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Direct-Coupling Analysis of nucleotide coevolution facilitates RNA secondary and tertiary structure prediction

Eleonora De Leonardis, Benjamin Lutz, Sebastian Ratz, Simona Cocco, Remi Monasson, Alexander Schug, Martin Weigt

arXiv:1510.03351v1q-bio.BMphysics.bio-ph

TL;DR

Experimental RNA structure determination is challenging, and computational prediction has accuracy and intervention limitations. This paper applies DCA to homologous RNA sequences and integrates its contact predictions into secondary-structure and molecular-modeling approaches. DCA improves secondary-contact prediction relative to MI-based approaches and enriches tertiary-contact predictions, while Rosetta modeling has limitations in scoring and contact detail.

  • Problem

    RNA structure is difficult to determine experimentally, and computational prediction often has limited accuracy or requires expert intervention.

    Source: INTRODUCTION · pp. 1–2

  • Method

    The authors analyze coevolution in homologous RNA sequences with DCA and integrate predicted contacts into secondary-structure prediction and Rosetta modeling.

    Source: INTRODUCTION · p. 2

  • Results

    Across six test families, DCA finds 54% of all contacts at 15% precision, compared with MI's 18% at 10% precision and MIapc's 25% at 13% precision.

    Source: DISCUSSION · p. 12

  • Takeaways & Limitations

    DCA contact predictions can be integrated into RNA structure-prediction tools, with improved secondary-structure results and tertiary-contact enrichment reported by the authors.

    Source: INTRODUCTION · p. 2, DISCUSSION · p. 10

    Rosetta's accuracy is limited because the input provides native residue-residue contacts but not native atom-atom distances, and its scoring can miss better models.

    Source: modeling tools · p. 10

Abstract

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Despite the biological importance of non-coding RNA, their structural characterization remains challenging. Making use of the rapidly growing sequence databases, we analyze nucleotide coevolution across homologous sequences via Direct-Coupling Analysis to detect nucleotide-nucleotide contacts. For a representative set of riboswitches, we show that the results of Direct-Coupling Analysis in combination with a generalized Nussinov algorithm systematically improve the results of RNA secondary structure prediction beyond traditional covariance approaches based on mutual information. Even more importantly, we show that the results of Direct-Coupling Analysis are enriched in tertiary structure contacts. By integrating these predictions into molecular modeling tools, systematically improved tertiary structure predictions can be obtained, as compared to using secondary structure information alone.

INTRODUCTION

RNA structure is biologically important but difficult to determine experimentally, while computational prediction faces accuracy and intervention challenges. The paper applies DCA to homologous RNA sequences and reports improvements in secondary-structure prediction and tertiary-contact enrichment, with DCA predictions also improving Rosetta modeling.

INTRODUCTION

  • RNA structure determination remains challenging: fewer than 6% of structures in the RCBS Protein Data Bank contain RNA, and only 59 of 2,450 Rfam families have a representative PDB structure.The paper notes that 954 families have more than 100 sequences and 566 have more than 200.Source: INTRODUCTION · pp. 1–2
  • Computational RNA prediction often yields RMSD values of 8–12 Å in blind prediction, may require expert intervention, and does not reliably predict topologically complex structures.The paper describes experimental contact restraints as one way to improve computational models.Source: INTRODUCTION · p. 2
  • DCA separates direct from indirect correlations, addressing transitivity effects that can confound local measures such as mutual information.The paper applies coevolutionary analysis to homologous RNA sequences to detect contacts, including tertiary contacts that may show weaker covariation.Source: INTRODUCTION · p. 2
  • DCA systematically improves secondary-structure prediction over MI-based methods and increases enrichment in 3D contacts when replacing local covariance analysis.The authors combine DCA with a generalized Nussinov algorithm for secondary-structure prediction.Source: INTRODUCTION · p. 2
  • Adding DCA-predicted tertiary contacts to Rosetta systematically improves results over Rosetta alone and is competitive with RNA-puzzle workflows that may require experimental information or expert intervention.The proposed scheme integrates DCA into Rosetta for automated tertiary-structure prediction.Source: INTRODUCTION · p. 2

MATERIAL AND METHODS

The pipeline identifies homologous sequences, uses DCA to predict contacts, and integrates those predictions into secondary- and tertiary-structure prediction. Its test set comprises selected riboswitch families, with additional blind predictions for two families lacking known 3D structures.

Inference pipeline

  • The modular pipeline identifies homologs, performs DCA, and integrates its results into generalized Nussinov secondary-structure prediction and Rosetta molecular modeling.The authors note that improving alignments, DCA signal extraction, or molecular-modeling inputs could improve overall performance.Source: Inference pipeline · p. 3

Selection of RNA families

  • Rfam riboswitch families were selected for more than 1,000 sequences to support coevolution statistics, PDB structures of at most 100 nucleotides, and complete PDB X-ray diffraction structures with resolution below 3 Å.Source: Selection of RNA families · p. 3
  • Rfam version 11.0 alignments and consensus structures were used, with consensus base pairs removed when incompatible with the target sequence and helices sometimes extended.These steps prepared the consensus structures for prediction of specific RNA sequences.Source: Selection of RNA families · pp. 3–4
  • The selection cutoffs are not applicability limits: DCA contact information changes little with subsamples of at least about 250 sequences, and the pipeline also applies to sequences over 100 nucleotides at increased computational cost, especially in modeling.Source: Selection of RNA families · p. 4
  • The authors provide blind predictions for the glnA riboswitch and C4 antisense RNA families, neither of which has a known 3D structure.The ten highest-scoring clusters are supplied as PDB models for possible experimental testing.Source: Selection of RNA families · p. 4

Direct-Coupling Analysis

DCA models sequence variability in a multiple-sequence alignment with a generalized Potts model. Its parameters are fitted to empirical nucleotide statistics, and the resulting coupling matrices are compressed into scalar scores for ranking position pairs.

Direct-Coupling Analysis

  • DCA models variability in an input multiple-sequence alignment using a generalized Potts model, assigning a probability to each aligned sequence of nucleotides or gaps.Source: Direct-Coupling Analysis · p. 4
  • The sequence-probability model includes pairwise direct couplings and single-position local biases, with a partition function that normalizes the probability.Source: Direct-Coupling Analysis · p. 4
  • Model parameters are adjusted to reproduce empirical single-position and paired-nucleotide statistics from the alignment, and are estimated using a mean-field approach.Source: Direct-Coupling Analysis · p. 4
  • Each 5x5 coupling matrix is compressed into the scalar score Fapc to rank position pairs by coupling strength.The paper contrasts DCA with local correlation measures such as mutual information.Source: Direct-Coupling Analysis · pp. 4–5

Secondary structure prediction

The study tests DCA scores in a generalized Nussinov algorithm against mutual-information-based scores, using the same algorithmic framework to compare score types. Its secondary-structure predictions are evaluated against PDB structures, and DCA performs better than MI and MIapc at comparable sensitivity.

Secondary structure prediction

  • Watson-Crick base pairs involve coordinated mutations, and RNA secondary-structure methods may incorporate residue co-variation alongside thermodynamic information.Source: Secondary structure prediction · p. 5
  • The generalized Nussinov algorithm compares MI, MIapc, and DCA's Fapc scores under otherwise identical conditions; the algorithms are intended to isolate score effects, not serve as state-of-the-art predictors.The minimum hairpin loop length is three nucleotides; integration into RNAalifold is outside the study's scope.Source: Secondary structure prediction · p. 5
  • The scoring matrix starts with -1 for incompatible pairs, retains only the L largest covariance scores, and updates entries only for mapped, base-pair-compatible nucleotide pairs.This construction limits the matrix to at most L positive entries, avoiding overpairing.Source: Secondary structure prediction · p. 5
  • At a cutoff of L positive entries, DCA predictions approach the Rfam consensus structure's sensitivity and precision against PDB secondary structure, while MI and MIapc are less accurate at comparable sensitivity.The number of potential base pairs and coevolutionary scores scales as L2, while actual base pairs scale as L.Source: Secondary structure prediction · p. 6

Tertiary contact enrichment

The analysis removes trivial spatial neighbors and secondary-structure-adjacent pairs before ranking candidates for tertiary contacts. It evaluates contact enrichment in sliding windows using a binomial null model and a local p-value criterion.

Tertiary contact enrichment

  • Pairs closer than five sequence positions and pairs neighboring secondary-structure base pairs are removed before DCA scores rank candidates for tertiary contacts.For each secondary-structure pair, the procedure also removes 25 nearby pairs.Source: Tertiary contact enrichment · p. 6
  • Contacts are defined from minimum heavy-atom distances in a representative PDB structure, using either an 8 Å or 4 Å cutoff.Source: Tertiary contact enrichment · p. 6
  • For each ranking position X, a sliding window covers predictions ranked X+1 through X+Y, and the analysis counts its true-positive contacts.Source: Tertiary contact enrichment · p. 6
  • The true-positive rate is calculated over the entire list of residue pairs remaining after the X highest-scoring pairs are excluded.Source: Tertiary contact enrichment · p. 7
  • A binomial null model supplies a local p-value, with window size Y set to 10% of the list as a compromise between resolution and reliability.The local criterion is more stringent than a global p-value over the first X predictions.Source: Tertiary contact enrichment · pp. 6–7

Tertiary Structure Prediction via Rosetta

Rosetta uses secondary-structure information to build RNA models, then incorporates predicted tertiary contacts as energetic constraints. The resulting conformations are scored and clustered to identify representatives.

Tertiary Structure Prediction via Rosetta

RESULTS

Direct-coupling scores improve secondary-structure prediction relative to mutual information, while some apparent errors may reflect alignment mismatches or a problematic reference structure. The results also identify conditions in which errors are more likely.

Direct-Coupling Analysis improves RNA secondary structure prediction

  • DCA increases secondary-structure sensitivity at almost unchanged precision compared with MI, and its improvement exceeds that of MI with average product correction.Direct-coupling scores are used as input to a Nussinov-type dynamic-programming algorithm.Source: Direct-Coupling Analysis improves RNA… · p. 7
  • Errors are more likely in regions that do not align between the crystal-structure sequence and the Rfam alignment, where the Nussinov scoring matrix cannot be properly defined.Source: Direct-Coupling Analysis improves RNA… · p. 8
  • For the 2gdi third stem, 54% of ungapped sequences were exclusively compatible with DCA-predicted pairs, while 2% were exclusively compatible with the selected PDB structure.Compatibility means the nucleotides may form a Watson-Crick or wobble pair; 31% were compatible with both structures.Source: Direct-Coupling Analysis improves RNA… · p. 8

Direct-Coupling Analysis detects coevolving tertiary structure contacts

The analysis asks whether RNA coevolution can reveal tertiary contacts despite their reportedly weaker signals than secondary-structure contacts. After secondary and neighboring pairs are removed, DCA shows higher tertiary-contact fractions than MI and MIapc, with a consistent improvement also reported for a broader family set.

Direct-Coupling Analysis detects coevolving tertiary structure contacts

  • The study addresses the concern that tertiary-contact coevolutionary signals may be weaker than secondary-structure signals or indistinguishable from noise in many RNA families.Source: Direct-Coupling Analysis detects… · p. 8
  • The analysis evaluates six RNA families at strict 4 Å and permissive 8 Å contact cutoffs, the latter intended to reflect structural variability among family members.Source: Direct-Coupling Analysis detects… · p. 8
  • After secondary-structure and neighboring pairs are removed, DCA predictions contain substantially higher tertiary-contact fractions than MI and MIapc, though they remain below the ideal ranking.The unfiltered rankings look similar because their strongest signal comes from secondary-structure contacts.Source: Direct-Coupling Analysis detects… · p. 8
  • A consistent DCA improvement over MI and MIapc is also observed across 15 Rfam families with more than 1,000 sequences and non-trivial tertiary contacts.These families had PDB structures better than 3 Å resolution; large ribosomal RNA were excluded from statistics.Source: Direct-Coupling Analysis detects… · pp. 8–9

Direct-Coupling Analysis facilitates RNA tertiary structure prediction using biomolecular

The authors add predicted tertiary contacts as Rosetta constraints and report that DCA-guided models generally outperform secondary-structure-only and MI-guided predictions. Results vary by riboswitch, and Rosetta scoring can fail to select accurate models.

modeling tools

  • Adding full tertiary-contact information strongly improves RMSD over secondary-structure information alone in five of six riboswitches.The comparison uses the best-scoring Rosetta model and the minimum RMSD among the best five or ten scores.Source: modeling tools · p. 9
  • DCA-guided predictions significantly improve prediction quality over secondary-structure-only models and, in most cases, over MIapc-guided models.Across the first 10 predictions, DCA sets IV and V had a mean best RMSD of 9.6Å, compared with 11.8Å for MIapc sets II and III.Source: modeling tools · pp. 9–10
  • For 2gdi, DCA identifies all native-contact clusters missed by MI, adding constraints that substantially reduce the feasible 3D structure space.Despite similar-looking contact maps, DCA-guided structures were more accurate.Source: modeling tools · p. 10
  • For 3owi, predictions remain relatively inaccurate despite few false positives because the contact maps add limited tertiary information beyond secondary structure.The authors note that the predicted maps are dominated by secondary-structure contacts.Source: modeling tools · p. 10
  • For 3vrs, Rosetta scoring misses better full-contact models near 9Å and consistently favors clusters at 12–16Å RMSD; residue-contact lists also omit native atom–atom distances.The reported limitation applies even when full native residue-residue contacts are provided.Source: modeling tools · p. 10

DISCUSSION

The discussion argues that DCA predictions can improve RNA 3D modeling despite weak tertiary-contact signals, while emphasizing alignment quality and contact precision as constraints. The authors also describe blind applications and future opportunities to improve statistical predictions and modeling.

DISCUSSION

  • DCA results can be integrated into RNA 3D prediction to systematically and robustly improve accuracy despite weak coevolutionary signals from tertiary contacts.For an alignment, DCA takes at most a few minutes on a standard desktop, while Rosetta modeling requires substantially more computation.Source: DISCUSSION · p. 10
  • The method is applied in blind predictions to the glnA riboswitch and C4 antisense RNA, with target sequences chosen where sequence-specific DCA and Rfam consensus secondary structures agree.No experimental PDB structures were known for these RNA families.Source: DISCUSSION · p. 11
  • The authors emphasize improving DCA statistical predictions, while noting future work may also improve Rosetta protocols or scoring schemes.They describe the pipeline as modular, allowing improvements to alignments, DCA signal extraction, or integration of other knowledge.Source: DISCUSSION · pp. 10–11
  • Alignment quality remains an unresolved constraint: improving quality at fixed sequence count or increasing family sampling yields almost comparable gains over a small, limited-quality alignment.The authors suggest improving alignment quality without relying on structural information to combine its benefits with large sequence samples.Source: DISCUSSION · p. 11
  • At the 0.01 enrichment-significance threshold, DCA finds 54% of contacts at 15% precision, versus 25% sensitivity and 13% precision for MI with APC.The authors caution that DCA's resulting precision may still be too low for practical tertiary-structure prediction.Source: DISCUSSION · p. 12

TABLE AND FIGURES LEGENDS

The legends map the DCA-guided prediction pipeline and compare secondary-structure, contact, and three-dimensional predictions. They also describe an alignment comparison for bacterial RNase P.

TABLE AND FIGURES LEGENDS

  • DCA-derived tertiary-contact constraints improve Rosetta RMSD over secondary-structure information alone in all but one riboswitch; DCA also has an edge over MIapc.The table compares best, best 5, and best 10 scoring clusters using SSI, MIapc, DCA, or the complete native contact map; constraints use unknown native distances.Source: TABLE AND FIGURES LEGENDS · p. 16, Table 1 · p. 16
  • The pipeline analyzes Rfam homologs with DCA, uses a generalized Nussinov algorithm for secondary structure, and supplies curated consensus structure and DCA contacts to Rosetta.Rosetta clusters and scores its predictions, returning representative structures from the best-scoring clusters.Source: TABLE AND FIGURES LEGENDS · p. 17, Figure 1 · p. 17
  • DCA consistently increases secondary-structure sensitivity over MI and MIapc without losing precision.Figure 2 plots sensitivity and precision for individual RNA families and their averages.Source: Figure 2 · p. 17, TABLE AND FIGURES LEGENDS · p. 18
  • Figure 3 distinguishes DCA-only, MI-only, shared true base pairs, and missed native pairs, while Figure 5 overlays native structures with DCA-guided predictions.Figure 5 shows predictions with the lowest native RMSD among the first 10 clusters; residuewise deviations are colored from green at 0Å to red at 15Å or more.Source: TABLE AND FIGURES LEGENDS · pp. 18, 20, Figure 3 · p. 18, Figure 5 · p. 20
  • For tertiary contacts, Figure 4 compares TP rates as predictions accumulate at 4Å and 8Å, both before and after secondary-structure pairs and neighbors are excluded.The all-pairs rankings are in panels A and C; panels B and D retain non-trivial three-dimensional contacts.Source: TABLE AND FIGURES LEGENDS · p. 19, Figure 4 · p. 19
  • For bacterial RNase P, the structural alignment performs best at a 4Å contact threshold, while the full Rfam alignment performs similarly at 8Å; the reduced alignment performs worst.The comparison plots TP rates against the number of predictions for three sequence alignments.Source: TABLE AND FIGURES LEGENDS · pp. 21–22, Figure 7 · p. 21

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