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TANGO: RNA Topology and Geometry Co-Design

Tianmeng Hu, Biao Luo, Ke Li

arXiv:2610.20277v2cs.LGcs.MA

TL;DR

RNA design methods often focus on tertiary geometry, although RNA folds also depend on secondary base-pairing topology. TANGO combines topology-aware sequence generation with geometry-conditioned training and target-specific frontier refinement. It improves both topology and geometry metrics over the strongest baseline.

  • Problem

    Existing 3D RNA design methods rarely optimize and evaluate base-pairing topology as a first-class objective alongside tertiary-structure fidelity.

    Source: §1 · p. 1

  • Method

    TANGO uses a staged multi-agent reinforcement learning curriculum that transfers topology-aware sequence generation to tertiary targets and fine-tunes target-specific trade-offs.

    Source: §1 · p. 2

  • Results

    TANGO improves sc-TM by 18.3% and sc-BP-F1 by 52.7% over RIDER, the strongest baseline.

    Source: §5.1 · p. 7

  • Takeaways & Limitations

    TANGO’s results support treating RNA 3D inverse design as co-design that recovers both target tertiary geometry and secondary topology.

    Source: §6 · p. 11

    The predictor-based benchmark favors RNAs that current structure predictors can fold reasonably well, and distance-to-native does not rule out all memorization or predictor-specific sequence bias.

    Source: §4 · p. 7, §5.4 · p. 10

Abstract

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Designing RNA sequences that satisfy target tertiary-structure objectives is an important problem in RNA engineering, with broad applications in synthetic biology and therapeutics. Existing 3D RNA design methods have made substantial progress, but they largely treat the target fold as a geometry-only objective. This is incomplete for RNA, whose functional folds are specified not only by tertiary geometry but also by secondary base-pairing topology. We therefore formulate RNA inverse design as a topology-and-geometry co-design problem and propose TANGO, a multi-objective multi-agent reinforcement learning framework for this task. TANGO adopts a staged curriculum: it first learns a topology-aware policy from secondary-structure targets, then transfers this policy to tertiary-structure targets to train a general co-design model, and finally applies frontier-guided fine-tuning to refine target-specific trade-offs among secondary-structure fidelity, tertiary-structure fidelity, and sequence diversity. Experiments show that TANGO generates diverse and novel designs, improving tertiary- and secondary-structure performance by 18.3% and 52.7%, respectively, over the strongest baseline.

1 Introduction

RNA inverse design must account for both base-pairing topology and tertiary geometry, because neither objective alone specifies the desired fold. TANGO addresses this with a topology-and-geometry co-design framework.

1 Introduction

  • RNA inverse design seeks sequences satisfying specified structural objectives, and recent deep learning has made tertiary-structure-based design increasingly practical.RNA structures participate in biological traits across gene regulation.Source: §1 · p. 1
  • RNA folds depend on base-pairing topology as well as 3D geometry, with topology constraining feasible folds and geometry determining spatial arrangement.The topology includes stems, loops, junctions, and pseudoknots, while long-range and non-canonical interactions stabilize 3D conformations.Source: §1 · p. 1
  • Existing methods may produce geometry-consistent designs that fail to recover target base pairs, while topology-preserving designs may miss the desired 3D arrangement.The paper therefore treats topology and geometry as complementary objectives.Source: §1 · p. 2, Figure 1 · p. 2
  • TANGO improves sc-TM by 18.3% and sc-BP-F1 by 52.7% over the strongest baseline while generating diverse non-native designs.These gains are reported on a curated PDB-derived benchmark.Source: §1 · p. 2
  • TANGO uses topology-derived structural units and a three-stage curriculum to learn topology-aware sequence decisions, transfer them to 3D targets, and refine target-specific trade-offs.Its stages are topology-aware initialization, geometry-conditioned co-design, and frontier-guided fine-tuning.Source: §1 · p. 2

2 Problem Setup

The problem setup defines RNA co-design around recovery of both a target base-pairing topology and a target tertiary structure. It also seeks diverse candidates with favorable trade-offs across these objectives.

2 Problem Setup

  • The target topology comprises target base pairs and unpaired positions, and may be represented in dot-bracket notation with crossing pairs denoting pseudoknots.The target tertiary structure is represented separately as G⋆.Source: §2 · p. 3
  • The tertiary target uses a 3-bead coarse-grained representation of backbone atoms and an unlabeled glycosidic nitrogen bead, without native nucleotide identities.This representation captures backbone conformation and approximate base placement.Source: §2 · p. 3
  • Topology-only initialization uses a sequence-based secondary-structure oracle, while later training and evaluation derive topology from the predicted tertiary fold.The latter uses a 3D-to-2D annotation procedure such as DSSR.Source: §2 · p. 3
  • Co-design requires both tertiary-structure fidelity and secondary-topology fidelity, with TM-score measuring global alignment and BP-F1 measuring target base-pair recovery.A sequence counts as a co-design success only when it satisfies both objectives.Source: §2 · p. 3
  • The design objective seeks a diverse set of sequences with favorable trade-offs among topology fidelity, geometry fidelity, and sequence novelty.Unlike prior sequence–structure co-design [16], this formulation designs sequences to recover prescribed topology and geometry targets.Source: §2 · p. 3

3 Method

TANGO generates RNA sequences cooperatively over topology-derived structural units and trains through topology-aware initialization, geometry-conditioned co-design, and target-wise frontier refinement.

3.1 Structural-unit Cooperative Generation

  • Structural units represent unpaired residues individually and paired residues jointly, exposing base-pair couplings and shortening the sequence-generation decision horizon.Agents fill contiguous segments in parallel, with an effective horizon of approximately ⌈M/N⌉ rather than M.Source: §3 · p. 3, §3.1 · p. 4

3 Method

  • TANGO trains in three stages: learn topology-compatible sequences, transfer that policy to geometry-conditioned co-design, then adapt each target by improving its Pareto frontier.The frontier balances topology fidelity, geometry fidelity, and sequence diversity.Source: §3 · p. 3, Figure 2 · p. 4

3.2 Stage I: Topology-aware Initialization

  • Topology-aware initialization trains agents to construct sequences satisfying secondary-structure scaffolds, providing a coordinated starting policy for later 3D co-design.Agents share the topology-only terminal reward.Source: §3.2 · p. 5

3.3 Stage II: Geometry-conditioned Co-design

  • Geometry-conditioned co-design transfers the topology-aware policy to tertiary targets and combines topology reward with a penalty for falling below a topology-fidelity threshold.The positive topology term encourages topology recovery while the hinge penalty discourages geometry-improving updates that violate the threshold.Source: §3.3 · p. 5

3.4 Stage III: Frontier-guided Fine-tuning

  • Frontier-guided fine-tuning rewards candidates for expanding each target’s non-dominated frontier rather than optimizing a fixed scalarized score.The batch-level reward is order-independent, and only candidates that expand the target-wise frontier receive positive reward.Source: §3.4 · p. 6

4 Experimental Setup

The benchmark uses predictor-filtered PDB RNA targets and structurally remote held-out examples. Evaluation compares fold-back geometry, topology recovery, and joint co-design success under a shared protocol.

4 Experimental Setup

  • The PDB-derived benchmark contains 1,213 targets after filtering for native-sequence TM-score ≥0.45 under both RhoFold and AlphaFold3.This reduces ambiguity in fold-back evaluation but biases the benchmark toward RNAs current predictors can fold reasonably well.Source: §4 · pp. 6–7
  • The held-out test set contains 50 structurally remote targets, with mean and maximum nearest-neighbor similarities of 0.34 and 0.42 to training targets.Among these targets, 44% contain pseudoknotted base pairs.Source: §4 · p. 7
  • Main results use RhoFold for self-consistency evaluation, reporting sc-TM and sc-RMSD for tertiary fidelity, sc-BP-F1 for topology, and joint co-design success.Each baseline generates K = 10 candidates per target, with methods retrained on the same training split.Source: §4 · p. 7
  • Continuous metrics aggregate candidates by mean-of-K per target before reporting mean ± standard deviation across targets.The study uses paired Wilcoxon tests for sc-TM, sc-BP-F1, and success rate, with Holm correction for multiple comparisons.Source: §4 · p. 7

5 Results

TANGO leads topology and geometry metrics over RIDER, while target-wise refinement and topology-aware initialization improve both objectives. Its designs remain non-native yet high-quality, and scores are comparable across two fold-back predictors.

5.1 TANGO improves topology and geometry fidelity

  • 18.3% relative gain in sc-TM (0.60 to 0.71) and 52.7% in sc-BP-F1 (0.55 to 0.84) over RIDER accompany TANGO’s lowest sc-RMSD.Table 1 reports structural design performance on the test set; Figure 3 shows representative successful designs.Source: §5.1 · pp. 7–8, Table 1 · p. 8, Figure 3 · p. 8
  • TANGO raises co-design success from 0.49 to 0.86 and solved target rate from 60.00% to 88.00% versus RIDER.A successful candidate must meet both geometry and topology thresholds.Source: §5.1 · p. 8, Table 1 · p. 8

5.2 Target-wise frontier-guided refinement expands the co-design frontier

  • 27.6% gains in sc-TM and 31.9% in sc-BP-F1 over TANGO-Base accompany target-wise refinement; TANGO-Div reaches hypervolume 0.374 versus 0.031 for TANGO-Base.TANGO’s hypervolume is 0.170; explicit sequence diversity raises diversity 90.1% over TANGO-Base while preserving competitive topology and geometry fidelity.Source: §5.2 · p. 8, Figure 4 · p. 9

5.3 Topology-aware initialization provides a useful scaffold for 3D design

  • Topology-aware initialization yields relative improvements of 38.9% in sc-TM, 93.3% in sc-BP-F1, and 106.0% in co-design success over training from scratch.The ablation keeps the structural-unit action space and geometry-conditioned architecture unchanged; Stage I optimizes only a secondary-topology objective.Source: §5.3 · p. 9

5.4 TANGO generates non-native high-quality designs

  • TANGO achieves the strongest combination of sequence novelty and design quality, with sequences far from native targets and the highest co-design success rate.Distance to native alone does not rule out all memorization or predictor-specific sequence bias, so this is evidence of non-native design, not definitive proof of memorization-free generation.Source: §5.4 · p. 10, Figure 6 · p. 10

5.5 Robustness across oracles and architectures

  • TANGO scores remain comparable across RhoFold and AlphaFold3, while its multi-agent policy improves both topology and geometry metrics over a single-agent variant.The cross-oracle evaluation is predictor-based, not experimental folding validation.Source: §5.5 · p. 10, Figure 7 · p. 11

6 Conclusion

TANGO treats RNA inverse design as a joint topology-and-geometry task and uses staged multi-agent training to refine that co-design. Experiments show improvements over recent 3D RNA design baselines.

6 Conclusion

  • TANGO improves fold-back geometry, topology recovery, and joint co-design success over recent 3D RNA design baselines.Its curriculum initializes from secondary-structure design, transfers to geometry-conditioned co-design, then refines target-wise trade-offs among topology, geometry, and diversity.Source: §6 · p. 11

A Related Work and Positioning

  • Existing 3D RNA methods rarely optimize topology fidelity jointly with tertiary-structure fidelity, a gap TANGO addresses with structural-unit actions and multi-objective rewards.Some prior methods use secondary structure as priors, constraints, or repair mechanisms.Source: A Related Work and Positioning · p. 17

B.1 Structural-unit Cooperative Generation

  • Agents cooperatively generate sequence segments from an ordered structural-unit schedule, and generation ends when all units are assigned.The resulting complete sequence is returned for reward evaluation.Source: §B.1 · p. 18

B.2 Multi-Agent Reinforcement Learning Framework

  • Across its three stages, TANGO keeps the rollout interface and MAPPO update while changing conditioning information and terminal reward construction.The rewards respectively target topology, topology-and-geometry co-design, and frontier-guided refinement.Source: §B.2 · p. 18, §C.1 · p. 20

C.2 Centralized training and decentralized execution

  • TANGO uses centralized training with a shared actor, while agents execute from local observations and a centralized critic evaluates global design state.This separates local structural-unit actions from global sequence-quality evaluation.Source: §C.2 · p. 21

C.4 Effective horizon

  • With M structural units split among N agents, a balanced rollout takes approximately ⌈M/N⌉ steps rather than M, shortening the effective horizon for delayed structural rewards.The paper links this shorter horizon to improved temporal credit assignment.Source: §C.4 · p. 21

D Additional Results

Additional experiments examine threshold sensitivity and whether frontier-guided fine-tuning outperforms post-hoc Top-10 selection. The results show sensitivity to stricter joint criteria and stronger performance from the full TANGO model than from the sampling variants.

D Additional Results

  • The appendix evaluates threshold sensitivity, Top-10 sampling, fixed weighted rewards, and the cooperative multi-agent formulation.These experiments are presented as further tests of TANGO's effectiveness and robustness.Source: D Additional Results · p. 21

D.1 Threshold Sensitivity

  • Raising the sc-TM threshold from 0.30 to 0.80 decreases successful design rate by 61.3%, while raising sc-BP-F1 from 0.30 to 0.80 decreases it by 31.0%.Each threshold is varied while the other is fixed at its main-experiment value; the rate decreases as either requirement becomes stricter.Source: §D.1 · p. 22, Figure A1 · p. 22

D.2 Top 10 Sampling versus Frontier-guided Fine-tuning

  • The full TANGO model outperforms all Top-10 sampling variants, with relative sc-TM/sc-BP-F1 improvements of 14.5%/12.0% over TANGO-Base with Top-10 sampling and 51.1%/100.0% over the variant without topology-aware initialization.Source: §D.2 · p. 22
  • Top-10 sampling improves sc-TM and sc-BP-F1 over raw sampling for both TANGO-Base and the variant without topology-aware initialization.For TANGO-Base, the gains are 10.7% and 17.2%; for the variant without topology-aware initialization, they are 17.5% and 27.3%.Source: §D.2 · p. 22

D.3 Frontier-guided Fine-tuning versus Weighted Rewards

Frontier-guided fine-tuning is compared with fixed scalarized rewards and a single-agent ablation. The reported results favor balanced multi-objective refinement and the cooperative multi-agent formulation.

D.3 Frontier-guided Fine-tuning versus Weighted Rewards

  • The 2D-heavy setting matches TANGO at sc-BP-F1 0.84 but has sc-TM 0.61 and diversity 0.08; the 3D-heavy setting reaches sc-TM 0.72 but sc-BP-F1 0.62.The comparisons illustrate how fixed scalarization can favor one structural objective at the expense of another.Source: §D.3 · pp. 22–23, Figure A3 · p. 23, Figure A4 · p. 24
  • TANGO-Div increases diversity from 0.10 to 0.22 with only small decreases in sc-TM and sc-BP-F1, while TANGO maintains a stronger topology–geometry balance than fixed-weight alternatives.The authors present frontier-guided refinement as target-wise multi-objective refinement without manually chosen scalarization weights.Source: §D.3 · p. 23, Figure A4 · p. 24

D.4 Effect of the Cooperative Multi-agent Formulation

  • The multi-agent formulation raises sc-TM from 0.52 to 0.71, sc-BP-F1 from 0.60 to 0.84, and success rate from 0.53 to 0.86 versus single-agent TANGO.These are relative improvements of 36.5%, 40.0%, and 62.3%, respectively.Source: §D.4 · p. 24, Figure A5 · p. 24

E Model Architecture

TANGO encodes target topology and geometry at the structural-unit level, with shared decentralized actors and a centralized training critic. Zero-initialized geometry adapters let the transferred topology-aware policy adjust toward tertiary targets.

E.1 Topology and Unit Encoders

  • The topology and unit encoders represent residues using dot-bracket tokens and structural metadata, then encode paired residues together as one coupled decision.Single-position and paired units are mapped into a shared 256-dimensional unit space.Source: §E.1 · pp. 24–25

E.2 Shared Actor with Unit-specific Heads

  • All agents share an actor with separate output heads for single-position and paired-unit nucleotide choices.The single-unit head selects among A, U, G, C; the paired-unit head selects among AU, UA, GC, CG, GU, and UG.Source: §E.2 · p. 25

E.3 Centralized Critic

  • During training, the centralized critic receives global partial-design information, while inference-time agents act only from local observations.The critic also receives pooled target 3D information during co-design and frontier-guided fine-tuning.Source: §E.3 · p. 25

E.4 3D Target Encoder

  • A GVP-GNN encodes the target 3D spatial graph into residue-level geometric embeddings, which are pooled into unit-level conditioning signals.Paired units use the mean of their residue embeddings, with local context pooled from 15 nearest units in the reported configuration.Source: §E.4 · p. 25

E.5 Zero-initialized Geometry Adapters

  • Zero-initialized 3D-conditioned paths keep the transferred policy near its topology-aware starting point, then allow geometry conditioning to adjust sequence decisions.The adapters use unit-level geometry and local 3D context.Source: §E.5 · p. 26

F Training Details

Training uses shared structural-unit rollouts and terminal rewards, progressing from topology learning to topology-and-geometry co-design and target-wise frontier refinement.

F Training Details

  • Across stages, agents fill ordered structural units until a complete sequence is generated, with the learning signal assigned at episode end.The stages use topology, co-design, and frontier-guided rewards, respectively; MAPPO updates are shared across stages.Source: F Training Details · p. 26

F.1 Stage I Hyperparameters

  • Stage I trains a topology-aware policy on secondary-structure targets, sharing the oracle-based topology reward across agents after each complete sequence.Training takes approximately 5 hours on one NVIDIA H100 GPU; single-sample inference takes a few seconds.Source: §F.1 · p. 26, Table A1 · p. 27

F.2 Stage II Hyperparameters

  • Stage II transfers the topology-aware policy to co-design, combining TM-score 3D fidelity, BP-F1 topology fidelity, and a hinge penalty below the 2D threshold.RMSD is recorded for evaluation but is not a reward term.Source: §F.2 · p. 26, Table A2 · p. 27

F.3 Stage III Hyperparameters

  • Stage III fine-tunes from co-design-policy samples, rewarding trajectories by their exclusive hypervolume contribution to each target’s frontier.The default frontier uses sc-BP-F1 and sc-TM; a diversity-aware variant also includes sequence diversity.Source: §F.3 · p. 27

G Evaluation Metrics

Evaluation folds both native and designed sequences through the same structure-prediction pipeline, then compares their tertiary folds and annotated secondary topologies. Metrics cover structural fidelity, target-level success, novelty, and sequence diversity.

G.1 Fold-back Self-consistency Protocol

  • The fold-back protocol compares designed-sequence predictions with references generated from the native sequence using the same oracle and annotation procedure.The authors expect shared predictor-specific bias to cancel in structural similarity and also report cross-oracle evaluation.Source: §G.1 · p. 28

G.2 3D Self-consistency Metrics

  • sc-TM measures global fold agreement, while sc-RMSD measures geometric deviation across the aligned region.sc-TM is computed by USalign; TM-score uses length normalization.Source: §G.2 · p. 28

G.3 2D Self-consistency Metrics

  • sc-BP-F1 compares target base pairs with pairs annotated from the designed sequence’s fold-back structure.The score is 1 when both pair sets are empty and 0 when only one is empty.Source: §G.3 · p. 28

G.4 Target-level Aggregation

  • Metrics are averaged first across sampled designs within each target and then across test targets, preventing prolific targets from dominating the benchmark average.Success rate is the average fraction of designs meeting both thresholds; solved-target rate is the fraction of targets with at least one successful design.Source: §G.4 · p. 29

G.5 Novelty and Diversity

  • Novelty is normalized Hamming distance from the target’s native sequence, while diversity is average pairwise normalized Hamming distance among designs for a target.For diversity conditioned on structural success, only successful designs are included.Source: §G.5 · p. 29

H Limitations and Broader Impact

The authors identify oracle dependence and untested biological settings as limitations, while describing possible applications and validation concerns for AI-driven RNA design.

Limitations

  • Future work includes richer interaction settings—non-canonical contacts, ligand-bound RNAs, and protein–RNA complexes—and experimental testing of selected designs.Source: H Limitations and Broader Impact · p. 29
  • Computational results rely on structure-prediction oracles, and RNA dynamics and limited high-quality data make prediction difficult.The authors report broadly consistent trends across fold-back models, but future evaluation could include biological-function measures.Source: H Limitations and Broader Impact · p. 29

Broader Impact

  • TANGO may support synthetic biology, RNA therapeutics, gene-regulation studies, and engineering RNA circuits, aptamers, and ribozymes; AI-driven sequence design also raises reliability, interpretability, and validation concerns.The passage calls for systematic assessment of explanations for consistency, faithfulness, and biological validity when guiding RNA engineering.Source: H Limitations and Broader Impact · p. 29

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