Hierarchical natural move Monte Carlo refines flexible RNA structures into cryo-EM densities

Abstract

Ribonucleic acids (RNAs) play essential roles in living cells. Many of them fold into defined three-dimensional (3D) structures to perform functions. Recent advances in single-particle cryo-electron microscopy (cryo-EM) have enabled structure determinations of RNA to atomic resolutions. However, most RNA molecules are structurally flexible, limiting the resolution of their structures solved by cryo-EM. In modeling these molecules, several computational methods are limited by the requirement of massive computational resources and/or the low efficiency in exploring large-scale structural variations. Here we use hierarchical natural move Monte Carlo (HNMMC), which takes advantage of collective motions for groups of nucleic acid residues, to refine RNA structures into their cryo-EM maps, preserving atomic details in the models. After validating the method on a simulated density map of tRNA, we applied it to objectively obtain the model of the folding intermediate for the specificity domain of ribonuclease P from Bacillus subtilis and refine a flexible ribosomal RNA (rRNA) expansion segment from the Mycobacterium tuberculosis (Mtb) ribosome in different conformational states. Finally, we used HNMMC to model atomic details and flexibility for two distinct conformations of the complete genomic RNA (gRNA) inside MS2, a single-stranded RNA virus, revealing multiple pathways for its capsid assembly.

Keywords: RNA folding; RNA virus; conformational sampling; molecular motions; structural modeling.

FIGURE 1.

HNMMC refinement of a deformed tRNA. (A) The DOF of a tRNA. Each helical stem (red, blue, green, and yellow) of a tRNA is defined as a natural move (indicated in each box), which can translate and rotate independently, with each red dot as a center of rotation and translation. Two flexible unpaired loops are colored gray. (B) The starting tRNA model with 8.72-Å C4′ RMSD to the target structure fitted in the target map. (C) The refined model with the lowest total energy (E_total) has a C4′ RMSD of 1.37 Å to the target structure. Each helical stem of the tRNA model is colored red, blue, green, and yellow, respectively, based on the DOF defined in A. The transparent density is Gaussian-blurred from the target structure to 5-Å resolution.

FIGURE 2.

HNMMC refinement of the native structure of the ribonuclease P S-domain against the cryo-EM map of the folding intermediate. (A) The flow chart of the refinement protocol of the S-domain. DOF 1 is applied in the first step to generate 10,000 conformations without the restraint from the cryo-EM density. DOF 2 with two levels is applied in the last step for a detailed refinement. (B) The conformational difference between the 500 representative conformations from clustering the 10,000 conformations. The scatter plot shows the differences among the 500 models by multidimensional scaling computed using the matrix of the pairwise C4′ RMSD among the 500 conformations. Each point represents one conformation. The 18 unique conformations with high cross-correlation to the target map are marked as solid purple or red dots, with the red dot representing the conformation with the highest cross-correlation. (C) The heat map of the normalized cross-correlation of the 500 representative conformations to the target map. The 18 unique conformations with high cross-correlations are marked as stars. The red star at the top-left corner indicates the conformation with the highest cross-correlation.

FIGURE 3.

HNMMC refinement of the handle in Mtb 50S rRNA. (A) Seven levels of the DOF to describe possible motions of the handle. For each level, the red fragment can move as a group while the black fragment is fixed. The magenta labels the sarcin-ricin motif (close to the three-way junction) and the tetra-loop (at the tip of the handle). Combining these seven levels can effectively describe the bending of the handle at each junction. Note that each nucleotide is still allowed to fluctuate around its position within the red fragment for subtle conformational variations. (B) The initial model of the handle obtained from the Mtb 50S is docked against the cryo-EM density of the handle from the Mtb 70S. (C) The HNMMC refined model of the handle.

FIGURE 4.

HNMMC refinement of the gRNA fragment 2394–2604 inside MS2. (A) The definition of DOFs of the gRNA fragment 2394–2604. The red fragment in Levels 1 and 2 of DOF 1 is the natural move that moves as a group. For Levels 3 and 4 of DOF 2, the different colors represent different natural moves. The black region at all levels is fixed. In Levels 3 and 4, the black region is the gRNA fragment 2468–2481 with a high-resolution EM structure. The gray color represents unpaired RNA loops that can also move. (B) The initial model of the gRNA fragment 2394–2604 and the corresponding cryo-EM density. The helical stems are colored as Level 3. (C) HNMMC refined model of the gRNA fragment 2394–2604 against the target cryo-EM density. The thin red line is the backbone trace from the previous published result (Dai et al. 2017).

FIGURE 5.

HNMMC refined models of the complete MS2 gRNA. (A) The ensemble of 20 refined models colored according to the genes in the schematic diagram at the bottom (MP: maturation protein, CP: coat protein, Rep: replicase, Lys: lysis protein). The lysis gene is not colored on the ribbon models due to the overlap with the genes for the coat protein and the replicase. (B) The conformational variation among the 20 refined models at each nucleotide colored by the average C4′ RMSD among the 20 models. The color scale from white to red denotes low to high RMSD.

FIGURE 6.

Two conformations of the gRNA inside MS2. (A,B) Two dominant gRNA conformations of the MS2 (C1,C2) are modeled based on the two cryo-EM maps. The gRNA fragments with large differences between the two models are colored yellow (gRNA fragment 614–879), green (gRNA fragment 1643–1700), blue (gRNA fragment 1992–2125), and red (gRNA fragment 2922–3087). Two copies of the coat protein dimers, which switch interacting stem–loop partners, are outlined by transparent green (Dimer 1: D1) and transparent blue (Dimer 2: D2). The insets of the capsids (magenta: maturation protein, green: D1, blue: D2, yellow: rest of the coat protein shell) show the viewing orientation for the corresponding columns and the location of the two dimers on the capsid.