Sequence-Informed Geometric Evaluation of RNA 3D Structures

Andrea Zerio; Yighua Yao; Alessandro Micheli; Roland G. Huber; Mile Sikic; Samir Bhatt; Andres R. Masegosa; Yuangang Pan

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Sequence-Informed Geometric Evaluation of RNA 3D Structures

Andrea Zerio, Yighua Yao, Alessandro Micheli, Roland G. Huber, Mile Sikic, Samir Bhatt, Andres R. Masegosa, Yuangang Pan

arXiv:2609.10644v1Sep 9, 2026q-bio.BMcs.LG

TL;DR

RNA structure pipelines need to rank multiple candidate conformations by compatibility with their sequence, not geometry alone. SIRGE conditions geometric representations on pretrained RNA language-model embeddings, and early benchmark analyses show improved rank alignment, candidate selection, and ordering. The results provide initial evidence that sequence representations complement geometric reasoning.

Problem
Multiple candidate RNA conformations require evaluation that determines whether their geometry is compatible with the originating sequence.
Method
SIRGE ranks RNA structure candidates by conditioning SE(3)-invariant geometric representations on contextual embeddings from a pretrained RNA language model.
Results
SIRGE improves Kendall–τ rank alignment, top-1 retrieval, top-3 ranking, and target-level candidate ordering over established evaluators and a structure-only variant.
Takeaways & Limitations
Early controlled analyses indicate that pretrained sequence representations supply ranking information that complements geometry and improves selection of high-quality RNA candidates.
Takeaways & Limitations
The evidence is early, and the authors plan to test SIRGE on candidates generated by modern structure-prediction models.

Abstract

from arXiv · show

Computational RNA structure pipelines generate many candidate conformations for the same sequence. Reliable evaluation therefore requires more than recognising plausible geometry, it requires determining whether that geometry is compatible with the sequence. We introduce SIRGE, a sequence-informed geometric evaluator that conditions structural representations on nucleotide embeddings from a pretrained RNA language model. Early results show that SIRGE outperforms established evaluators in Kendall--$τ$ alignment, Top-1 selection, and Top-3 ranking. Controlled comparisons further show that sequence conditioning corrects errors made by an otherwise matched geometric model and improves target-level rank structure. These findings provide initial evidence that pretrained sequence representations supply ranking information that complements geometric reasoning.

1 Introduction

SIRGE addresses RNA candidate evaluation as a sequence–geometry compatibility problem, combining geometric representations with pretrained sequence context. The paper reports early improvements across ranking and retrieval measures.

1 Introduction: RNA evaluation matters because computational pipelines generate multiple conformations whose quality varies for the same sequence.Errors during evaluation can negate improvements made by the structure predictor.
1 Introduction: SIRGE combines an SE(3)-equivariant atom transformer, nucleotide-local frames, dense invariant point attention, and atom residual connections before scoring candidates.This architecture integrates sequence context with both nucleotide-level interactions and fine-grained atom-level geometry.
1 Introduction: Pretrained sequence representations provide context about which structural arrangements are plausible for a particular RNA and may transfer to unseen targets.The sequence is available when candidates are scored, enabling sequence–geometry alignment to be learned directly.
1 Introduction: Existing geometric evaluators use increasingly expressive geometry but do not condition those representations on contextual nucleotide embeddings pretrained across large RNA sequence collections.RNA language models learn dependencies across sequences through self-supervised pretraining.
1 Introduction: SIRGE ranks RNA 3D candidates by combining candidate geometry with contextual nucleotide embeddings from a pretrained RNA language model.The evaluator is designed to assess sequence–geometry compatibility rather than geometry alone.
1 Introduction: Early results show improvements in Kendall–τ rank alignment, top-1 retrieval, top-3 ranking, and candidate ordering from sequence-informed geometric reasoning.Controlled comparisons include a structure-only variant and target-level analyses.

2 Sequence-Informed Geometric Evaluation

SIRGE constructs invariant geometric representations at atomic and nucleotide levels, conditions them on pretrained sequence embeddings, and optimizes candidate ordering without requiring native structures at inference.

2 Sequence-Informed Geometric Evaluation: SIRGE learns a scoring function whose candidate ordering is inverse to RMSD ordering and trains it with a within-RNA ListNet ranking objective.The objective uses relative ordering rather than absolute RMSD, and scoring requires only candidate coordinates and sequence at evaluation time.
Hierarchical geometric representation: An Equiformer atom encoder maps candidate atom graphs to equivariant features, which are expressed in nucleotide-local frames and pooled into invariant nucleotide representations.Local-frame construction preserves invariance to global SE(3) transformations.
Sequence–geometry conditioning: SIRGE augments geometric nucleotide representations with nucleotide identity and pretrained contextual embeddings to capture local and long-range sequence dependencies.RiNALMo supplies 1280-dimensional final-layer representations learned from 36 million ncRNA sequences.
Sequence–geometry conditioning: Sequence-only information cannot change the relative ordering of candidates for one RNA because all candidates share the same sequence.SIRGE instead evaluates how each candidate geometry agrees with the sequence context.
Geometric reasoning and readout: Four dense invariant point-attention blocks propagate conditioned information across nucleotide frames while preserving SE(3) invariance.A residual atom path retains invariant atom-level information that may be diluted during atom-to-nucleotide aggregation.
Geometric reasoning and readout: The model combines pooled nucleotide-level and residual atom-level paths to produce the final candidate score.The two paths preserve both integrated contextual geometry and fine-grained geometric information.

3 Experimental Validation

The evaluation benchmarks SIRGE against established evaluators and a structure-only ablation using rank-alignment, retrieval, and ranking metrics. SIRGE consistently performs best, with sequence conditioning providing additional gains, especially for poorer candidates.

Dataset and experimental setup: The benchmark contains 190 non-redundant single-chain RNA targets with candidate conformations from molecular dynamics, ARES, and RNA-Puzzles pools.The study compares SIRGE with seven baselines.
Dataset and experimental setup: Kendall–τ alignment is measured globally and on ten-candidate lists stratified into D1 (2–5 Å), D2 (5–10 Å), and D3 (10–15 Å) bands.The reported metrics evaluate agreement between predicted scores and inverse RMSD ordering.
Sequence information complements geometry: Pairwise accuracy gains from RiNALMo conditioning are largest for poorer candidate structures relative to a matched structure-only backbone.Candidate quality is represented by within-RNA RMSD percentile, with 0 denoting the best candidate.
Sequence information complements geometry: The results suggest that sequence embeddings provide conformational priors that complement geometric features rather than replacing geometric reasoning.This interpretation is supported by the separation between SIRGE-SO and sequence-conditioned SIRGE.
Sequence information complements geometry: SIRGE produces sharper target-level rank-density diagonals and fewer dispersed high-density regions than HomRank and SIRGE-SO.Diagonal concentration indicates closer agreement between predicted and true candidate ordering.

4 Conclusion

SIRGE frames RNA candidate ranking as sequence–geometry compatibility and reports early evidence that pretrained sequence conditioning improves evaluation beyond geometry alone.

Conditioning geometric representations on pretrained RNA language-model embeddings improves global rank alignment and selection of high-quality candidates.Controlled analyses indicate that sequence information complements the signal available from geometry alone.

A Related Work

RNA structure evaluation has progressed from hand-crafted potentials to learned geometric models, while pretrained sequence representations remain underused for ranking alternative conformations.

Hand-crafted RNA evaluation objectives are limited by how well their terms approximate RNA folding physics.
Learned evaluators derive candidate representations from voxelised atomic environments or geometric graph networks.Later methods add nucleotide-local frames, invariant point attention, and hierarchical equivariant representations.
RNA-FM and RiNALMo learn contextual nucleotide embeddings from unlabelled sequences, but their structural use has focused mainly on predicting properties rather than ranking conformations.

B Formal Properties and Learning Objective

The formal analysis frames RNA candidate evaluation as sequence–geometry compatibility and shows why candidate-dependent sequence conditioning can improve ranking, while preserving rigid-motion invariance. The ListNet objective uses homogeneous candidate lists and concentrates supervision on selecting the best candidate.

B.1 Sequence–geometry alignment: Sequence–geometry alignment relates each candidate’s spatial organisation to pretrained sequence features at the same nucleotide indices.The geometric representation describes the realised candidate environment, while contextual embeddings provide sequence-derived structural preferences.
B.1 Sequence–geometry alignment: A shared sequence-only scalar cannot change candidate ordering because it cancels from pairwise score differences and leaves the ListNet objective unchanged.The added term preserves pairwise orderings and ties because the embedding is identical across candidates for one RNA.
B.1 Sequence–geometry alignment: Candidate-dependent interaction is therefore required for explicit sequence embeddings to affect relative scores and ranking.The auxiliary-score analysis distinguishes sequence information that interacts with geometry from an independent sequence bias.
B.1 Sequence–geometry alignment: I(J; S | UL) ≥0 formalises that conditioning ranking on sequence can reduce Bayes-optimal risk relative to geometry alone.The reduction equals the conditional mutual information between the top-one target variable and the sequence given candidate geometry.
B.1 Sequence–geometry alignment: I(J; E | UL) ≤ I(J; S | UL) shows that contextual embeddings cannot contain more ranking-relevant information than the underlying sequence.They can nevertheless reduce Bayes-optimal ranking risk when I(J; E | UL) > 0.
B.2 Rigid-motion invariance: IPA geometric reasoning remains invariant under global rigid transformations because point differences rotate while Euclidean distances and attention terms remain unchanged.Invariant value projections ensure that all IPA outputs remain invariant.
B.2 Rigid-motion invariance: Rigid-motion invariance follows because transformed local frames preserve invariant geometric nucleotide representations and sequence embeddings depend only on the unchanged sequence.The atom encoder is equivariant, local frames co-transform, and nucleotide pooling operates on invariant features.
B.3 Listwise objective and homogeneous batches: Homogeneous batches compare alternative conformations of one RNA, and the temperature-τ ListNet loss primarily supervises top-one selection.Candidates are grouped within lists by RMSD rank, with tied relevance for RMSD differences no greater than δ = 0.1 Å and temperature τ = 0.1.

C Architecture and Implementation Details

SIRGE builds candidate representations from atomic geometry, projects them into nucleotide-local frames, and combines them with pretrained nucleotide embeddings. Dense invariant point attention then reasons across nucleotides before scalar candidate scoring.

Atomic encoder: Each candidate is encoded as a heavy-atom graph with nearest-neighbour connections and three Equiformer blocks using equivariant geometric features.Node features represent C, N, O, P, and S; distances use 16 radial basis functions over 30 Å.
Nucleotide projection and sequence conditioning: SIRGE combines nucleotide representations derived from atomic geometry with corresponding 1280-dimensional RiNALMo embeddings.The structure pathway uses local nucleotide frames, while RiNALMo supplies the sequence-conditioned representation.
Nucleotide reasoning and readout: Four dense invariant point-attention blocks allow every nucleotide to attend to every other nucleotide within a candidate.A learned-query pool produces a 64-dimensional candidate representation for scalar readout.

D Dataset Construction and Split Integrity

The experiments use a 190-target RNA benchmark with candidate ensembles generated from experimental and established benchmark sources. Sequence-based target-level partitions and leakage controls keep complete RNA candidate ensembles within one split and reserve distinct sequence-similarity clusters for training, validation, and testing.

Data sources and candidate generation: The benchmark contains 190 non-redundant single-chain RNA targets, with candidate ensembles from newly collected structures, ARES, and RNA-Puzzles.HomRank generated 1,000 candidates for each of the 151 newly collected targets and ARES targets.
Sequence-based partitioning: Hierarchical clustering produces CLS-0, CLS-1, and CLS-2 sequence-similarity groups used for training, final evaluation, and validation respectively.After excluding 15 RNA-Puzzle targets from CLS-0, 131 CLS-0 targets form training; CLS-2 has 23 RNAs and CLS-1 has 21.
Leakage controls: Splitting at the RNA-target level keeps each sequence, native structure, and complete candidate ensemble in a single partition.Validation and test candidates do not appear during training, and the partitions use distinct sequence-similarity clusters.
Dataset summary: Table 2 documents dataset partitions and reports candidate counts for the complete source benchmark before evaluation-time subsampling.

E Experimental Protocol

SIRGE is compared with learned evaluators spanning voxel, physics-aware graph, frame-based, equivariant, and listwise approaches, alongside Rosetta. All learned methods are retrained under a shared training protocol and evaluated with rank-alignment and candidate-selection metrics over repeated runs.

Baselines: The comparison includes six learned evaluators and Rosetta, covering complementary geometric and physics-aware modelling approaches.The learned baselines are RNA3DCNN, PAMNet, lociPARSE, EquiRNA, HomRank, and ARES.
Training and model selection: All learned methods are retrained for five epochs on the same CLS-0 training set, with model-specific optimisation settings following published implementations.SIRGE uses AdamW with warm-up, cosine decay, weight decay, clipping, and a 3 × 10^-3 learning rate.
Evaluation metrics: Kendall alignment uses the full candidate pool, while Top-1 and Top-3 evaluate sampled ten-candidate lists for retrieval and ordering accuracy.RMSD differences below 0.1 Å are treated as ties for Top-3 ranking.
Reproducibility and hardware: Each learned method is evaluated across three independent training runs, with mean and standard deviation reported.Experiments use four NVIDIA RTX PRO 6000 Blackwell GPUs with 98 GB each.

F Complete Quantitative Results

SIRGE achieves the strongest reported candidate-selection and ranking results globally and across all three quality regimes. The matched structure-only variant already improves over existing evaluators, while sequence conditioning adds gains in every setting, especially for lower-quality candidate lists.

Selection and ranking metrics: Top-1 retrieval measures selecting the lowest-RMSD candidate, whereas Top-3 ranking measures correctly ordering the three best candidates.The tables report global results and D1, D2, and D3 bands based on the best candidate’s RMSD.
Reported result tables: Tables 3–5 report Test-CLS-1 Top-1 retrieval, Top-3 ranking, and Spearman alignment as mean ± standard deviation over three random seeds.Higher values are better for each table.
Complete quantitative results: SIRGE achieves the strongest result for every reported metric globally and across D1, D2, and D3 quality regimes.The reported measures include Top-1 retrieval, Top-3 ranking, and Spearman alignment; results are averaged equally across RNAs.
Sequence-conditioned comparison: Sequence conditioning improves candidate-selection decisions and overall rank agreement beyond the matched structure-only architecture.The gains are particularly clear in D2 and D3, where candidate quality is lower.