RNA-FrameFlow: Flow Matching for de novo 3D RNA Backbone Design
Authors: Rishabh Anand
Chaitanya K. Joshi
Alex Morehead
Arian Rokkum Jamasb
Charles Harris
Simon V Mathis
Kieran Didi
Rex Ying
Bryan Hooi
Pietro Lio
Venue: Accepted by TMLR ()

Abstract: We introduce RNA-FrameFlow, the first generative model for 3D RNA backbone design. We build upon SE(3) flow matching for protein backbone generation and establish protocols for data preparation and evaluation to address unique challenges posed by RNA modeling. We formulate RNA structures as a set of rigid-body frames and associated loss functions which account for larger, more conformationally flexible RNA backbones (13 atoms per nucleotide) vs. proteins (4 atoms per residue). Toward tackling the lack of diversity in 3D RNA datasets, we explore training with structural clustering and cropping augmentations. Additionally, we define a suite of evaluation metrics to measure whether the generated RNA structures are globally self-consistent (via inverse folding followed by forward folding) and locally recover RNA-specific structural descriptors. The most performant version of RNA-FrameFlow generates locally realistic RNA backbones of 40-150 nucleotides, over 40% of which pass our validity criteria as measured by a self consistency TM-score ≥ 0.45, at which two RNAs have the same global fold. Open-source code: https://github.com/rish-16/rna-backbone-design

Published in Transactions on Machine Learning Research (07 (07/202) 2025)
RNA-Frameelow:
Flow Matching for de novo 3D RNA Backbone Design
Rishabh Anand
Chaitanya K. Joshi Alex Morehead Arian R. Jamasb
Charles Harris²
Simon V. Mathis Kieran Didi
Rex Ying' Bryan Hool
Pietro Lid
Eqqual contribution
Yole University 2 University of Combridge (UK) Lawrence Berkeley National Laboratory
Prescient Design Genentech, Roche
à University of Oxford (UK) 6 "Ntioonl University of Singapore
Corvespondence to: rishabh. anand@yale. edu, chaitanya. tochhat cam. com.ac.w.
Reviewed on OpenReview: https: // openreview. net/ pet/forum? id id=w0c1Y55s0
Abstract
We introduce RNA-FRAMEFLOW the first generative model for 3D RNA backbone de- sign. We build upon SE(3) flow matching for protein backbone generation and estab- lish protocols for data preparation and evaluation to address unique challenges posed by RNA modeling. We formulate RNA structures as a set of rigid-body frames and asso- ciated loss functions which account for larger, more conformationally flexible RNA back- bones (13 atoms per nucleotide) vs. proteins (4 atoms per residue). Toward tackling the lack of diversity in 3D RNA datasets, explore training with structural clustering and cropping augmentations. Additionally, we define a suite of evaluation metrics to mcasure whether the generated RNA structures are globally self-consistent (via inverse folding fol- lowed by forward folding) and locally recover RNA-specific structural descriptors. The most performant version AANAFFRMMFLOW generates locally realistic RNA backbones of 40-150 mucleotides, over 40% of which pass our validity criteria as mcasured by a self- consistency TM-score 2 0.45, at. which two RNAs have the same global fold. Open-source code:
1 Introduction
Designing RNA structures. Protcins, and the diverse structures they can adopt, drive essential biological functions in cells. Deep learning has led to breakthroughs in structural modeling and design of proteins (Jumper et al., 2021; Dauparas et al., 2022; Watson et al., 2023), driven by the abundance of 3D data from the Protein Data Bank (PDB). Concurrently, there has been surge of interest in Ribonucleic Acids (RNA) and RNNA-assed therapeutics for gene editing, gene silencing, and vaccines (Doudna & Charpentier, 2014; Metkar et al., 2024). RNAs play several roles in cells: they carry genetic information coding for proteins (mRNA) as well as perform functions driven by their tertiary structural interactions (riboswitches and ribozymes). While there is growing interest in designing such structured RNAs for a range of applications in biotechnology and medicine (Mulhbacher et al., 2010; Damase al., 2021), the current toolkit for 3D RNA design uses classical algorithms and hcuristics to assemble RNA motifs as building blocks (Han et al., 2017: Yesselman et al., 2019). However, hand-crafted heuristics are not always broadly applicable across multiple tasks and rigid motifs may not fully capture the conformational dynamics that govern RNA functionality (Ganser et al., 2019; Li et al., 2023b). This presents an opportunity for deep generative models to learn data-driven design principles from existing 3D RNA structures.
What makes deep learning for RNA hard? The primary challenge is the paucity of raw 3D RNA structural data, manifesting as an absence ML-ready datasets for model development (Joshi et al., 2025). Protein structure primarily driven by hydrogen bonding along the backbone, and current deep learning models incorporate this inductive bias through backbone frames to represent residues (Jumper et al., 2021).

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RNA structure data pipeline
Structural clustering with US-align
ML-ready datasel
RN
RNA nucleotides frame
Training
Local structural metrics: distances, angles, torsions
data
FrameFlow
Evaluation protocol gRNAde -Rooold
04
SE(3) flow matching
0Z
Global self-consistency: scRMSD, scTM
Figure 1: The ANN--Frmeeloow pipeline for 3D backbone generation. Our implementation estab- lishes RNA-specific protocols for data preparation and evaluation for FrameFlow (Yim et al., 2023a). (1) Each nucleotide in the RNA backbone is converted into frame parameterize the placement of C4' by translation, C3' C4' 04' by rotation, and the rest of the atoms via 8 torsion angles +. (2) We train generative models all RNA structures of length 40-150 nucleotides from RNAssolo (Adamczyk et al., 2022). We also explore training with structural clustering and cropping augientattioss to tackle the lack of diversity in 3D RNA datasets. (3) We introduce evaluation metrics to measure the recovery of local struc- tural descriptors and global self-consistency of designed structures via inverse-folding with gRNAde (Joshi et al., 2025) followed by forward-folding with RhoFold (Shen et al., 2022).
RNA structure, however, is often more conformationally flexible and driven by base pairing interactions across strands as well base stacking between rings of adjacent nucleotides (Vicens & Kieft, 2022).
Additionally, RNA nucleotides, the equivalent of amino acids in proteins, include siguificantly more atoms part of the backbone (13 compared to 4) which necessitates a generalization of backbone frames where the placement of most atoms needs to be parameterized by torsion angles. These complexities have contributed to relatively poor performance of deep learning for RNA structure prediction compared to proteins (Kretsch et al., 2023; Abramson et al., 2024). Additionally, structure prediction models cannot directly be used for designing or generating novel RNA structures with desired constraints. Thus, the lack of de novo RNA design models presents gap worth addressing, which aim to do in this work.
Our Contributions. We develop RNA-FRAMEFI.OWw the first generative model for 3D RNA backbone design, which trains on RNA of length 40-150 from the PDB; see Figure 1. We devise RNA frames to capture the significantly larger RNA nuclcotides while still supporting the modelling of all backbone atoms implicitly. Our method can unconditionally sample plausible backbones with over 40% validity, as measured by our custom evaluation pipeline that computes global self-consistency and local structural measurements. We also explore data augmentation protocols to address the paucity of diverse RNA structural data, which improves the novelty of designed RNA. We hope this work stimulates future research in generative models for RNA design.
2 The RNA-FrameFlow Pipeline
We are concerned with building a generative model that unconditionally outputs 3D RNA backbone struc- tures, sampled from a distribution of realistic structures. Formally, given an RNA sequence of N₂, mu- cleotides, we aim to generate a real-valued tensor X of shape Nm, 13 x representing 3D coordinates for backbone atoms per nucleotide. the following sections, we will describe how we adapt FrameFlow (Yim al., 2023a), SF()) equivariant flow matching model for protein backbones, to setting.
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2.1 Representing RNA Backbones as Frames
Rationale for RNA frames. In proteins, it is standard to represent each residue by a frame centered at Ca with vectors along C., N and C. - C, and O is placed assuming an idealized planar geometry (Jumper et al., 2021). However, such canonical frame representation exists for RNAs. Furthermore, the RNA nucleotide contains significantly more backbone atoms (13) compared to proteins (4). As shown in Figure 1, the backbone fragment of RNA nucleotides comprise a phosphate group (P, IPPOPI, OP2, O5'), a ribose sugar (C1' - 02', , and a nitrogen atom N at the stem of the base To avoid the high modelling complexity of explicitly generating coordinates for all 13 backbone atoms, we decide to represent the atoms within each nucleotide as a rigid-body frame; this enables inferring the positions of all intra-nucleotide aloms via a frame center and orientation.
Constructing RNA frames. We select the C3', and O4' atoms to create the frame for each mucleotide,
as in Morehead et al. (2023). All other backbone atoms are inferred with 8 torsions +b = [+x) ) that are predicted post-hoc after frame generation. The Gram-Schmidt process is used on v1, 02 defined by the vectors along the C4' - O4' and C4' - C3' bonds; C5' is imputed based the positions of the other 3 aloms and retrahedral geometry. Given the torsion angles, we autoregressively place non-frame aloms in order of the torsions & in Figure 1, constructing the final set of all-atom RNA nucleotides. We describe this imputation of non-frame atoms as well as the choice of torsion angle parameterization in Appendix A.4.
dhe E SO(2)
Choice of frame atoms. We consider two main factors for selecting the atoms to create RNA frames: (1) atoms should have roughly the same spatial orientation w.r.t. each other; and (2) atoms should be reasonably close to the centroid in the nucleotide to reduce error accumulation when placing the furthest non-frame atoms. We choose (C3', C4', 00') as these atoms have relatively lower atomic displacement in natural RNA (Harvey & Prabhakaran, 1986); see Appendix C.5 for empirical evidence on atomic displacements. The remaining non-frame backbone atoms in the ribosc ring and the phosphate group are parametorized by torsion angles to account for their relative conformational flexibility. We also believe this choice of frame enables models to capture ring puckering, by which the five ribose atoms contort the ideal plane of the sugar ring to alleviate steric strain. This also influences how RNA interacts with partners to form complexes (Clay et al., 2017); see Appendix C.6 for additional details and results on puckering.
2.2 SE(3) Flow Matching on RNA Frames
Input. Given a set of 3D coordinates, simultaneous rotation and translation (r, forms an orientation- preserving rigid-body transformation of the coordinates. The set of all such transformations in 3D is the Special Euclidean group SE(3), which composcs the group of 3D rotations 50(3) and 3D translations in R We can represent an RNA frame T = (r, x) as a translation x E R from the global origin to place C4' and a rotation r E S3()) to orient C3' - C4' 04'. Compared to working with raw 3D coordinates for each backbone atom, using the frame representation entails performing flow matching on the space of SE3(). This is an inductive bias to reduce the degrees of freedom the generative model needs to learn. Instead of predicting 13 correlated 3D coordinates independently (39 quantities) for each ideleotide, we instead predict one 3D coordinate (of C4') and one 3x3 rotation matrix (12 quantities). We follow Chen & Lipman (2024) and Yim et al. (2023a)²s 's framework for flow matching on SE((), which we summarise subsequently.
Overview. Flow matching generates or learns how to place and orient a set of N frames T = [T()) J where T(m) (r(m), (n)),, to form an RNA backbone of length N. To do so, we initialize frames at random in 3D space at time 0, and train a denoiser flow model to iteratively refine the location and orientation of each frame for specified number of steps until time = 1.
Suppose PT)T and (TiT are the marginal distributions of randomly oriented and ground truth frames from our dataset of RNA structures, respectively. Suppose a time-dependent vector field u, leads to an ODE between the two distributions Po and Pl, ie., assume there is a way to map from noisy samples to the corresponding true samples. This solution forms a ground truth probability path P. between the two distributions at time t E [o. 1], which we can use to transform noisy samples to the true distribution. The continuity equation dp
or = - (pou:) relates the vector field i, to the evolution of the probability path pt-
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Given noisy frame To sampled from (To) and the corresponding ground truth frame T1 sampled from Pi (Ti), we construct a flow Tr by following the probability path between To and Ti for any time step sampled from ((0, 1). As shown by Chen & Lipman (2024) for the SE(3) group (and other manifolds), the geodesic between the states To and T1 can be used to define an interpolation:
T = expr, (L logr, (Ti)).
(1)
Here, exp(-) and log(-) are the exponential and logarithmic maps that enable moving (taking random walks) on curved manifolds such as the SE(3) group. As we can decompose a frame T = (r,z) into separate rotation and translation terms, we can obtain closed-form interpolations for the group of rotations S0(3)
and translations Ra. This gives us two independent flows:
(2) The random translation zo is sampled from a zero-centered Gaussian distribution (O, 1) in I., and the random rotation ro is sampled from ((SO(3)), generalization of the uniform distribution for the group of rotations, SO(3). For RNA backbone consisting of set of N frames T = { T(m)) > interpolation for each frame in parallel via the aforementioned procodure.
Translations: Ft tm (1 t)
Rotations:
rt = expro (t logr, (r1))
define the
Training. During training, we would like to learn a parameterized vector field vo (T,, a deep neural network with parameters 0, which takes as input the intermediate frames Tr at time t sampled from u(0,, 1), and predicts the final frames T = (T()) >== where f(() (f("), ,.(()). The ground truth vector field un for mapping from the intermediate frames T, to the ground truth frames Tr can also be decomposed into ground truth rotation and translation for each frame T(x);
Translations: u,(x<"))o0""
(n) x1 (n)) = =1 (n)
Rotations:
".(r("))rb" (n) ,((i)) = =log, (r("))-
To train the model va, we compute separate losses for the predicted rolation f. E SO(3) and translation à 13 The combined SE(3) flow matching loss over N frames is follows:
CSE(3) =E, Po())), (T))
(n)
(n)
R3 +
Log (ff - log (r (r 2
(4)
(1
5O(3)
(n) 500
The architecture of the flow model va is similar to the structure module from AlphaFold2 comprising Invariant Point Attention layers interleaved with standard Transformer encoder layers, following Yim et al. (2023a;b). We use an MLP head to predict torsion angles $
Auxiliary losses. The inclusion auxiliary loss terms to the objective Equation 4 can be seen as a form of adding domain knowledge into the training process (Yim et al., 2023b). We include 3 additional losses that operate all the backbone atoms from the predicted frames, weighted by tunable coefficients to modulate their contribution to the total loss:
Lit LSF(3) + Lub + Liist. Lrors
(5)
Suppose $ {C4', CC',,C3', 04'} is the set of frame atoms? and the sequence length is N. We summarise the auxiliary losses subsequently.
Coordinate MSE Lbb: A direct MSE computed between generated and ground truth coordi- nates. Here, a, are the ground truth and predictod atomic coordinates for the frame atoms:
Lbb
Σ
Σ |a a12)
(6)
S
aES
In Appendix B.I, show how including more backbone atoms better accounts larger RNA nucleotides and improves validity of generated samples.
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Distogram loss Ldist: A distogram D E NNSxNS containing all-to-all coordinate differences be- tween the atoms in an RNA structure computed. Let D(um) = ||a(*) {(m) || be the elements of the distogram for the ground truth structure. Here, atom a belongs to nucleotide n and atom b to nucleotide m. Given the corresponding predicted distogram ((rm), we compute another difference between the tensors:
ab
ab
N
Ldist (1S)N)2 N
Σ
Σ a,PES
11
-D D(mm) 1?
11,7
Torsional loss Liora: An angular loss between the 8 predicted torsions by the auxiliary ML.P head and the angles from the ground truth structure with all backbone atoms. Suppose E 4,, and & &n the ground truth and predicted torsion angles for residue n, we compute:
Liors
1 8N
Σ DE
(10 ( a11²
Sampling. To generate or unconditionally sample an RNA backbone of length N, we initialize a random point cloud of frames. We use our trained flow model 89 within an ODE solver to iteratively transform the noisy frames into a realistic RNA backbone. For each nucleotide, we begin with a noisy frame To (ro, time step 0, and integrate step size At 1/Nr- At each step t, the flow model Uo predicts updates for the frames via a rotation A and translation .
using the Euler method for specified number of steps Nr,, with
Translations: T++Ar It At (f) xz)
(9)
Rotations:
TitA = exp,, ( c At log,, (fi))
(10)
where c c= is a tunable hyperparameter governing the exponential sampling schedule for rotations.
Conditional gencration. The unconditional sampling strategy described above aims to generate realistic RNA backbones sampled from the training distribution. However using generative models in real-world design tasks entails conditional generation based on specified design constraints or requirements (Ingraham et al., 2022; Watson et al., 2023), which we are currently exploring. For example, unconditional models can leverage inference-time guidance strategies (Wu et al., 2024). be fine-tuned conditionally (Denker et al., 2024) or in an amortized fashion for motif-scaffolding (Didi et al., 2023). For sequence conditioning and structure prediction, embeddings from language models can also be incorporated (Penic et al., 2024; He et al., 2024).
3 Experiments
3D RNA structure dataset. RNAsolo (Adamczyk et al., 2022) is a recent dataset RNA 3D structures extracted from isolated RNAs, protein-RNA complexes, and DNA-RNA hybrids from the Protein Data Bank (as of January 5, 2024). The dataset. contains 14,366 structures at resolution S Á À 0.1nm). We select sequences of lengths between 40 and 150 nuclcotides (5,319 in total) as envisioned this size range contains structured RNAs of interest for design tasks.
Evaluation metrics. We evaluate our models for unconditional RNA backbone generation, analogous to recent work in protein design (Yim et al., 2023b;a; Bose et al., 2023; Lin & AlQuraishi, 2023); see Figure 2. We generate 50 backbones for target lengths sampled between 40 and 150 at intervals of 10. We then compute the following indicators of quality for these backbones:
Validity (sCTM 2 0.45): We inverse fold each generated backbone using gRNAde (Joshi et al., 2025) and pass Non generated sequences into RhoFold (Shen et al., 2022). We then compute the self-consistency TM-score (SCTM) between the predicted RhoFold structure and our backbone at the C4' level. We say backbone valid if ScTM 2 0.45; this threshold corresponds roughly the same fold between two RNAs (Zhang et al., 2022). Alternatively, we use an RMSD threshold of 4.3 A, corresponding to the median RMSD of RhoFold on RNAsolo sequences.
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Compute self-consistency (TM. RMSD, GDT_TS)
Generative
Inverse
Structure
AUUCG...
Model
Folding
Prediction
Noise
Backbone
Sequence
All-atom
Figure Structural self-consistency evaluation. We sample backbone from our model and pass it through inverse folding model (gRNAde) to obtain Neeq = sequences. Each sequence is fed into structure prediction model (RhoFold) to get the predicted all-atom backbone. Self-consistency between each predicted backbone and the generated sample is measured with TM-score (we also report RMSD and GDT TS). For a given generated sample, we thus have Neeq = TM--scores of which we take the maximum as the ScTM score for that sample.
Diversity: Among the valid samples, we compute the number of unique structural clusters formed using qTMclust (Zhang et al., 2022) and take the ratio to the total number of samples. Two structures are considered similar if thoir TM-score 0.45. This metric shows how much cach generated sample varies from others across various sequence lengths.
Novelty: Among the valid samples, we use US-align (Zhang et al., 2022) at the C4' level to compute how structurally dissimilar the generated backbones are from the training distribution, For set of samples for given sequence length, compute the TM-score between all pairs of generated backbones and training samples, and for each generated backbone, we assign the highest TM-score. We call the average across this set, pdbTM.
Local structural mcasurements, We mcasure the similarity between bond distances, bond angles, and dihedral angles from the set of generated samples and the training set. To do so, we compute histograms for each of the local structural metrics and use 1D Earth Mover's distance to measure the similarity between generated and training distributions.
Hyperparameters. We use IPA blocks in our flow model, with an additional 3-layer torsion predictor MLP that takes in node embeddings from the IPA module. Our final model contains 16.8M trainable parameters. We use AdamW optimizer with learning rate 0.0001, 81 0.9, B2 0.999. We train for 120K gradient update steps on four NVIDTA GeForce RTX 3090 GPUs for ~1 hours with batch size B 28. Each batch contains samples of the same sequence length to avoid padding, Further hyperparameters are listed in Appendix A.1.
4
Backbone Generation Results
4.1 Global evaluation of generated RNA backbones
We begin by analyzing RNA-FRAMEFLOW'S samples using the aforementioned evaluation metrics. For validity, we report percentage of samples with ScTM 2 0.45; for diversity, we report the ratio of unique structural clusters to total valid samples; and for novelty, we report the highest average pdbTи to match from the PDB. For each sequence length between 40 and 150, at intervals of 10, we generate 50 backbones. Table reports these metrics across different variants for the number of denoising steps Ny. The average SCTM and scRMSD of valid samples are 0.641 + 0.161 and 2.298 + 0.892 respectively. We compare our model to MMDiff (Morehead et al., 2023), a protein-RNA-DNA complex co-design diffusion model. As the original best-perforning version of MMDiff was trained on shorter RNA sequences, we retrain it on our training set. We also inverse-fold MMDiff's backbones using gdN
We identify Ny 50 as the perfororforming model that balances validity, diversity, and novelty; furthermore, it takes 4.74 seconds (averaged over 5 runs) to sample backbone of length 100, as opposed to 27.3 seconds

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Table 1:
Unconditional RNA backbone generation. We evaluate the performance of RNNA- FRAMEFLOw for multiple values for denoising steps Nr. The best-performing model uses Nr 50 steps, taking 4.74s to sample backbone of length 100. We include the forward-folding model used in the self- consistency pipeline. We green-highlight the best result per column.
Model
Timesteps Ny
% Validity
Diversity
Novelty +
RNA-PRAMEF L.W RhoFold
10
16.7
0.62
0.70
50
41.0
0.61
0.54
100
20.0
0.61
0.69
500
20.0
0.57
0.67
MMDiff
100
0.0
0.75
pdb TM
SCTM
0.6
PDB: 7QVP(B)
0.5
Length: 70
pdbTM: 0.76
RhoFold scTM: 0.78
POB: 8FCS/B) pdbTM:
80
0.25
100
120
Sequence Length
130
0.0 0.0
0.25
0.5
0.75
140
1.0
Length:
RhoFold scTM: 0.94
SCTM
Figure 3: Validity and novelty of generated backbones. (Left) ScTM of backbones of lengths 40-150 with the mean and spread of scTM for each length; we select the top 10 structures with the best validation scores per length. (Middle) Scatter plot of self-consistency TM-score (scTM) and novelty (pаьTм) across lengths. Vertical and horizontal dotted lines represent TM-score thresholds of 0.45. (Right) Selected samples with high pdbTM scores (colored) with the closest, aligned match from the PDB (gray). Our model generales valid backbones for certain sequence lengths and tends to recapitulate the most frequent folds in the PDB (e.g., tRNAs, small rRNAs).
for MMDiff with 100 diffusion steps. We note that inereasing Nr does not improve validity despite allowing the model to perform more updates to atomic coordinate placements. Our model also outperforms MMDiff. On manual inspection, samples from MMDiff had significant chain breaks and disconnected floating strands; see Appendix C.1. We report fine-grained self-consistency metrics factoring in the rotational component of frames well as all backbone atoms in Appendix B.4.
4.2 Local evaluation with structural measurements
For our best-performing model using diffusion timesteps NT = 50, we plot histograms of bond distance, bond angles, and dihodral angles in Figure (Subplots 1-3). We include the Earth Mover's distance (EMD) between measurements from the training and generated distributions as an indicator of local realism (using bins for each quantity). An idcal generative model will score an EMD close to 0.0 (i.c. consistent with the training set comprising naturally occurring RNA). In Table 2, we observe EMD values from our best- performing model's backbones being significantly closer to 0.0 compared to MMDiff. We include histograms of local structural descriptors for MMDiff in Appendix C.1.
We also show RNA Ramachandran angle plots for generated samples and the training distribution in Figure 4 (Subplot 4). Keating et al. (2011) introduce 7 - plots, similar to Ramachandran angle plots for pro- teins, that track the separate dihodral angles formed by (C4, P.+1, C4 P and (P,, C4', P.41, C4'+1 respectively, for each nucleotide along the chain. We observe that the dihedral angle distribution from RN RNA-FRAMBFI.OW closely recapitulates the angular distribution from naturally occurring RNA structures
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Earth Mover's Distance (-)
Model
distance
angles
tonsions
50/50 training dist.
6.25
10
8.97 10
7.24 10
Model
% Validity 1
Divensity f
Novelty +
RNA FRAMEFLLOW
0.17
0.11
2.36
Base
41.0
0.62
0.54
(Nr = 50)
+ Clustering
12.0
0.88
0.49
MMDiE (original)
1.38
0.43
3.06
MMDiff (retrained)
0.39
3.23
Cropping 11.0
0.85
0.47
Gaussian noise
29.00
4.37
Table 3: Impact of data preparation strategics. Increasing the diversity of the training dataset using a combination of strategies improves diversity and nov- elty of generated structures but leads to fewer designs passing the validity threshold.
Table Local structural metrics. Earth Mover's Distance for local structural measurements com- pared to ground truth measurements from RNAsolo. We also include EMD for 50/50 train split as a san- ity check. Our model shows improved recapitulation of local structural descriptors compared to baselines.
@robability
Generated
Taining
0.150
0.175
0.200
0.125
Trining
0.175
0:125
0.150
Training
(degrees)
180
0.100
0.100
0.075
0.075
0.050
0.050
0.05
0.025
0.025
2
0.000
0.0 055
10
1.5
2.0
2.5
3.0
0.000
-3 -2
-180
C4/-C4; bond distances
C4,-C4/-C4, bond angles (radian)
C4,,ca/ dihedrals (radian)
-180
180
(Angstrom)
n (degrees)
Figure 4: Local structural metrics from 600 generated backbone samples, compared to random Gaussian point cloud as a sanity check. Our model can recapitulate local structural descriptors. (Subplots 1-3) Histograms of inter-nucleotide bond distances, bond angles between nucleotide triplets, and torsion angles between every four mucleotides. (Subplot 4): RNA-centric Ramachandran plot of structures from the training set (purple) and generated backbones (green).
in the training set. We provide additional evidence on the successful modeling of ring puckering in RNA- FRAMBFL.ow's generated backbones Appendix C.6.
4.3 Generation quality across sequence lengths
We next investigate how sequence length affects the global realism of generated samples (measured by ScTM), Figure 3 (Left) shows the performance of R-A-FF Fi-FFAFMLLLW for different sequence lengths. We observe our model generates samples with high SCTM for specific sequence lengths like 50, 60, 70, and 120 while generaling poorer quality structures for other lengths. We believe the overrepresentation of certain lengths in the training distribution causes the fluctuation of TM-scores. We can also partially attribute this the inherent length bias of RhoFold; see Appendix A.3. With better structure predictors, we expect more samples to be valid. We provide additional local evaluations of angular distributions in Appendix C.3. We also provide an ablation using Chai-1 (Boitreand et al., 2024) as the forward-folding model in Appendix B.3; we do not observe a significant change in validity with Chai-l.
We also analyze the novelty of our generated samples (measured by PdьTM) in Figure 3 (Middle). We are particularly interested in samples that lie the right half with high scTM and low рdbTм, which means that the designs are highly likely to fold back into the sampled backbone but are structurally dissimilar to any RNAs in the training set. It is worth noting that our training set has high structural similarity among samples: running qTMclust on training dataset revealed only 342 unique clusters from 5,319 samples, which indicates that the model does not encounter a diverse set of samples during training. This contributes to many generated samples from our model looking similar to samples from the training distribution. We include two such examples in Figure 3 (Right). Both generated RNAs yield relatively high PdbTM scores and look similar their respective closest matching chain from the training set: a tRNA length 70 and a 5S ribosomal RNA at length 120, respectively. We include comparative results on validity and novelty for MMDiff in Appendix C.1, finding that MMDiff does not generate any samples that pass the validity criteria.
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B
C
A
E
D
Figure 5: Physical violations in generated samples. (A) Inter-chain clashes (highlighted yellow). (B)
Chain breaks and stray strands (highlighted yellow). (C)-(E) Excessive loops and helices.
4.4 Data preparation protocols
Due to the overrepresentation of RNA strands of certain lengths (mostly corresponding to tRNA or 5S ribosomal RNA) in our training set, our models generate close likenesses for those lengths that achieve high self-consistency but are not novel folds. To avoid this memorized recapitulation and promole increased diversity among samples, we sought to develop data preparation protocols to balance RNA folds across soquence lengths. We identically train RNA-FRAMEFLLOW on these data splits for 120K gradient steps, with results reported in Table 3.
We cluster training set using qTMclust. When creating a training batch, sample random clusters, and from each cluster, random structures. This ensures batches do not solely contain samples for single sequence length or are dominated by over-represeneed folds. There are only 342 structural clusters for the 5,319 samples within sequence lengths 40-150, highlighting the lack of diversity in RNA structural data. Each batch comprises padded samples up to a maximum length of 150 from randomly selected clusters across sequence lengths.
Structural clustering:
Cropping augmentation: We expand our training set by cropping longer RNA strands beyond length 150 by sampling a random crop length in [40, 150] and extracting a contiguous sogment from the larger chains. As cropped RNA are not standalone molecules and serve only to augment the dataset, we consider randomly chosen 20% of the training set size to balance uncropped and cropped samples; this gives 1,063 extra cropped samples.
We observe improved diversity and novelty the cost of reduced validity. Randomly cropping may introduce subsequences that fold into significantly different structures than the substructure extracted from the original RNA; these subsequences may even unfold in real life. As a result, the augmented dataset may contain folds that are unstable or implausible. The structure prediction and inverse-folding models may not have encountered these folds loosely recapitulated by our model, resulting poor validity. We are actively developing principled cropping methods that capture unique, realistic folds. We include additional results on these data preparation protocols in Appendix C.2.
5 Limitations and Discussions
Altogether, our experiments demonstrate that the SE(3) flow matching framework is sufficiently expressive for learning the distribution of 3D RNA structure and generating realistic RNA backbones similar to well- represented RNA folds in the PDB. Select examples are shown Figure We have also identified notable limitations and avenues for future work, which highlight below.
Physical violations. While well-trained models usually generate realistic RNA backbones, we do observe some physical violations: generated backbones sometimes have chains that are cither too close by or directly clash with one another, are highly coiled, have excessive loops and unrealistically intertwined helices, or have chain breaks. We highlight these limitations in Figure and analyze steric clashes in our generated backbones in Appendix C.4. RNA tertiary structure folding driven by base pairing and base stacking which influence the formation of helices, loops, and other tertiary motifs (Vicens & Kieft, 2022). Base pairing refers nucleotides along adjacent chains forming hydrogen bonds, while base stacking involves interactions bet

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rings of adjacent mucleotide bases along a chain. RNN-FRRMMEFT attempts model these phenomena using auxiliary losses but still operates at the backbone-only gramularity, not including base atoms (barring N1/N9). An array of complex tertiary folds (e.g,, kissing loops, tetraloops, junctions) oceur through base- mediated interactions, meaning R.N--RRAMFLOWW can only implicitly learn base pairing and stacking. Developing explicit representations of these interactions as part of the architecture may further minimize physical violations and provide stronger inductive biases to learn complex tertiary RNA motifs.
Generalization and novelty. We observed that the best designs from our models (as measured by SCTM score) are sampled at lengths 70-80 and 120-130, and often have closely matching structures in the PDB (high TM-scores). This suggests that models can recapitulate well-reprosented RNA folds in their training distribution (e.g., both (RNAs at length 70-90 and small 5S ribosomnl RNAs at length 120 are very frequent). However, self-consistency metrics were relatively poorer for less frequent lengths, suggesting that models are currently not designing novel folds.
We would also like to note that the models we use for structure prediction and inverse folding may be similarly biased to perform well for certain sequence lengths, leading to the overall pipeline being reliable for commonly occurring lengths and unreliable for less frequent ones. We also provide an empirical upper bound on the error accumulated in the seff-consistency pipeline in Appendix A.2. We evaluated preliminary strategies for structural clustering and cropping augmentations during training, which improved the novelty of designed structures but led to fewer designs passing the validity filter. Overall, the relative scarcity of RNA structural data compared to proteins necessitates greater care in preparing data pipelines for scaling up training and incorporating inductive biases into generative models.
6 Related Work
Recent end-to-end RNA structure prediction tools include RhoFold (Shen et al., 2022). RoseTTAFold2NA (Back et al., 2022a), DRFold (Li et al., 2023a), and AlphaFold3 (Abramson et al., 2024), each with varying performance that is yet to match the current state-of-the-art for proteins. Other approaches use GNNs as ranking functions (Townshend et al., 2021) together with sampling algorithms (Boniecki et al., 2016; Watkins et al., 2020). However, structure ure prediction Lools are not directly capable of designing new structures, which this work aims to address by adapting an SE(3) flow matching framework for proteins (Yim et al., 2023a). MMDiff (Morehead et al., 2023), a diffusion model for protein-nucleic acid complex generation, can also sample RNA-only structures in principle. Our evaluation shows that our flow matching model significantly outperforms both the original and RNA-only versions of MMDiff that we re-trained for fair comparison.
Joshi et al. (2025) introduce gRNAde, GNN-based encoder-decoder for 3D RNA inverse folding, a closely related task of designing new sequences conditioned on backbone structures. Tan et al. (2023) and Shulgina et al. (2024) have also developed GNNs for 3D RNA inverse folding. We use gRd (Joshi et al., 2025) followed by RhoFold (Shen et al., 2022) in our evaluation pipcline to forward fold designed backbones and measure structural self-consistency.
Independently and concurrent to our work, Nori & Jin (2024) propose RNAFlow, an SE(3) flow matching model to co-design RNA sequence and structure conditioned on protein partners. At each denoising step, RNAFlow uses a protein-condiitoonel variant of ARNAde (Joshi et al., 2025) to inverse fold noised structures, followed by Rose Rose TAAFooN2NAA (Baek et al., 2022a) to predict the structure of the designed sequence. The performance of RNAFFow is upper-bounded by Rose TTAFoldNAA as pre-trained structure generator, which is kept frozen and not developed for designed R.NA which do not have co-evolutionary MSA information. Our work tackles de novo 3D RNA backbone generation, an orthogonal design task of sampling RNA backbone structures. We train RNA structure generation models from scratch, akin to recent developments in protein design (Yim et al., 2023b;a; Bose et al., 2023; Lin & AlQuraishi, 2023). Backbone generation followed by inverse folding has shown experimental success in designing functional proteins (Dauparas et al., 2022; Watson et al., 2023; Ingraham et al., 2022), as the framework is flexible for including specific structural motifs and sequence constraints. Since the original release of several methods employ a similar SE()) flow matching setup. Rubin et al. (2025) incorporate an additional soquence track for RNA structure-soquence co-design, using the MultiFlow framework from Campbell et al. (2024). Tarafder & Bhattacharya (2025) condition the 3D structure generation on pre-determined sequences and secondary structural contact maps, enabling all-atom resolution with base identities.
LOW and its source code in 2024,
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Length: 70
ScTM: 0.763
ScRMSD: 1.54
ScGDT: 0.803
pdbTM: 0.652
Length: 50
Length: 40 ScTM: 0.482
ScTM: 0.458
scRMSD: 2.41
ScRMSD: 16.91
ScGDT: 0.681
ScGDT: 0.455
pdbTM: 0.385
pdbTM: 0.492
Length: 90
Length: 120
ScTM: 0.627
ScTM: 0.948
scRMSD: 12.51
ScRMSD: 0.88
scGDT: 0.241
ScGDT: 0.943
pdbTM: 0.611
pdbTM: 0.896
Length: 130
ScTM: 0.493
ScRMSD: 8.53
scGDT: 0.250
pdbTM: 0.598
Figure 6: Generated RNA backbones (colored) of varying lengths aligned with their RhoFold-predicted structure (gray). We provide post-evaluation metadata obtained from self-consistency pipeline.
7 Conclusion
We introduce RNA-FRAMEFLOW, generative model for 3D RNA backbone design. Our evaluations show that model can design locally realistic and moderately novel backbones of length 40 150 nucleotides. We achieve validity score of 41.0% and relatively strong diversity and novelty scores compared to diffusion model basclines and ablated variants. While generative models can successfully recapitulate well-represented RNA folds (e.g,, iRNAs, small rRNAs), the lack of diversity in the training data may hinder broad generalization at present. Directions for future research include exploring improved data preparation strategics combined with inductive biases that explicitly incorporate physical interactions that drive RNA structure, including base pairing and base stacking. We hope as foundations for the community to explore 3D RNA design, towards developing conditional generative models for real-world design scenarios.
and the associated evaluation framework can
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References
Josh Abramson, Jonas Adler, Jack Dunger, Richard Evans, Tim Green, Alexander Pritzel, Olaf Ronneberger, Lindsay Willmore, Andrew J Ballard, Joshua Bambrick, et al. Accurate structure prediction of biomolec- ular interactions with alphafold 3. Nature, 2024.
Bartosz Adamczyk, Maciej Antezak, and Marta Szachniuk. RNAsolo: repository of cleaned PDB-derived RNA 3D structures. Bioinformatics, 2022.
Minkyung Baek, Ryan McHugh, Ivan Anishchenko, David Baker, and Frank DiMaio. Accurate prediction of nucleic acid and protein-mucleic acid complexes using rosettafoldna. bioRrie, 2022a.
Minkyung Back, Ryan McHugh, Ivan Anishchenko, David Baker, and Frank DiMaio. Accurate prediction of mucleic acid and protein-mucliic acid complexes using rosettafoldna, 09 2022b.
Jacques Boitreaud, Jack Dent, Matthew McPartlon, Joshua Meier, Vinicius Reis, Alex Rogozhnikov, and Kevin Wu. Chai-1: Decoding the molecular interactions of life. bioRriu, pp. 2024-10, 2024.
Michal J Boniecki, Grzegorz Lach, Wayne K Dawson, Konrad Tomala, Pawel Lukasz, Tomasz Soltysinski, Kristian M. Rother, and Janusz M Bujnicki. Simrna: a coarse-grained method for rna folding simulations and 3d structure prediction. Nucleic acids research, 2016.
Avishck Jocy Bosc, Tara Akhound-Sadegh, Kilian Fatras, Guillaume Huguct, Jarrid Rector-Brooks Chong- Hao Liu, Andrei Cristian Nica, Maksym Korablyov, Michael Bronstein, and Alexander Tong. Se(3)- stochastic flow matching for protein backbone generation, 2023.
Andrew Campbell, Jason Yim, Regina Barzilay, Tom Rainforth, and Tommi Jaakkola. Generative flows on discrete state-spaces: Enabling multimodal flows with applications to protein co-design, 2024. URL btttss//arxiin www.aaiwwwaaaaaaaaae.eeeeoooleee org/ wwrg/abs/2402. 2492009977 04997.
Ricky T. Q. Chen and Yaron Lipman. Flow matching on general geometries, 2024.
Mary Clay, Laura Ganser, Dawn K Merriman, and Hashim M Al-Hashimi. Resolving sugar puckers in rma excited states exposes slow modes of repuckering dynamics. Nucleic acids research, 45(14):e134-0134, 2017.
Tulsi Ram Damase, Roman Sukhovershin, Christian Boada, Francesca Taraballi, Roderic Pettigrew, and John P Cooke. The limitless future of rna therapeutics. Frontiers in bioengineering and biotechnology, 9: 628137, 2021.
Justas Dauparas, Ivan Anishchenko, Nathaniel Bennett, Hua Bai, Robert Ragotte, Lukas F Milles, Basile IM Wicky, Alexis Courbet, Rob de Haas, Neville Bethel, et al. Robust deep learning based protein sequence design using proteinmpun. Science, 2022.
Alexander Denker, Francisco Vargas, Shreyas Padhy, Kicran Didi, Simon Mathis, Vincent Dutordoir, Ric- cardo Barbano, Emile Mathieu, Urszula Julia Komorowska, and Pictro Lio. Deft: Efficient finetuning of conditional diffusion models by learning the generalised h-transform. arXie preprint arXiv:2406.0m 01....17755 781, 2024.
Kieran Didi, Francisco Vargas, Simon Mathis, Vincent Dutordoir, Emile Mathicu, Urszula Julia Komorowska, and Pietro Lio. A framework for conditional diffusion modelling with applications in motif scaffolding for protein design. In NewrIPS 2023 Machine Learning for Structural Biology Workshop, 2023.
Jennifer A Doudna and Emmanuelle Charpentier. The new frontier of genome engineering with crispr-cas9. Science, 2014.
Laura R Ganser, Megan Kelly, Daniel Herschlag, and Hashim M Al-Hashimi. The roles of structural dynamics in the cellular functions of rnas. Nature reviews Molecular cell biology, 2019.
12

---

Published in Transactions on Machine Learning Research (07/2025)
Anke Gelbin, Bohdan Schneider, Lester Clowney, Shu-Hsin Hsich, Wilma K Olson, and Helen M Berman. Geometric parameters in nucleic acids: sugar and phosphate constituents. Journal of the American Chem- ical Society, 118(3):519 529, 1996.
Dongran Han, Xiaodong Qi, Cameron Myhrvold, Bei Wang, Mingjie Dai, Shuoxing Jiang, Maxwell Bates, Yan Liu, Byoungkwon An, Fei Zhang, et al. Single-stranded dna and rma origami. Science, 2017.
Joel M Harp, Terry P Lybrand, Pradeep S Pallan, Leighton Coates, Brendan Sullivan, and Martin Egli. Cryo neutron crystallography demonstrates influence of rma 2-oh orientation on conformation, sugar pucker and water structure. Nucleic acids research, 50(13):7721-77 7738, 2022.
Stephen C Harvey and M Prabhakaran. Ribose puckering: structure, dynamics, energetics, and the pseu- dorotation cycle. Journal of the Americon Chemical Society, 108(20):6125 6136, 1986.
Shujun He, Rui Huang, Jill Townley, Rachael C Kretsch, Thomas G Karagianes, David BT Cox, Hamish Blair, Dmitry Penzar, Valeriy Vyaltsev, Elizaveta Aristova, et al. Ribonanza: deep learning of rna structure through dual crowdsourcing. bioRriv, 2024.
John Ingraham, Max Baranov, Zak Costello, Vincent Frappier, Ahmed Ismail, Shan Tie, Wujie Wang, Vincent Xue, Fritz Obermeyer, Andrew Beam, et al. Illuminating protein space with a programmable generative model. bioRriv, pp. 2022 12, 2022.
Yu Jingcheng, Chen Zhaoming, Li Zhaoqun, Zeng Mingliang, Lin Wenjun, Huang He, and Ye Qiwei. Code of opencomplex. https://githe: tttp///gtttubb...//// htwechu...ooobeeeeeeeeeeeeeeeee. cwm/ http/bbaaaiaaaaa wwaahhaalthhppeComppphpp 2022.
Chaitanya K. Joshi, Arian R. Jamasb, Ramon Viñas, Charles Harris, Simon Mathis, Alex Morehead, Rishabh Anand, and Pietro Liò. gRNAde: Geometric deep learning for 3d rm inverse design. In International Conference on Learning Representations (ICLR), 2025.
John Jumper, Richard Evans, Alexander Pritzel, Tim Green, Michael Figurnov, Olaf Ronneberger, Kathryn Tunyasuvunakool, Russ Bates, Augustin Zidek, Anna Potapenko, et al. Highly accurate protein structure prediction with AlphaFold. Nature, 2021.
Kevin S Keating, Elisabeth I. Humphris, and Anna Marie Pyle. new way to see rna. Quarterly reviews of biophysics, 44(4):433 466, 2011.
Rachael C Kretsch, Ebbe S Andersen, Janusz M Bujnicki, Wah Chiu, Rhiju Das, Bingnan Luo, Benost Masquida, Ewan KS McRae, Griffin M Schroeder, Zhaoming Su, et al. Rna target highlights in casp15: Evaluation predicted models by structure providers. Proteins: Structure, Function, and Bioinformatics, 2023.
Yang Li, Chengxin Zhang, Chenjie Feng, Robin Pearce, P Lydia Freddolino, and Yang Zhang. Integrat- ing end-to-end learning with deep geometrical potentials for ab initio rna structure prediction. Nature Communications, 2023a.
Yueyi Li, Anibal Arce, Tyler Lucci, Rebecca A Rasmusssn, and Julius Lucks. Dynamic rma synthetic biology: new principles, practices and potential. RNA biology, 2023b.
Yeqing Lin and Mohammed AlQuraishi. Generating novel, designable, and diverse protein structures by equivariantly diffusing oriented residue clouds, 2023.
Mihir Metkar, Christopher Pepin, and Melissa Moore. Tailor made: the art of therapeutic mrna design. Nature Reviews Drug Discovery, 23(1):67 83, 2024.
Alex Morchcad, Jeffrey Ruffolo, Aadyot Bhatnagar, and Ali Madani. Towards joint sequence-structure generalion of nucleic acid and protein complexes with se(3)-discrete diffusion, 2023.
Jerome Mulhbacher, Patrick St-Prerre, and Daniel A Lafontaine. Therapeutic applications of ribozymes and riboswitches. Current opinion in pharmacology, 2010.
13

---

Published in Transactions on Machine Learning Research (07 (07/2025)
Divya Nori and Wengong Jin. Rnaflow: Rna structure & sequence co-design via inverse folding-based based flow matching. In ICLR 2024 Workshop Generolive and Eaperimental Perspectives for Biomolecular Design, 2024.
Rafacl Josip Penic, Tin Vlasic, Roland G Huber, Yue Wan, and Mile Sikic. Rinalmo: General-purpose rna language models can generalize well on structure prediction tasks. arXiv preprint, 2024.
Dana Rubin, Allan dos Santos Costa, Manvitha Ponnapati, and Joseph Jacobson. Ribogen: Rna sequence and structure co-generation with equivariant multiflow, 2025. URL https: petttps:/aatte //arxiv http//ovvvvoo//////////// wrgg/ba///5ate aba////3......./////// .20058.
Jason Salter, Jolanta Krucinska, Shabnam Alam, Valerie in the active site of all-rna hairpin ribozyme and effects of gua8 base variants on the geometry of phosphoryl transfer. Biochemistry, 45(3):686 700, 2006.
and Joseph E Wedekind. Water
Robert Setlik, Masayuki Shibata, Ramaswamy H Sarma, Mukti H Sarma, A Latif Kazim, Rick L Ornstein, Thomas Tomasi, and Robert Rein. Modeling of possible conformational change associated with the catalytic mechanism in the hammerhead ribozyme. Journal of Biomolecular Structure and Dynamies, 13 (3):515 522, 1995.
Tao Shen, Zhihang Hu, Zhangzhi Peng, Jiayang Chen, Peng Xiong, Liang Hong, Liangzhen Zheng, Yixuan Wang, Irwin King, Sheng Wang, Siqi Sun, and Yu Li. E2efold-3d: End-to-end deep learning method for accurate de novo rna 3d structure prediction, 2022.
Honglue Shi, Atul Rangadurai, Hala Abou Assi, Rohit Roy, David A Case, Daniel Herschlag, Joseph D Yesselman, and Hashim M Al-Hashimi. An rna dynamic ensemble at atomic resolution. bioRriv, pp. 2020-05, 2020.
Yekaterina Shulgina, Marena Trinidad, Conner J Langeberg, Hunter Nisonoff, Seyone Chithrananda, Petr Skopintsev, Amos J Nissley, Jaymin Patel, Ron S Boger, Honglue Shi, et al. Rna language models predict mutations that improve function. bioRriv, 2024.
Cheng Tan, Yijie Zhang, Zhangyang Gao, Hanqun Cao, and Stan Z. Li. Hierarchical data-efficient represen- tation learning for tertiary structure-based rna design, 2023.
Sumit Tarafder and Debswapna Bhattacharya. Rnabpflow: Base pair-augmented se (3)-flow matching for conditional mn 3d structure generation. bioRriv, 2025.
Sumit Tarafder, Rahmatullah Roche, and Debswapna Bhattacharya. The landscape of rna 3d structure modeling with transformer networks. Biology Methods and Protocols, 9(1):bpae047, 2024.
Raphael JL Townshend, Stephan Eismann, Andrew M Watkins, Ramya Rangan, Maria Karelina, Rhiju Das, and Ron O Dror. Geometric deep learning of rna structure. Science, 2021.
Quentin Vicens and Jeffrey S Kieft. Thoughts on how to think (and talk) about ma structure. Proceedings of the National Academy of Sciences, 2022.
W Wang, C Feng, R Han, Z Wang, L Ye, Z. Du, H Wei, F Zhang, Z Peng, and J Yang. trrosettarna: automated prediction of raa 3d structure with transformer network. nat. commun. 14, 7266, 2023.
Androw Martin Watkins, Ramya Rangan, and Rhiju Das. Farfar2: improved de novo rosctta prediction of complex global rna folds. Structure, 2020.
Joseph L Watson, David Juergens, Nathaniel R. Bennett, Brian L Trippe, Jason Yim, Helen E Eisenach, Woody Ahern, Andrew J Borst, Robert J Ragotte, Lukas F Milles, et al. De novo design of protein structure and function with rfdiffusion. Nature, 2023.
Luhuan Wu, Brian Trippe, Christian Nacsscth, David Blei, and John P Cunningham. Practical and asymp- totically exact conditional sampling in diffusion models. Advances in Neural Information Processing Sys- tems, 36, 2024.
14

---

Published in Transactions on Machine Learning Research (07/2025)
Joseph D Yesselman, Daniel Eiler, Erik D Carlson, Michael R. Gotrik, Anne E d' d'Aquino, Alexandra N Ooms, Wipapat Kladwang, Paul D) Carlson, Xuesong Shi, David A Costantino, et al. Computational design of three-dimensional rna structure and function. Nature nanotechnology, 2019.
Jason Yim, Andrew Campbell, Andrew Y. K. Foong, Michael Gastegger, José Jiménez-Tuna, Sarah Lewis, Victor Garcia Satorras, Bastiaan S. Veeling, Regina Barzilay, Tommi Jaakkola, and Frank Noć. Fast protein backbone generation with se(3) flow matching, 2023a.
Jason Yim, Brian L. Trippe, Valentin De Bortoli, Emile Mathicu, Arnaud Doucet, Regina Barzilay, and Tommi Jaakkola. Se(3) diffusion model with application to protein backbone generation, 2023b.
Chengxin Zhang, Morgan Shine, Anna Marie Pyle, and Yang Zhang. Us-align: universal structure alignments proteins, nucleic acids, and macromolecular complexes. Nature methods, 2022.
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Appendices
Additional Experimental Details
17
A.1 Denoiser Hyperparameters...
A.2 Upper bound performance of the Self-consistency Pipeline
17
A.3 RhoFold Length Bias
17
A.4 Imputing Non-frame Atoms from Torsion Angles
19
B Ablations
20
B.1 Composition of Backbone Coordinate Loss
20
B.2 Composition of Auxiliary Loss
20
B.3 Choice of Forward-folding Model
21
B.4 Rotational and All-atom Self-consistency.
22
C Additional Results
23
C.1 Evaluation of MMDiff Samples
23
C.2 Evaluation of Data Preparation Stralegies
C.3 Comprehensive local evaluation of angular distributions
................................
25
C.4 Measuring All-atom Steric Clashes
26
C.5 Atomic Displacement of Frame Atoms
27
C.6 Modeling Ring Puckering
27
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A Additional Experimental Details
A.1 Denoiser Hyperparameters
Category
Hyperparameter
Value
Invariant Point Attention (IPA)
Atom embedding dimension D₁
256
Hidden dimension Dz Number of blocks
128
6
Query and key points
8
Number of heads
8
Key points
12
Transformer
Number of heads
4
Number of layers
2
Torsion Prediction MLP
Input dimension Hidden dimension
256
128
Schedule
Translations (training sampling)
lincar / lincar linear exponential
Rotations (training / sampling)
Number of denoising steps NT
50
Table 4: Hyperparameters for best performing denoiser model.
A.2 Upper bound performance of the Self-consistency Pipeline
Our self-consistency pipeline to compute validity involves inverse and forward folding using gRRNAde (Joshi et al., 2025) and RhoFold (Shen et al., 2022). Placing upper bounds on the performance our RNA backbone design pipeline offers insights into areas of improvement using available open-source tools.
To quantify the total error accumulated in our self-consistency pipeline, and its impact on downstream validity, we study the extent to which gRNAde and RhoFold retrieve the ground truth sequences and structures from the RNAsolo training set. To assess RhoFold's structure prediction performance, we take all ground truth sequences of length 40 - 150 from RNAsolo, forward-fold (FF) them using RhoFold, and compute self-consistency metrics (TM-score, RMSD) by comparing them with the sequences" associated 3D folds. To assess gRNAde's sequence recovery performance, we inverse-fold (IF) 3D backbones from RNAsolo through gRNAAe to get 16 likely sequences and pass them to RhoFold for wrwarddfolding.
As shown in the table below, the average self-connistency of the gRNAde ground truth backbone structures is 43.7%, close that the generated backbones from RNA-FRAMEFLON closely retain the validity of RNAsolo backbones and corresponding sequences from gRNAde. In Figure 7, we also show the self-consistency TM-scores per length bins.
pipeline with RNAsolo volidity of 41.0%. This shows
Pipeline
Self-consistency (%) 1 Avg scTM f Avg scRMSD +
RNAsolo + FF only
55.1
0.690
2.804
RNAsolo + IF FF
43.7
0.663
3.085
RNA-FRAMEFLOW + IF + FF (ours)
41.0
0.641
2.298
A.3 RhoFold Length Bias
We investigate the performance of RhoFold representative subset of the training dataset used to train RNA-FRAMEFLLOW Figure 8 shows that RhoFold has a sequence length bias where it predicts accurate structures with low RMSDs (to the ground (ruth) for specific sequence lengths (like 70, 100, and 120) while predicting poor structures for other lengths. The performance across lengths disparate and may influence what is considered valid in our unconditional generation benchmarks. This affects efficacy when used in self-consistency pipeline with the RMSD metric. To minimize the influence of this length bias, we use TM-score for self-consistency because it does not penalize flexible regions much RMSD.
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1.0
Pipeline RMAsclo FF
RNAsclo
0.8
0.6
SCTM
0.4
0.2
0.0
(40. 501
(50, 601
(60, 701
(70, 801
(80. 901
(90, 1001
(100, 1101
(110. 1201
(120, 1301
(130, 1401
(140, 150)
Length Bin
Figure 7: Self-consistency scores on RNAsolo samples by sequence length. We observe that gener-
aled backbones from FRAA-RRMEFLLOW relain the sell-consistency of gRNNdde-redielee sequences.
60
RNASolo median RMSD
50
40
RhoFold RMSD
30
20
10
X
0
20
30
40
50
60
70
80
90
100
110
120
130
Sequence Length (# RNA nucleotides)
Figure 8: RhoFold length bias. The blue dotted line represents the median RMSD of RhoFold predictions the RNAsolo samples. RhoFold performs well for over-represented sequence lengths in the PDB, and poorly for under-represented sequence lengths.
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A.4 Imputing Non-frame Atoms from Torsion Angles
Here, we describe how we autoregressively impule the remaining non- frame atoms using 8 torsion angles & = {Φi + Φs}. For a nu- cleotide n along the generated RNNA backbone, we assume we have its final frame T(1) = (y(x), xx(0)) obtained from the denoiser's out- put after NT diffusion timesteps. Going by our choice of frame {C3', C4', O4'), we place non-frame atoms in the following order: C2', CV' N1/N9, 03', O,,, P,OP1, OP2, each corresponding to its respec- tive & E Φ as shown in Figure 1.
Uro
B
Referring to the figure on the right, suppose we have three atoms A, B, and with coordinates AI yA, AA); (. Vn: zn), (Ic, Nc: zc). They are connected by bonds AB and BC denoted by vectors AB B A and BC - with lengths TAB |AB] and rBc BC respectively. To rotate BC around AB by some angle Φ, we perform the following procedure:
n2
A
1. Compute unit vector UAn AB along bond AB by normalizing AB.
2. Compute vector perpendicular to UAB by choosing random normal vector ñ (like [1, 0, 0J or 1,07, and laking their cross product to get ū Üan nr.
3. Compute the unit vector Thot rotated by ø around AB using Rodrigues' rotation formula:
Tot cos (Ø) ūn + sin (Ø) (MAB x ū1) + (1 cos (o)) TT) -AB
4. Compute the coordinates of atom C as follows:
[xc. tc, 2c] [LB, yB. =Bl TBC Urot
We use predetermined bond lengths between atoms in the idealized geometry of the Adenine (A) mucleotide from OpenComplex (Jingeheng et al., 2022) in the same way Yim et al. (2023b;a) use Alanine for generated protein backbones. We use the following atom triplets and predicted torsion angles to build the all-atom nucleotide, starting from the ribose sugar ring towards the 5' end (i.e., the phosphate group):
Fixed bond
Non-frame atom Torsion angle
C4' C3'
C2'
Φ1
C4' 04'
C1'
22
04' C1'
N9 (or N1)
C4' C3'
03'
04
C4' C5'
05'
Ø5
C5' - 05'
96
05 P
OP1
@7
05'
OP2
08
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B
Ablations
B.1
Composition of Backbone Coordinate Loss
We also analyze how changing the composition of atoms in the inter-atom losses affects performance. We increase the number of atoms being supervised in the Lbb loss described above. Aside from the frame comprising {C3', C4', O4',, we try two settings with 3 and 7 additional non-frame atoms included in the loss. For the non-frame atoms, we additionally choose {C1', P, 03'} and for the non-framc atoms, we choose superset {C1' P, O3', C5', OP1, OP2, NI/N9). We posit the additional supervision may increase the local structural realism, which may further improve validity, shown in Table 5.
We indeed observe incrcasing validity as we increase the frame complexity in the auxiliary backbone loss. The minute RMSD contributions from disordered fragments of the RNA may be minimal, accounting for greater likeness to the RhoFold predicted structures, scoring relatively higher scTM scores. However, the original frame-only baseline model has better diversity and novelty which we attribute to high local variation in atomic placements. This variation causes two generated structures for the same sequence length to look very different at an all-atom resolution.
Frame composition in Lbb
% Validity f Diversity t
Novelty
Frame only (baseline)
41.0
0.62
0.54
Frame and 3 non-frame
45.0
0.28
0.79
Frame and 7 non-frame
46.7
0.35
0.85
Table 5: Ablating composition of backbone loss Lbb. Supervising more non-frame atoms improves validity but worsens diversity and novelty. Best result per column highlighted.
B.2 Composition of Auxiliary Loss
We ablate the inclusion of different auxiliary loss terms that guide our SF1(3) flow matching setup; results are in Table 6. Although, there an increase in EMD for bond distances as we remove distance-based losses like backbone coordinate loss Lsb and all-to-all pairwise distance loss (Lait). However, also observe the model still learns realistic distributions despite removing different loss terms, indicating that each loss makes for the absence of the other. Moreover, the best model still uses all losses with any removal causing a drop in validity. Further inspecting the samples from the models without each loss term reveals structural deformities at the all-atom level. Figure 9 shows such artifacts resulting from not enforcing geometric constraints through explicit losses.
Lbb
Caist Lso(3)
EMD (distance) J.
EMD (angles)
EMD (torsions)
1
% Validity f
0.17
0.11
2.36
41.0
/
0.18
0.14
3.85
35.0
0.23
0.11
3.72
13.3
4
0.18
0.18
3.59
16.7
Table 6: Ablations of loss terms on Farth Mover's Distance scores for structural measurements compared to ground truth measurements from the training set. The first row corresponds to the baseline model. Distance-based losses like the backbone coordinate loss (Cab) and all-to-all pairwise distance loss (Caist are necessary learn geometric properties like bond distances adequately.
20

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Published in Transactions on Machine Learning Research (07 (07/2025)
A
B
C
Figure 9: Not including auxiliary losses causes structural deformities in generated RNAs. (A) RNA backbone from our baseline model with expected adherence to bonding between nucleotides. (B) Not including the rotation loss (so causes nucleotides to have random orientations, preventing them from connecting contiguously. (C) Not including the backbone atom loss Lbb places intra-residue atoms too close
another resulting in bonds that should not exist. (D) Not including the all-to-all pairwise distance loss Edist. causes adjacent frames to fuse and loses contiguity, especially along helices and loops.
B.3 Choice of forward-folding Model
In our work, we rely on RhoFold (Shen et al., 2022) to forward fold the inverse-folded sequences from gRN Here, reperform our evaluation from Section 4.1 with Chai-1 (Boitreaud et al., 2024), recent open-source structure prediction model with results similar to AlphaFold2, replacing RhoFold in the self-consistency pipeline in Figure 2. We do not use MSAs for Chai-l. We do not observe any signif- icant difference in self-consistency distributions: for RNA-FRAMBFLLOWE w.w.MFFFFFWoaaaaaa..aaaa 41.0% while Rohooaal,,, report validity of ily of 39.5%.
1.0
0.8
Chai-1 SCTM
0.6
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gives volid-
Recent benchmarks (Tarafder et al., 2024) also ob- serve that existing RNA structure prediction tools like RhoFold, RF2NA (Baek et al., 2022b), and RosettaRNA (Wang al., 2023) perform similarly due to similarities in their architectures and train- ing data. For 600 generated backbones from RNA- FRAMBFLLOW, we get predicted sequences from gRNAde, giving us 4800 predicted backbones from RhoFold and Chai-1. We compare this SCTM distri- bution across predicted structures in Figure 10.
0.2
0.0
RhoFold SCTM
Figure Correlation between RhoFold and Chai-1 8cTM scores. Horizontal and vertical dotted lines denote the median SCTM score from each method across all samples.
21

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Published in Transactions on Machine Learning Research (07 (025)
B.4 Rotational and All-atom Self-consistenn
Our self-consistency pipeline currently computes TM-score and RMSD with C4' coarse graining, reflecting performance only along the translational component. However, our frames not only comprise the C''l atom but the C3' and 04' atoms as well, forming rotational component. Factoring in this rotational component into the self-consistency metrics would offer a clearer picture of RINA-FRAMELLOW' ability to precisely orient frames. In Table 7, we report scRMSD statistics over our generated backbones. We observe that the scRMSD values from RANA-FRAMEFLLON samples correlate positively with the self-consistency scores in Figure 3 (left). For sequence lengths with high % volidity, SCTM scores.
relatively lower ScRMSD values and higher
Sequence length
Median scRMSD
Mean scRMSD L
Std. Dev. ScRMSD
40
3.81
6.01
4.15
50
3.66
9.36
10.6
60
5.12
9.36
9.98
70
3.74
6.88
8.85
80
6.06
8.43
5.95
90
10.38
11.71
6.74
100
13.27
13.54
6.65
110
14.36
13.33
6.43
120
1.89
3.034
3.89
130
17.45
16.23
5.82
140
11.17
13.06
4.90
150
20.28
20.29
4.67
Table 7: Statistics of rotational scRMSD across sequence lengths. We observe RNA-FRAMEFILOW orients frames realistically, correlating positively with reported SCTM in Section 4.1 across sequence lengths.
RNA-FRAMBELLOW generates backbones at an all-backbone-stom granularity. We additionally compute ScRMSD across all 13 nucleotide atoms in Table 8. We similarly observe RNA-FRAMEFLOW can generate roalistic fine-grained nucleotides: for sequence lengths with relatively higher % validity, see lower all-atom scRMSD values.
Sequence length
Median ScRMSD
Mean ScRMSD 1
Std. Dev. SCRMSD
40
4.22
6.36
3.88
50
4.05
9.73
10.48
60
5.41
9.65
9.85
70
4.19
7.27
8.71
80
6,20
8.70
5.78
90
10.53
11.87
6.65
100
13.26
13.65
6.57
110
14.39
13.48
6.25
120
2.82
3.85
3.67
130
17.47
16.31
5.74
140
11.29
13.19
4.85
150
20.29
20.32
4.64
Table 8: Statistics of all-backbone-alom scRMSD across sequence lengths. We observe generates realistic fine-grained ancleotidss correlating positively with reported EMD scores for local struc- tural descriptors in Table across sequence lengths.
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Published in Transactions on Machine Learning Research (07 (07/202) 2025)
C Additional Results
C.1 Evaluation of MMDiff Samples
Here, we document global and local metrics from samples generated by MMDiff. MMDiff has validity score of 0.0% as all the samples have a poor SCTM score below the 0.45 threshold to the RhoFold predicted backbones. Even though none of the samples are valid, we show the average PdbTM scores for the samples, which are trivially low as there are no structures from the PDB that match them due to poor quality.
While MMDiff's samples locally resemble RNA structures given realistic, manual inspection reveals multiple chain breaks and disconnected floating strands, resulting in 0.0% validity. In Figure 12 (Subplot 1), we see inter-residue C4' distances slightly varying, causing the chain breaks and clashes. Furthermore, the Ramachandran plot in Figure 12 (Subplot 4) reveals a more complex angular distribution than found in the training set, which may be consequence of excessively folded regions or substructures that may have folded in on themselves.
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60 70 80 90 100110 130 150
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Sequence Length
SCTM
Figure 11: Validity and novelty of retrained MMDiff's top-10 generated backbones. (Left) SCTM of backbones of lengths 40-150 with the mean and spread of scTM for each length. (Middle) Scatter plot of self-consistency TM-score (scTM) and novelty (рdьTм) across lengths. Vertical and horizontal dotted lines represent TM-score thresholds of 0.45. Overall, MMDiff retrained on our training set does not generale realistic RNA structures.
@robability
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C4/-C4/ bond distances (Angstrom)
C4/ C4, bond angles
C4/-C4/ C4,-C44 dihedrals (radian)
-180
180
(radian)
n (degrees)
Figure 12: Structural measurements from samples generated by MMDiff. (Subplots 1-3) Left: his- togram of inter-mucleotide bond distances in Angstrom. Middle: histogram bond angles between nucleotide triplets. Right: histogram of torsion (dihedral) angles between every four nucleotides. (Subplot 4): RNA- centric Ramachandran plot of structures from the training (purple) and MMDiff's generated backbones (green).
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Published in Transactions on Machine Learning Research (07 (025)
C.2
Evaluation of Data Preparation Strategies
We include global evaluation metrics for the two data preparation strategies presented in the main text, namely structural clustering and cropping augmentation.
0.8
pdbTT
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0.66
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50 60 70 80 90 100 110 120 130 140 150
SCTM
Sequence Length
Figure 13: Validity and novelty of top-10 generated backbones from the model trained with only structural clustering. (Left) ScTM of backbones of lengths 40-150 with the mean and spread of ScTM for each length. (Middle) Scatter plot of self-consistency TM-score (sCTM) and novelty (pdbTM) across lengths. Vertical and horizontal dotted lines represent TM-score thresholds of 0.45.
0.35
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pdbTM
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70 80 90 100 100 120 130 140 150
0.0
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SCTM
0.75
Sequence Length
Figure 14: Validity and novelty of top-10 generated backbones from the model trained with structural clustering and cropping. (Left) SCTM of backbones of lengths 40-150 with the mean and sprcad of scTM for each length. (Middle) Scatter plot of self-consistency TM-score (scTM) and novelty (pdьTM) across lengths. Vertical and horizontal dotted lines represent TM-score thresholds of 0.45.
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Published in Transactions on Machine Learning Research (07 (07/2025)
C.3 Comprehensive local evaluation of angular distributions
Following the empirical structural analysis of RNA by Gelbin et al. (1996), compare local bond angle distributions among triplets of atoms from the generated backbones. We sample 50 all-atom backbones for each sequence length in [70, 90, 110, 130, 150], sieve out the valid samples, and extract relevant bond angles. As shown Figure 15, we observe that R.NA-FRAMEFLOW can retrieve angular distributions between distant and nearby atoms the nucleotides, providing preliminary evidence that modern protein design models are sufficiently expressive model RNA tertiary structure.
1.2
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C2'-C3'-03' bond angles (degree)
C1'-C2'-C3 bond angles (degree)
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OP1-P-OP2 bond angles
C3'-03'-p bond angles (degree)
(degree)
Generated
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0.02
0.00
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50
100
150
50
100
150
-3'-P-PP2 bond angles (degree)
03'-P-OP1 bond angles (degree)
Figure 15: Bond angle distributions between triplets of atoms. We select these atomic triplets from the empirical study of RNA's 3D geometry by Gelbin et al. (1996).
25

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Published in Transactions on Machine Learning Research (07 (025))
C.4 Measuring All-atom Steric Clashes
We compare the all-atom-level steric clashes between filtered RNAsolo samples used for training and the gencrated backbones from RNA-FRAMBFLOW We say two unbonded atoms i, clash the distance between them Maj is within a threshold dateric:
dsteric = + - 0.6
(11)
rig S dsteric
Inj =
(12)
otherwise
# clashes
Lij
(13)
1.
Here, V, E IR are the Van der Waals (VdW) radius of the atoms i,j in Angstrom. Based on its identity, each atom has its own VdW radius which we factor into our computation. We leave generous tolerance of 0.6 Å (corresponding to half the Hydrogen atom's VdW radius of 1.20 Å) to account for random deviations in atomic placements. We ignore Phosphodiester and Glycosidic bonds when computing clashes because the covalent radius is smaller than the VdW radius. As nucleotides constructed using idealized bonds, there may be fewer inter-nucleotide clashes, resulting in fewer clashes for RNA-FRAMEFION backbones.
In Figure 16, we compare the steric clashes across sequence length bins. We observe that RNA- F-FAARFFLLO generates backbones that have a similar distribution of inter-atom steric clashes as samples from RN Asolo. We also include validity for each sequence length bucket. We see that samples from certain sequence lengths (like 70, 80, 120) contain relatively fewer steric clashes are over-represented in RNAsolo. This means R.NA-FRAMEE'S LOW might be better at recapitulating atomic positions for such lengths than others. The steric clashes are normalized by the number of heavy atoms in the molecules, giving us steric clashes per 100 atoms. For the RNAsolo samples, we see 10.03 + 1.52 clashes per 100 atoms while our generated backbones have 25.55 + 5.43 clashes per 100 atoms.
samples within that length bucket since they
50
40
Steric Clashes Atoms
30
Training
Generated
40
50
60
70
80
90
100
110
120
130
140
150
(52%)
Sequence Length
Figure 16: All-atom steric clashes by sequence length. We obscrve similar number of steric clashes between training and generated backbones across sequence lengths. We include the (% validily) for generated samples from each sequence length below the length labels along the horizontal axis.
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Published in Transactions on Machine Learning Research (07 (075)
C.5 Atomic Displacement of Frame Atoms
To further motivate choice of frame aloms, examine the B-factor of each alom provided in the RNAsolo PDB files. B-factor is measure of atomic displacement, i.e. how much an atom wiggles in its place when the structure is undergoing X-ray crystallography or Cryo-EM. Empirically, we observe our frame construction {C4', C3', 04') collectively deviates the least compared to the frame construction RF2NA (Back al., 2022b), (P,OP1, OP2). We report this Table below:
Atom
Mean B-factor (A²) Median B-factor (A²)
111.44
84.84
C3'
111.74
85.41
04'
111.22
84.86
P
114.03
88.69
113.46
OP2
112.35
86.11
Table 9: Statistics of B-factor values (atomic displacement) of nucleotides from 500 random samples in RNAsolo. We observe our frame construction {C4', C3', O4') experiences lower collective spatial uncertainty compared to alternate frame constructions such as (POP1,OP2)
C.6 Modeling Ring Puckering
Puckering refers to non-planar deformations or contortions of the ribose sugar ring RNA comprising the atoms {C1', C2', C3', C4', O4'}. Instead of forming an ideal flat plane, the ring atoms alternately move above and below the idcal plane to relieve steric strain (see Figure 17 (A)). The five atoms collectively define five out-of-plane torsion angles: No (C4' -0''--'''--22// 21 (O4' CC' C2' C33), V2 (C1'
C4'), (C2'-CC - C4' - -44) and (C3' - C4' - 04' C1'). For nucleotide along the backbone, these angles define Cremer Pople gseudo-rotations parameterized by a phase angle P, that locates which atom is displaced towards the endo position (i.e., above the flat plane), and an amplitude Tmi that quantifies the maximum magnitude displacement. Tracking these quantities provides insights into the conformational diversity and intcractions of RNA. Specifically, C2'-cndo and C3'-cndo puckering are known mediate these behaviours. Several riboswitches, ribozymes, and RNA-protein interfaces exploit such endo orientations of ribose atoms trigger mechanism during molecular binding (Setlik et al., 1995; Salter et al., 2006).
In naturally-ocurring RNA (c.g., RNAsolo), the phase angle P distribution is sharply bimodal with a domi- nant C3' -endondo near 0 and a smaller C2'-endo near 180 The puckering amplitude Tm forms narrow band near 32 - 38 (0.55-0.66 rad) (Shi et al., 2020; Harp et al., 2022). In Figure 17 (B), we demonstrate that RNA-FRAMEFL.OM captures key ring puckering motions, with similar distributions for P and Tm-
A
B
0.8
270
30
So
0.2
Cemenated
180
Traning
Generated
Figure 17: Analysis of ring puckering motions. (A) Puckering occurs when atoms comprising the ribose sugar ring move above (endo) or below (ero) the idcal flat plane (cyan box). (B) Rose chart of phase angle P distribution (left)) and violin plot of amplitude Tm distribution (right). RNA-FRAMEFLLOW (green) generates RNA backbones that capture an appropriate degree puckering seen in natural RNA (purple).
27


Reviews:
[{"review_id": "Azcvp5jfiN", "reviewer": "Reviewer_Ym8X", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Strengths:\n- The paper provides details of data preparation and evaluation protocols, which I think is one of the main contributions of this paper.\n- The authors have discussed how they define the RNA backbone frames and discuss the motivation behind this. Nice illustrations are also presented to help readers better understand the definition.\n- The paper has designed several evaluation metrics, which I think are all rational. \n- The paper has discussed limitations, which I think is good for community development and helps readers to better understand the methods.\n\nWeakness:\n- The baseline, MMDiff, is not designed for RNA-only structure, though it supports this in principle. So the comparison might be slightly unfair. I think a better baseline is atom-level flow models trained on same data.\n- The authors explicitly discuss physical violations within the limitations, highlighting all-atom clashes. However, this raises the question of whether \"all-atom\" specifically refers to backbone atoms, as only frames and backbone torsions are predicted. What about the side-chains?\n- (Note: this point does not influence my assessment.) When discussing the choice of frame atoms, the authors mentioned several motivations. Could the author provide more quantitative evidence for this? For example, \"the chosen atoms spatially shift the least in naturally occurring RNA\". This matters because the definition of frames determine the upperbound performance of this method.", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "This work delves into RNA backbone structure generation, introducing the RNA-FrameFlow approach. The paper's key contributions include advancements in data preparation, evaluation protocols, and modeling techniques for RNA structures, focusing on the use of frames. From an algorithmic standpoint, the work is primarily centered around SE(3) flow matching, a technique extensively utilized in various domains such as protein design. The paper offers a wealth of content, providing a thorough analysis of the results and a clear discussion regarding its limitations.", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "Please see the weaknesses above. \nThe first two points would influence my recommendation. The third one would strengthen the work.", "broader_impact_concerns": "None.", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "eFHpgwqwUJ", "reviewer": "Reviewer_fANp", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "**Strength**\n\n1. Introduces the very first generative model dedicated to 3-D RNA backbone design.\n\n2. Extends SE(3) flow matching from proteins to RNA by adding RNA-specific frame parameters and torsion-based atom placement\n\n3. Builds a full metric suite (global TM/EMD, local angle plots, clash checks, self-consistency, etc.), which may offer the community a solid benchmark for future RNA generators.\n\n4. Demonstrates solid performance on common RNA families (tRNA, 5S rRNA, …) and provides thorough ablations plus some discussion of remaining challenges.\n\n5. Clear writing and intuitive figures\n\n**Weakness**\n1. After only a preliminary search, I found this paper \"A Hyperbolic Discrete Diffusion 3D RNA Inverse Folding Model for functional RNA design\" published recently that seem also leverage inverse folding for 3D and functional RNA design. This might invalidate author's claim of first generative model for such task. Perhaps, it would be useful to add discussion of this paper as well and highlight the distinction and novelty as compared to this work\n2. The methodological novelty here feels modest. The authors simply apply FrameFlow to RNA backbone design, but using FrameFlow to produce frames isn’t new—and RoseTTAFoldNA has already shown how to frame RNA structures. So this looks more like an incremental mash-up than a breakthrough worthy of a flagship conference. To stand out, the paper should surface deeper insights—e.g., unique hurdles when porting FrameFlow to RNA and concrete solutions. While the authors mention data scarcity and frame representation, those points aren’t fresh: limited 3-D RNA data is already well known, and the proposed fixes—structural clustering and cropping—are routine techniques, not strong innovations in themselves. However, the acceptance criteria of TMLR does not particularly emphasize on novelty. Therefore, this is not a major weakness that drives my decision making\n3. Because the cropping augmentation chops sequences in ways nature never would, it may sometimes spits out fragments that can’t fold", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "RNA-FRAMEFLOW is **claimed to be the first generative framework** for building 3-D RNA backbones from scratch. By extending the SE(3) flow-matching approach—originally crafted for proteins—the authors tailor the method to cope with RNA’s higher flexibility and 13-atom backbone. The backbone is encoded as rigid-body frames, while extra auxiliary losses smooth the training. A variety of evaluation metrics checks both self-consistency and physical plausibility, and new data augmentation tricks boost the variety and novelty of samples.", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "I would like to see a more thorough discussion of the novelty and additional technique innovations that are introduced as compared to \n\n[1] Yim, Jason, et al. \"Fast protein backbone generation with SE (3) flow matching.\"\n[2] RoseTTAFoldNA\n\nI am not demanding a ground breaking innovations to be distilled out of the comparison but rather a more clear and dedicated section or perhaps a table outlining similarity and RNA specific adaptation. \n\nOther than the above demand, i think this is a solid piece of work and meet TMLR's criteria for acceptance.", "broader_impact_concerns": "NA", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "AS281mwVaR", "reviewer": "Reviewer_dYWX", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Strengths:\n1. Novel Application Domain: This work is the first to adapt and apply the SE(3) flow matching paradigm to de novo RNA backbone generation, opening a promising new avenue for RNA design.\n2. RNA-Specific Adaptations: The authors demonstrated significant engineering effort in adapting the SE(3) flow matching framework from proteins to RNA by thoughtfully addressing RNA's distinct structural properties; this involved defining a suitable RNA frame with a mechanism for all-atom reconstruction via predicted torsion angles, and incorporating auxiliary loss functions specifically relevant to RNA geometry.\n3. Comprehensive evaluation framework: The paper establishes rigorous evaluation protocols combining global (TM-score, scRMSD) and local (bond angles, distances) metrics that provide a multi-faceted assessment of generated RNA structures.\n4. Clarity and Openness: The paper is generally well-written, the methodology is clearly explained, and the authors are transparent about limitations (e.g., physical violations, novelty of folds). \n\nWeakness:\n1. Limited Technical Novelty in Core Algorithm: The fundamental flow matching mechanism is a direct adaptation of the existing FrameFlow for proteins. While the RNA-specific frame definitions and auxiliary losses are important contributions, the core generative algorithm itself does not introduce new principles to flow matching. \n2. Sensitivity to Training Data Distribution and Limited Representation of RNA Conformational Space: The model's performance, particularly in achieving high scTM validity and generating truly novel folds (as measured by pdbTM), appears significantly constrained by the characteristics of the available RNA structural data, such as that in RNAsolo. Current RNA 3D structure databases are notably less extensive and diverse than their protein counterparts. Many existing RNA datasets, including RNAsolo, exhibit high structural similarity within certain sequence families and an over-representation of common classes (e.g., tRNAs, 5S rRNAs at specific lengths). This inherent lack of diversity in the training data means it may not adequately represent the full breadth of the natural RNA conformational space. Consequently, training a generative model solely on such data, even with augmentation, might inherently limit its ability to generalize and design truly diverse and novel structural motifs, potentially leading to the preferential recapitulation of observed folds rather than exploration of uncharted structural territories.\n3. Inherent Uncertainty in Evaluation Pipeline: The \"validity\" metric is contingent upon the performance of external tools like gRNAde and RhoFold. As the authors acknowledge in the appendix, RhoFold exhibits its own length biases and inaccuracies. While this is a common challenge in evaluating generative models, it means the reported 41% validity is an estimate influenced by the capabilities and potential systematic errors of these downstream predictors, rather than an absolute measure of intrinsic structural quality.\n4. Backbone-Only Representation Overlooks RNA's Primary Folding Determinants: A fundamental distinction between RNA and protein folding is their primary driving forces. While protein folding is significantly influenced by backbone hydrogen bonding and hydrophobic collapse, RNA tertiary structure is predominantly dictated by base pairing (both canonical and non-canonical) and base stacking interactions. By focusing exclusively on backbone atom generation, RNA-FrameFlow does not explicitly model base identities or these crucial base-mediated interactions. Although auxiliary losses on backbone geometry attempt to implicitly capture some consequences of these interactions, the absence of direct base modeling inherently limits the model's capacity to learn the true biophysical drivers of RNA folding. This makes it challenging to generate and stabilize complex tertiary arrangements, especially those involving intricate non-canonical interactions or long-range pairings, which are critical for RNA function.\n5. Focus on Unconditional Generation: The current work primarily addresses unconditional backbone generation. While foundational, the practical application in RNA design often requires conditional generation (e.g., based on sequence constraints, secondary structure motifs, or functional sites). The pathways to effectively integrate such conditions into the RNA-FrameFlow framework are mentioned but remain largely unexplored in this submission.", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "This paper introduces RNA-FrameFlow, the first generative model specifically designed for de novo 3D RNA backbone generation. The authors adapt SE(3) flow matching, a technique previously successful for protein backbone generation, to the unique challenges of RNA modeling. The key contributions include:\n1. RNA Frame Parameterization: The model defines the RNA backbone frame using the rigid body formed by C4′, C3′, and O4′ atoms. The positions of the remaining backbone atoms are then determined via 8 predicted torsion angles, enabling the end-to-end generation of full-atom RNA backbones.\n2. Flow Matching Training for RNA: Application of the SE(3) flow matching framework where the model learns a time-dependent vector field to map noisy, randomly initialized frames to ground-truth RNA frames. This learning process involves separate supervision of the rotation and translation components of the SE(3) transformations.\n3. RNA-Specific Data Preparation and Augmentation: Development of a data preparation protocol using RNA sequences (40–150 nt) from the RNAsolo dataset. To address the scarcity and limited diversity of 3D RNA structural data, this protocol incorporates structural clustering and random cropping augmentations to expand and diversify the training samples.\n4. Comprehensive Evaluation Protocol: Establishment of a rigorous evaluation suite to assess the quality of generated RNA backbones. This includes global self-consistency checks and the assessment of local structural realism.", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "1. Expanded Analysis of Evaluation Tool Limitations: While the appendix touches on RhoFold's biases, integrate a more prominent discussion in the main text about how the limitations of gRNAde and RhoFold might affect the interpretation of the reported \"validity\" and self-consistency scores. This adds a layer of critical self-assessment.\n2. Expanded Analysis of Evaluation Tool Limitations: While the appendix touches on RhoFold's biases, integrate a more prominent discussion in the main text about how the limitations of gRNAde and RhoFold might affect the interpretation of the reported \"validity\" and self-consistency scores. This adds a layer of critical self-assessment.\n3. Acknowledge Backbone-Only Limitations More Directly in Main Results: When discussing the generated structures and their novelty, more explicitly connect the backbone-only nature of the model to its potential limitations in capturing folds heavily reliant on specific base-mediated interactions. This manages reader expectations regarding the types of structures the current model can realistically generate.\n4. Briefly Outline Future Directions for Conditional Generation: While a full exploration is beyond scope, a short paragraph outlining potential strategies or initial thoughts on how conditional information (e.g., secondary structure constraints) could be incorporated into the RNA-FrameFlow framework would be beneficial for readers interested in practical design applications.\n5. Update Related Work/Discussion with Recent Advances: In the \"Related Work\" or \"Discussion\" sections, incorporate a brief mention and contextualization of other very recent or concurrent works in RNA backbone/structure generation (e.g., RiboGen, RNAbpFlow, or other flow/diffusion models for RNA that may have emerged). This demonstrates awareness of the rapidly evolving field.", "broader_impact_concerns": "None. This work focuses on foundational generative modeling for RNA structures. The research is aimed at advancing scientific understanding and tool development for RNA engineering. The potential for misuse is low and in line with other generative models in computational structural biology.", "additional_comments": "", "extra_scores": {}, "extra_text": {}}]

Author rebuttal:

Decision: Accept (poster)