Building steps of the deformation profile. (A) A predicted model (PM) will be compared with the reference model (RM). After superimposing PM over RM, minimizing the RMSD between nucleotides 2 (B) and 4 (C), the average distances between all atoms of corresponding nucleotides is calculated and recorded in DP matrix (D).

FIGURE 6.

Deformation Profile between predicted model 553 and the hammerhead ribozyme crystal structure. (A) DP matrix. Blue and pink squares inside the matrix correspond to intra- and interdomain similarity relationships, respectively. Numbers in the left top corner of each square are the average value of all positions inside the square. Color scale goes from 0 Å (white) to (but not including) 20 Å (dark green) in 10 equal steps and from 20 Å (yellow) to 80 Å (red) in five equal steps. (B) Average values of rows (green), columns (black), and main diagonal (red) of the matrix. (Shaded green regions) Helical strands. (C) 3D structure of the model. Each nucleotide is colored according to the respective row average value, from minimum (white) to maximum deformation (red) value. (D) Superimposition of the model and reference 3D structures. (E) Interaction network of the original molecule.

FIGURE 7.

Same as Figure 6 but for model 633.