Predicting RNA scaffolds with a hybrid method of Vfold3D and VfoldLA

Abstract

The ever-increasing discoveries of noncoding RNA functions draw a strong demand for RNA structure determination from the sequence. In recently years, computational studies for RNA structures, at both the two-dimensional and the three-dimensional levels, led to several highly promising new developments. In this chapter, we describe a hybrid method, which combines the motif template-based Vfold3D model and the loop template-based VfoldLA model, to predict RNA 3D structures. The main emphasis is placed on the definition of motifs and loops, the treatment of no-template motifs, and the 3D structure assembly from templates of motifs and loops. For illustration, we use the ZIKV xrRNA1 as an example to show the template-based prediction of RNA 3D structures from the 2D structure. The web server for the hybrid model is freely accessible at http://rna.physics.missouri.edu/vfold3D2.

1. Introduction

To perform crucial cellular functions, RNA molecules fold up to form compact three-dimensional (3D) structures.^1-5 A comprehensive understanding of RNA structures, therefore, can not only provide the fundamental insights into the cellular functions of RNAs, but also promote the development of structure-based bioengineering, such as precise gene regulation and editing, as well as effective drug design. However, experimental determination of RNA 3D structures is usually laborious and challenging, leading to the fast development of predictive computational modeling for RNA 3D structure predictions.^6-24 Structure predictions from sequence alone may achieve (near) atomic resolutions for most short RNAs, due to the relatively small degrees of freedom in the conformational space. Additional structural information, such as the base pairing pattern at two-dimensional (2D) level and tertiary contact maps at the 3D level, may be needed to further reduce the conformational searching space and increase the prediction accuracy for large RNAs.^19-33

RNA 2D structure as defined by the base pairing pattern provides structural constraints for 3D structure folding. Different approaches have been developed to investigate the impact of RNA 2D structural constraint on 3D conformations.^34-40 For example, conformational analysis based on TOPRNA³⁸ and MC-sym²⁰ showed that RNA global conformation is largely defined by topological constraints of RNA secondary structure while the electrostatics, intra- and inter-loop and other interactions select specific conformations from the accessible conformational ensemble. Recent investigation for RNA tertiary motifs containing the cross-linked base pairs indicates that, tertiary motif can further decrease the 3D conformational space and impose much stronger topological constraints than the secondary structural motifs, which lack cross-linked base pairs.⁴⁰

Taking the advantage of the strong topological constraints of secondary structural motifs, template assembly-based RNA 3D structure models, such as RNAcomposer,¹⁹ MC-sym,²⁰ and Vfold3D,^21,22 select templates from known structures with homologous sequence information to predict 3D structures for large RNAs. For example, with the given RNA sequence and 2D structure, Vfold3D extracts the secondary structural motifs of helices, hairpin loops, internal/bulge loops, and multi-branched junctions, and predicts the 3D structures through the assembly of templates of non-helix motifs and A-form helices. With the existence of homologous structures for motifs, the knowledge-based methods for RNA 3D structure prediction can usually achieve higher accuracy and efficiency than the physics-based approaches. However, due to the limitation of current motif template database, the methods are severely limited by the low success rate of finding a proper template for a given motif.

Recently, we introduced VfoldLA,^23,24 a hierarchical loop template-assembly method for RNA 3D structure prediction. Unlike the previous models which search for templates based on the whole motif or piece-wise fragments, VfoldLA searches for templates for single-stranded loops, and predicts 3D structures through the assembly of loop templates and A-form helices. It has a much higher success rate to find proper templates than the motif-based approaches, and has also a much higher computational efficiency than fragment-based approaches. In general, VfoldLA can predict a set of all-atom structures from any 2D structure. However, due to the large number of combinations for the different templates of the different loops, it can only handle RNAs containing small number of helices to avoid excessively long computational times.

By combining Vfold3D and VfoldLA, in this chapter, we present a hybrid model for RNA 3D structure predictions with given 2D structures. The model takes the advantage of the conserved 3D structures for secondary structural motifs and the high success rate of finding templates for single-stranded loops. The predicted structures may serve as useful scaffolds for further structure refinement studies.

2. Algorithms

2.1. RNA secondary structural motifs and single-stranded loops.

An RNA 2D structure contains helices of canonical base pairs and the single-stranded loops of unpaired nucleotides. According to the different loop-helix connection modes, we define four types of loops, as shown in Fig. 1(A): “helix2” loop for a single strand that connects two helices; “hairpin” loop as a special “helix2” loop whose two ends connect to the same helix; “tail5” and “tail3” loops for segments of unpaired nucleotides at the 5’ and 3’ ends, respectively. The length of each loop L is the number of unpaired nucleotides.

Figure 1:

The definition of (A) single-stranded loops of hairpin, helix2 and tails, and (B) secondary structural motifs of internal/bulge loops and multi-branched junctions. Double-stranded helices are represented by cylinders. The red oval shape in each helix denotes the terminal base pair attached to the loops (shown as red lines). Sequences of loops and motifs are in the format of W-W (terminal base pair) and N (unpaired nucleotide), with all loops in the 5’ → 3’ directions.

According to the different connection modes between helices, we define the secondary structural motifs of internal/bulge loops and multi-branched junctions, as shown in Fig. 1(B) (see Note 1). Motif size is defined by the length of each loop L within a motif. For example, the three-way junction has three helices connected by three loops of L1, L2 and L3. The size of a three-way junction is denoted by L1-L2-L3. Other motifs, such as pseudoknots and hairpin-hairpin kissing motifs with the cross-linked base pairs, are not included in this model.

As shown by the red oval shapes in Fig. 1, we include the loop-connected terminal base pair(s) in the definition of loops and motifs to account for the loop-helix structural interference. The sequence of a loop/motif is formatted in the 5’ → 3’ direction with W-W and N denoting the terminal base pair and the unpaired nucleotides, respectively. For example, W-5’W and W3’-W in the “helix2” loop are the base pairs connected to the 5’ and 3’ ends of the loop, respectively.

2.2. RNA motif-based template library.

The (3D structure) template library for secondary structural motifs was built from 4659 PDB structures (see Note 2), including the RNA-involved complexes. It contains 3D templates for bulge loops, internal loops, and multi-branched junctions. The motif-based template library can be built in four steps:

1. For a given RNA 3D structure, extract the A-form helices. From the base pairing pattern, the corresponding 2D structure is determined.

2. Identify all the secondary structural motifs for the given 3D structure, according to the linkage between helices.

3. Remove the redundant templates for those with root mean square deviation (RMSD) ≤ 1.5 Å for the same motif type, same size and identical sequence.

4. Collect all the nonredundant motif structures to construct a template library. Table 1 shows the statistics for the current template library for motifs.

Table 1:

RNA loop- and motif-based template libraries

Loop name	Number of templates	Motif name	Number of templates
Hairpin loops	2562	Internal/Bulge loops	4387
Helix2 loops	8612	3-way junctions	1230
Tail5 loops	739	4-way junctions	1168
Tail3 loops	1046	5-way junctions	380
		6-way junctions	144
		7-way junctions	217

2.3. RNA loop-based template library.

The template library for single-stranded loops was built from 4659 PDB structures. It contains 3D templates for hairpin, helix2, tail5 and tail3 loops. The loop-based template library can be built in the following steps:

1. For a given RNA 3D structure, extract the A-form helices.

2. Identify all the single-stranded loops for the given 3D structure, according to the linkage between helices and loops.

3. Remove the redundant templates for those with RMSD ≤ 1.5 Å for the same loop type, same size and identical sequence.

4. Collect all the nonredundant loop structures to construct a template library. Table 1 shows the statistics for the current template library for loops.

2.4. Sequence similarity-based score.

Given a query loop/motif sequence, the model scores the sequence similarity according to the following rule: The score s_i for nucleotide position i is equal to 0 for perfect match, otherwise equal to 1 for purine/pyrimidine-type match, and 2 for no match. For example, s^A→G = 1 and s^A→C = 2 when nucleotide A is substituted with G and C, respectively. We rank the loop/motif templates according to the total score defined as the sum over all the nucleotides: S_loop/motif = Σ_i s_i. This scoring scheme considers the similarity of nucleotides, assuming that less changes in base substitution result in less changes in 3D structure.

3. Methods

The Vfold3D and VfoldLA combined model predicts RNA 3D structure from a 2D structure by the structural assembly from the templates of motifs and loops. If the specific whole motif-based templates are available and can be successfully found, we predict the 3D structure from the motif-based templates. The motif-based templates usually give more accurate predictions than the VfoldLA model alone. If a motif does not have available 3D templates in the library, the model breaks the whole motif into single-stranded loops and applies the VfoldLA strategy to predict the 3D structures. Such an approach would lead to a much broader applicability than the Vfold3D alone. As shown in the workflow in Fig. 2, the model works with the following steps.

Figure 2:

The workflow of the hybrid model.

1. Identify the structural components of double-stranded helices (see Note 3), secondary structural motifs, and single-stranded loops from the given 2D structure. For the motif types excluded in the motif library (such as pseudoknot, and hairpin-hairpin kissing), we break the whole motifs into the single-stranded loops. For example, a pseudoknot with two helices and three loops can be divided into three “helix2” loops. Same treatment can be applied to all the secondary structural motifs without templates.

2. Build the all-atom A-form helical structures.

3. Assemble the helix configurations in 3D space based on templates of all the motifs (with available templates) and “helix2” loops, according to the aforementioned sequence similarity-base scoring scheme. The optimal templates are selected with minimal scores.

4. Exclude helix configurations that involve steric clash or improper chain connectivity. To check steric clash between atoms in the assemble structures, we allow at most five atom pairs with a distance ≤ 2.0 Å. To check chain connectivity at the loop-helix interfaces, we allow at most a 5.0 Å heavy-atom RMSD of the helix terminal base pairs for each loop-closing (helix2) loops.

5. For each viable helix configuration, select the optimal templates for other (hairpin, tail5 and tail3) loops to build the whole structure. The optimal templates are chosen from the sequence similarity-based score.

6. Repeat step 5 until the assembled whole structure is clash-free (see Note 4 and 5). The overall score is calculated by the sum over the scores of all the templates.

7. Terminate the assembly process when the number of the assembled 3D structures reaches a pre-set value or the computational time reaches a specific amount of time (see Note 6).

8. Cluster the overall score-ranked structures (see Notes 7) and refine the structures of clusters. The assembled structures may contain structural clash and non-ideal bond lengths, bond angles, or bond torsional angles, especially at the loop-helix interface regions. To avoid long computational time, the web server utilizes the IsRNA model,¹⁶ which employs a coarse-grained representation of RNA conformations and the knowledge-based interaction potentials to refine the all-atom structures assembled by the model (see Notes 8).

9. The centroid structures of the top clusters are considered as the predicted structures for the given 2D structure (see Note 9).

We use the ZIKV xrRNA1⁴¹ for the illustration of the 3D structure prediction (see Note 10). The native 2D structure (Fig. 3(A), see Note 11) contains five helices, one three-way junction, and several single-stranded loops with a loop-kissing helix (H4, shown in red). Because of the loop-kissing helix, Vfold3D gives no predictions. However, the hybrid model builds 3D structures of the 3-way junction and loops from the motif template and loop template libraries, respectively, and assemble A-form helical structures to generate all-atom structures. As shown in Fig. 3(B), the RMSD between the (best) predicted structure and the experimental determined structure is 8.5 Å. This RMSD is smaller than the prediction from the VfoldLA model alone (RMSD = 10.6 Å). The use of the Vfold3D strategy for the secondary structural motif structure prediction contributes to the improved accuracy.

Figure 3:

The prediction of the ZIKV xrRNA1. (A) Snapshot of the server input, which indicates the RNA sequence and 2D structure in dot-bracket format, as well as other job information, such as number of clusters, RMSD cutoff for clustering, job name and email address. The input 2D structure contains five helices, one three-way junction and several single-stranded loops, with a loop-kissing helix (H4 as shown in red). (B) Snapshot of the server output, which shows the detailed job information and a JSmol applet for visualization of predicted structures. The best prediction has the RMSD of 8.5 Å, compared with the experimentally determined structure.

4. Notes

1. Other multi-way junctions, such as four-way and five-way junctions, are not shown in Fig. 1(B) for clarity.

2. The list of the RNA PDB structures used for constructing the template library includes all the PDB entries released before February of 2020.

3. Each helix should contain at least 2 base pairs. A lone base pair is treated as an inter-loop interaction.

4. For each helix configuration, the model predicts one all-atom structure with the optimal score, since different loop conformations usually do not cause significant changes to the global fold.

5. If none of the loop templates can satisfy the clash-free criteria, the specific helix configuration would be removed.

6. Currently, the web server terminates predictions when the computational time exceeds 12h or the number of assembled structures reaches 100, which may lead to no predictions.

7. As shown in Fig. 3(A), the RMSD cutoff for clustering is set to 5.0 Å by default. The server users are free to select other values (≤10 Å) before submission.

8. The IsRNA can resolve most of the structural clash while keeping the overall 3D fold unchanged through small-RMSD conformational sampling.

9. As shown in Fig. 3(A), the number of clusters is set to 5 by default. The server users are free to select other values (≤ 5) before submission.

10. The sequence of the ZIKV xrRNA1 is: 5 ’GGGUCAGGCCGGCGAAAGUCGCCACAGUUUGGGGAAAGCU GUGCAGCCUGUAACCCCCCCACGAAAGUGGG3’.

11. The native 2D structure is: ….(((((((((….)))).((((((..[[[[…))))))..)))))…]]]](((((….))))), which is extracted from the published paper⁴¹ of the crystal structure (PDB ID: 5tpy).