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La-Ribo: RNA Co-Design via Geometry-Latent Flow Matching

Runze Ma, Will Hua, Shuangjia Zheng

arXiv:2610.12236v1q-bio.BMcs.AI

TL;DR

RNA co-design must coordinate nucleotide identity with global folding despite limited structural supervision. La-Ribo jointly generates sparse scaffold geometry and residue-wise latents, improving designability and codesignability over evaluated baselines while supporting scaffold-conditioned inverse folding without further training.

  • Problem

    RNA co-design must coordinate nucleotide identity with global folding, while structural supervision is limited and predicted structures vary in reliability.

    Source: §1 · p. 1

  • Method

    La-Ribo jointly models sparse RNA scaffold geometry and residue-wise latents with a shared flow, then decodes sequence and heavy-atom structure.

    Source: §1 · p. 2

  • Results

    La-Ribo improves designability and codesignability over evaluated baselines across sampling budgets and refolding models.

    Source: §1 · p. 2, §5 · p. 10

  • Takeaways & Limitations

    The same trained prior supports scaffold-conditioned inverse folding without additional training.

    Source: §1 · p. 2, §5 · p. 10

    Most corpus structures are predicted or synthetic, creating an atom-level geometry distribution gap that limits attainable atomistic accuracy.

    Source: H LIMITATIONS AND BROADER IMPACT · p. 35

Abstract

from arXiv · show

RNA function arises from the coupling of nucleotide sequence and three-dimensional structure, motivating their joint design. Coordinating global folding with nucleotide-level detail remains challenging under limited structural supervision. We introduce La-Ribo, a generative framework for RNA sequence-structure co-design via geometry-latent flow matching. La-Ribo retains a sparse phosphate-sugar--base scaffold and encodes nucleotide identity and local conformation in residue-wise latents. A shared flow network generates both jointly, and an RNA-specific decoder then reconstructs all heavy atoms. To expand supervision, we construct a quality-controlled corpus of 168,561 RNA structures, integrating experimental data with predictions from three folding models, including 10,631 MSA-supported structures generated in this work. La-Ribo improves designability and codesignability over the evaluated baselines across sampling budgets and two refolding models, and the same prior supports scaffold-conditioned inverse folding without additional training.

1 INTRODUCTION

La-Ribo addresses RNA co-design’s representation and supervision challenges with a geometry–latent flow framework and a quality-controlled structural corpus. It improves designability and codesignability over evaluated baselines.

1 INTRODUCTION

  • RNA co-design must preserve long-range organization and nucleotide-specific local conformations despite sparse experimental structures and variable, potentially biased predictions.The paper identifies representation and structural supervision as its two challenges.Source: §1 · p. 1
  • La-Ribo jointly generates sparse P, C4′, and glycosidic-N scaffold coordinates with residue-wise latents encoding nucleotide identity and local conformation.A learned scaffold-to-sugar frame transformation links the informative anchors to atom construction.Source: §1 · p. 2
  • The quality-controlled corpus contains 168,561 RNA structures, including 10,631 MSA-supported trRosettaRNA2 structures generated in this work.Predictions from three folding models are screened by source-specific confidence and common eligibility criteria.Source: §1 · p. 2
  • La-Ribo improves designability and codesignability over evaluated baselines across sampling budgets and refolding models.The corpus integrates experimental and predicted structures under source-specific screening.Source: §1 · p. 2

2 RELATED WORK

Prior RNA-generation work spans sequence generation, inverse folding, structure generation, and joint co-design. La-Ribo combines sparse RNA geometry with continuous residue-wise latents and reuses its prior for scaffold-conditioned inverse folding.

2.1 RNA GENERATION, INVERSE FOLDING, AND CO-DESIGN

  • RNA-generation approaches cover sequence-centric design, structure generation, inverse folding, and co-design, with co-design methods differing in conditioning and sequence–structure representations.La-Ribo uses continuous latents rather than a discrete nucleotide variable, avoiding a discrete–continuous hybrid flow and separate conditional training for scaffold-conditioned inverse folding.Source: §2.1 · p. 2

2.2 EXPLICIT AND LATENT BIOMOLECULAR REPRESENTATIONS

  • La-Ribo pairs sparse RNA geometry with continuous residue-wise latents and a learned scaffold-to-sugar frame transformation, addressing RNA anchors’ mismatch with rigid-frame atom construction.Unlike La-Proteina’s protein representation, informative RNA anchors span distinct chemical groups.Source: §2.2 · p. 3

3 METHOD

La-Ribo first learns an RNA-specific geometry–latent representation, then trains a shared flow over scaffold and latent states. Its decoder reconstructs sequence and heavy-atom structure, while sampling supports both unconditional design and approximate scaffold-conditioned inverse folding.

3.1 GEOMETRY–LATENT REPRESENTATION

  • Each residue combines nine explicit scaffold coordinates for P, C4′, and glycosidic nitrogen with 16 latent dimensions for nucleotide identity and local atomic detail.The scaffold captures backbone and base-attachment geometry; the latents encode detail not determined by it.Source: §3.1 · p. 3

3.2 SCAFFOLD-CONDITIONED AUTOENCODING

  • The scaffold-conditioned autoencoder encodes residue-wise latents and decodes nucleotide identity, a scaffold-to-sugar rotation, and torsions for structured heavy-atom reconstruction.A learned transformation bridges informative scaffold anchors and the canonical sugar frame required for atom construction.Source: §3.2 · pp. 3–4, Figure 1 · p. 4

3.3 GEOMETRY–LATENT FLOW MATCHING

  • With the encoder and decoder fixed, a shared velocity network learns flow dynamics over scaffold and latent states using independently sampled modality times.Training fits geometry–latent targets directly, without decoded-coordinate or sequence losses.Source: §3.3 · p. 5

3.4 SAMPLING

  • Unconditional sampling jointly integrates scaffold and latent states with modality-specific schedules, while scaffold-conditioned inverse folding fixes the observed scaffold and integrates only latents.The inverse-folding procedure is approximate: fixing the scaffold at tB = 1 slightly extrapolates beyond training times and does not exactly recover the joint distribution’s conditional.Source: §3.4 · p. 5

4 EXPERIMENTS

Experiments test La-Ribo’s representation, unconditional generation, ablations, and scaffold-conditioned inverse folding. La-Ribo-Tri leads strict designability across sampling budgets, while latent interventions and ablations probe what contributes to performance.

4.1 EXPERIMENTAL SETUP

  • The cluster-held-out validation set contains 8,606 structures; comparisons include released RNA-FrameFlow weights, retrained RiboFlow regimes, and La-Ribo-Base and La-Ribo-Tri variants.RiboGen, Joint Diffusion, and DuetRNA were not rerun because code was unavailable; the two La-Ribo variants share a pretrained scaffold-conditioned autoencoder.Source: §4.1 · pp. 5–6

4.3 UNCONDITIONAL RNA GENERATION

  • At 200 steps, La-Ribo-Tri reaches 39.11 ± 2.12% strict designability (both@4.0), versus 27.61 ± 1.07% for RiboFlow-Mix, and 32.06±0.75% strict codesignability, versus 26.00±1.38%.La-Ribo-Tri leads strict designability at all four step counts; OpenDDE also favors both La-Ribo variants over their baselines.Source: Table 1 · p. 6, §4.3 · p. 8

4.2 REPRESENTATION AND LATENT ANALYSIS

  • With the scaffold fixed, posterior latents yield 100% sequence recovery, while zero latents reduce recovery to 24.77% and raise non-scaffold RMSD to 0.773 Å.Shuffling latents raises RMSD to 0.965 Å; single-residue perturbations displace edited-residue atoms far more than others, indicating residue-local effects.Source: Figure 2 · p. 6, §4.2 · p. 7

4.4 ABLATION STUDIES

  • At 200 steps, E-VAE/Tri reaches 30.17% strict designability using experimental-only training, while expanding flow training data adds 8.39 points for La-Ribo and 7.11 for RiboFlow.Tri improves on Base across five metrics under both representations; triangle-update variants have indistinguishable strict designability (37.33–39.11%), but the two-block variant reaches 58.83% topology success versus 53.00% for Base.Source: Table 2 · p. 7, §4.4 · pp. 8–9, Figure 5 · p. 9

4.5 SCAFFOLD-CONDITIONED INVERSE FOLDING

  • Without conditional training, La-Ribo-Tri attains the highest best-of-eight strict success (14.84 ± 0.70%) and scTM (0.313), while La-Ribo-Base has the lowest scRMSD (11.91 Å).La-Ribo conditions on three anchors per residue and is cluster-held-out; the compared gRNAde and NA-MPNN models receive native structures and may have training-data overlap.Source: §4.5 · p. 9, Table 4 · p. 9

5 CONCLUSION

La-Ribo jointly generates a sparse RNA scaffold and residue-wise latents, and reuses the same prior for scaffold-conditioned inverse folding without further training. The conclusion reports improved designability and codesignability over evaluated baselines, while identifying experimental evaluation and longer-RNA scaling as future work.

5 CONCLUSION

  • La-Ribo improves designability and codesignability over evaluated baselines across sampling budgets and refolding models.The conclusion also identifies experimental evaluation and scaling to longer RNAs as future work.Source: §5 · p. 10
  • The same geometry–latent prior supports scaffold-conditioned inverse folding without additional training.Nucleotide identity is carried by the residue-wise latents.Source: §5 · p. 10
  • A quality-controlled corpus of 168,561 RNA structures combines experimental data with predictions from three folding models.The paper also describes future corpus expansion as new structures become available.Source: §5 · p. 10

A DATASET CONSTRUCTION AND CORPUS STATISTICS

The corpus combines curated experimental structures with filtered predictions and newly generated MSA-supported structures, then applies common eligibility checks and cluster-held-out partitioning. Its sources share dominant local-geometry modes but differ in joint geometry and length distributions.

A DATASET CONSTRUCTION AND CORPUS STATISTICS

  • 168,561 structures pass the 16–256-nucleotide length range and minimum 90% valid-frame coverage after source-specific screening and common eligibility checks.The corpus combines curated experimental entries, filtered existing synthetic resources, and newly generated trRosettaRNA2 structures.Source: A DATASET CONSTRUCTION AND CORPUS… · p. 16, Table 5 · p. 16
  • 10,631 newly generated trRosettaRNA2 structures come from MSA-supported predictions filtered by mean pLDDT above 80 and relaxed top-ranked structure selection.Sequences were drawn from bpRNA-1m(90) and RNAStralign, length-restricted, and deduplicated.Source: A DATASET CONSTRUCTION AND CORPUS… · p. 16

A.1 DATASET CONSTRUCTION

  • 90%-identity sequence clusters are assigned wholly to one split, yielding 159,955 training and 8,606 validation records.Both autoencoder and flow training use only the training partition; validation is reserved for evaluation.Source: §A.1 · p. 17

A.2 PREPARED REPRESENTATION

  • The prepared representation pairs canonical sequence and atomistic structure, extracts scaffold and geometric targets, and uses residue, atom, and torsion masks for valid supervision.MSAs are used upstream to generate part of the synthetic corpus, not as model inputs.Source: §A.2 · p. 17

A.3 CORPUS DISTRIBUTIONS AND SAMPLING

  • One-dimensional local-geometry divergences are below 0.055 bits, while joint (η, θ) divergence is 0.1007 bits and OpenFold3–trRosettaRNA2 divergence is 0.1697 bits.Experimental and synthetic structures share dominant modes; Figure 7 shows pooled and source-specific distributions of distances, angles, dihedrals, and joint (η, θ) density.Source: §A.3 · p. 17, Figure 7 · p. 18
  • The pooled length distribution peaks near 73 nucleotides because of the large OpenFold3 collection, while experimental, NuFold, and trRosettaRNA2 sources provide complementary coverage.Figure 8 shows pooled and source-specific length distributions and labels the fraction above 160 nt.Source: §A.3 · p. 17, Figure 8 · p. 19

B.1 ARCHITECTURE AND OPTIMIZATION

The appendix details a geometry-aware autoencoder and a shared flow network that model RNA scaffold and residue-wise latent states. Interventions and representation comparisons indicate that latents contribute information beyond the scaffold, while the three-anchor, width-16 setting gives the lowest reported RMSD values among tested widths.

B.1 ARCHITECTURE AND OPTIMIZATION

  • The autoencoder uses six token–pair blocks in each encoder and decoder, while the flow uses a 12-block trunk with residue and pair features.La-Ribo-Base keeps pair features fixed; La-Ribo-Tri updates them every two blocks using token-to-pair projections and triangle multiplicative updates.Source: §B.1 · p. 20, Table 7 · p. 20, Table 8 · p. 20

B.2 SCAFFOLD-CONDITIONED AUTOENCODING: EXACT OBJECTIVE

  • The autoencoder reconstructs nucleotide identity and geometry through sequence, rotation, torsion, and template-dependent geometric losses, with masked entries excluded from the geometric sums.Predicted-template selection is non-differentiable, so its geometric losses do not backpropagate through argmax to nucleotide logits; the nucleotide head receives cross-entropy supervision.Source: §B.2 · p. 22

B.3 GEOMETRY–LATENT FLOW: TRAINING AND SAMPLING

  • The flow is trained after freezing the encoder and decoder, using geometry–latent targets rather than decoded atom or sequence losses.For scaffold-conditioned inverse folding, the observed scaffold is fixed and only the latent modality is integrated before decoding with that scaffold.Source: §B.3 · pp. 23–25

C.1 LATENT INTERVENTIONS

  • Zeroing or shuffling latents lowers sequence recovery and increases reconstruction error, showing that latent values and residue assignments contribute information beyond the supplied scaffold.The interventions are paired by structure on cluster-held-out validation data, with the scaffold fixed.Source: §C.1 · p. 25, Table 10 · p. 25

C.2 SCAFFOLD CHOICE AND LATENT DIMENSIONALITY

  • The three-anchor scaffold reduces all-atom and non-scaffold RMSD relative to one- and two-anchor alternatives; width 16 gives the lowest reported RMSD values among three-anchor variants.Mean non-scaffold RMSD is 0.1225 Å at width 16, versus 0.1334 Å at width 8 and 0.1227 Å at width 32.Source: §C.2 · p. 25, Table 11 · p. 26

D.1 COMPLETE BENCHMARK METRICS

The appendix expands benchmark protocols and reports that denser triangle updates improve strict codesignability over sparser variants, while secondary-structure agreement and atomistic geometry are assessed with distinct reference comparisons. The reported atomistic results also identify geometry-specific strengths and residual mismatches.

D.1 COMPLETE BENCHMARK METRICS

  • The expanded benchmark tables report percentages for success rates, continuous errors and cluster counts alongside thresholded endpoints, with sampling steps counted as velocity-network evaluations.Table 12 provides expanded unconditional-generation metrics under the main benchmark protocol.Source: §D.1 · p. 26, Table 12 · p. 27

D.2 TRIANGLE-UPDATE FREQUENCY ACROSS BUDGETS

  • At 200 steps, the two-block triangle-update variant gains 5.23 and 6.89 percentage points in strict codesignability over the sparser variants.Across 50–400 steps, it has higher strict codesignability than either sparser variant, although Base remains competitive and triangle refinement is not uniformly preferable for every endpoint.Source: §D.2 · p. 28, Table 14 · p. 28

E.1 SECONDARY-STRUCTURE AGREEMENT

  • DSSR yields higher RNAfold agreement than geometric-contact annotations, and La-Ribo-Tri’s mean F1 and MCC are within 0.05 of experimental-reference values under either annotation.Table 15 compares RNAfold agreement with geometric-contact and DSSR annotations on RNASolo and 600 La-Ribo-Tri structures.Source: §E.1 · p. 29, Table 15 · p. 29

E.2 ATOMISTIC GEOMETRY

  • Both La-Ribo variants produce fewer clashes than either baseline, and La-Ribo-Tri reduces clash count by 37% relative to La-Ribo-Base.Their three-way ribose-pucker populations track the experimental distribution; reported residuals include slightly undersampled syn conformations and slightly loose base pairing.Source: §E.2 · pp. 29–30, Table 16 · p. 29

E.3 NOVELTY RELATIVE TO THE TRAINING CORPUS

The novelty analysis calibrates generated structures against both training data and held-out experimental structures, while the schedule sensitivity collection varies scaffold and latent schedules across architectures and step budgets.

E.3 NOVELTY RELATIVE TO THE TRAINING CORPUS

  • 31.1% and 37.8% of La-Ribo variants have training neighbours at TM ≥0.8, below the held-out experimental cohort’s 67.6%.The validation structures show that sequence-level clustering does not ensure structural separation at this length range.Source: §E.3 · p. 30, Table 17 · p. 30
  • The Base, Tri, and RiboFlow-Mix TMexp-to-TMtrain gaps are +0.002, +0.015, and +0.032, respectively; La-Ribo-Tri has the highest TMexp..Source: Table 17 · p. 30, §E.3 · p. 31
  • 12.7% of held-out experimental structures meet the near-copy criteria, close to the generated cohorts’ 14.7–16.1%.The assessment requires TM ≥0.8, sequence identity ≥0.8, and coverage ≥0.8 in both directions.Source: Table 17 · p. 30, §E.3 · p. 31

F.1 MODALITY-SCHEDULE SENSITIVITY

  • The sensitivity grid varies scaffold and latent schedule powers across four architectures and three step budgets, with 600 generated RNAs at every operating point.Figures 10 and 11 show strict designability and codesignability across the schedule grid.Source: §F.1 · p. 31, Figure 10 · p. 31, Figure 11 · p. 32

F.2 SAMPLING-FACTOR RESPONSE AND RUNTIME

Across the sensitivity collection, strict endpoint success changes little with additional steps and remains high across broad schedule-power ranges; measured sampling costs differ across model variants.

F.2 SAMPLING-FACTOR RESPONSE AND RUNTIME

  • Increasing the budget from 100 to 400 steps changes either marginal strict endpoint by less than two percentage points.The reported marginal responses average over the other grid factors.Source: §F.2 · p. 33, Table 18 · p. 33
  • Sensitivity flattens at scaffold powers 0.70–1.25 and latent powers 1.80–2.00, without establishing an interior optimum.Some architecture-specific maxima remain at the upper latent-power boundary.Source: §F.2 · p. 33, Table 18 · p. 33
  • Base has the lowest measured sampling cost, Tri costs approximately four times as much, and the measured RNA-FrameFlow pipeline costs about three times as much as Tri.These are implementation-level comparisons because the timing scopes differ; La-Ribo timing uses eight A800 GPUs and excludes inverse folding, refolding, and scoring.Source: §F.2 · p. 33, Figure 12 · p. 33

G.1 PRIMARY EVALUATION SETTINGS AND BASELINE IMPLEMENTATION

The evaluation measures unconditional generation under shared inverse-folding and refolding settings, and also tests scaffold-conditioned inverse folding on held-out experimental targets. With OpenDDE replacing RhoFold, both La-Ribo variants retain higher strict success than the corresponding baselines.

G.1 PRIMARY EVALUATION SETTINGS AND BASELINE IMPLEMENTATION

  • Each unconditional campaign contains 600 direct sampler outputs, with three independently seeded campaigns per model and sampling budget.Designability uses eight inverse-folded candidate sequences per structure; codesignability evaluates the emitted sequence.Source: §G.1 · p. 34
  • gRNAde ARv1 inverse-folds candidates and RhoFold refolds them without external MSA search; these settings are shared across methods.Strict designability requires at least one of eight candidates to meet both thresholds.Source: §G.1 · p. 34

G.2 UNCONDITIONAL GENERATION WITH AN ALTERNATIVE REFOLDING MODEL

  • With OpenDDE replacing RhoFold, both La-Ribo variants retain higher strict designability and codesignability than the corresponding baselines.Table 19 reports this alternative-refolding evaluation under the settings of Table 1.Source: §G.2 · p. 34, Table 19 · p. 35

G.3 SCAFFOLD-CONDITIONED INVERSE-FOLDING PROTOCOL

  • The scaffold-conditioned protocol tests all 1,002 held-out experimental targets, giving each method eight candidate sequences without access to native sequence.La-Ribo evolves latents for 200 steps with a fixed scaffold; dedicated inverse folders receive canonicalized native structures.Source: §G.3 · p. 34

H LIMITATIONS AND BROADER IMPACT

The corpus is dominated by predicted or synthetic structures, limiting attainable atomistic accuracy, and has sparse coverage of long RNAs. Functional applications require experimental validation and biosafety review.

H LIMITATIONS AND BROADER IMPACT

  • Because most corpus structures are predicted or synthetic and differ atomistically from experimental structures, corpus distribution limits attainable atomistic accuracy.The authors expect this gap to narrow as structure-prediction models improve.Source: H LIMITATIONS AND BROADER IMPACT · p. 35
  • Only 0.31% of the corpus exceeds 160 nt, and strict success declines toward the upper end of the 40–150-nt benchmark range.The authors attribute the persistent long-RNA gap to scarce high-quality long structures in experimental and synthetic sources.Source: H LIMITATIONS AND BROADER IMPACT · pp. 35–36
  • Generated sequences may have unintended biological effects, so functional applications should undergo experimental validation and biosafety review.Source: H LIMITATIONS AND BROADER IMPACT · p. 36
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