Introduction

Over 95% of the human genome is transcribed to non-coding RNA, which serves pivotal roles in biomolecular processes1. The intrinsic dynamic flexibility and pronounced conformational heterogeneity of RNA endow it with diverse functional capabilities2. Deciphering the conformational ensembles of RNA is fundamental for understanding its intricate mechanisms of action, advancing RNA-targeted drug discovery, and facilitating the design of RNA-based therapeutic strategies3. However, traditional experimental methods, including NMR, X-ray, and cryo-electron microscopy, encounter considerable limitations in resolving the complex conformational ensembles of RNA4. On the one hand, these methods often average signals from multiple conformations, making it difficult to accurately capture RNA’s highly heterogeneous structural characteristics5. On the other hand, the intrinsic properties of RNA structures further complicate their resolution by experimental approaches6. Conventional computational methods, such as Molecular dynamics simulations (MDs), are too expensive to explore RNA’s vast conformation space7. Besides, inaccuracies in RNA force fields severely limit the application of MDs8,9,10,11.

Recently, the rapid advancement of artificial intelligence methodologies has provided novel opportunities for structural biology12. AlphaFold2 significantly improved the accuracy of protein structure prediction, but it does not include RNA13. AlphaFold3 introduced a substantially updated diffusion-based architecture that extends beyond protein to nucleic acids and other biomolecule structure prediction14. AlphaFold3 is predominantly confined to predicting single stable conformations rather than generating a conformation ensemble of RNA, which is important for comprehensively characterizing the heterogeneity of RNA15. Diffusion model has shown promise in generating protein conformation ensemble16, but has not been used in predicting RNA conformation ensemble to our best knowledge.

In this work, we developed DynaRNA to generate an RNA dynamic conformation ensemble based on a particular generative model. We herein demonstrated the capability of the diffusion model in RNA conformation generation with the development DynaRNA model in an attempt to directly model 3D coordinates of RNA, orders of magnitude faster than MDs. We show that DynaRNA can generalize across various molecular systems and propose diverse structures that agree with experimental results. We employed several RNA molecular systems, including tetranucleotides17, tetraloop18,19, and HIV-1 TAR20,21, to demonstrate applications of DynaRNA. DynaRNA showed the ability to generate an RNA dynamic conformation ensemble in agreement with experimental observations. Besides, DynaRNA can capture the excited-ground state (GS) of HIV-1 TAR and the de novo folding of the tetraloop. These results demonstrate that DynaRNA extends the application of diffusion models to RNA conformational ensemble generation, offering a novel approach for exploring the vast dynamic conformational space of RNA.

Results

DynaRNA architecture

Diffusion models have been widely used and proven effective in molecule generation. In this study, we employed a denoising diffusion probabilistic model (DDPM) tailored for RNA conformational ensemble generation, which operates directly on the 3D atomic coordinates of a given input structure. Distinct from conventional DDPMs that gradually diffuse inputs into pure Gaussian noise22, our model adopts a partial noising scheme, where the diffusion is applied only up to an intermediate noise step rather than a full corruption. This enables a tunable balance between preserving structural information from the original input and introducing stochastic variability for sampling diverse conformations23. The generative pipeline of DynaRNA, shown in Fig. 1A, consists of two stages: a forward diffusion process that incrementally adds Gaussian noise to the coordinate space, and a reverse denoising process that iteratively reconstructs the conformation. The denoising network is implemented using equivariant graph neural networks (EGNNs)24, which are designed to respect the Euclidean symmetries (E(3)) of molecular structures, such as rotation and translation equivariance. By modeling the molecule as a spatial graph, EGNNs ensure that the generative process remains consistent with the physical geometry of the system25.

Fig. 1: Overview of DynaRNA architecture.
figure 1

A The framework of DynaRNA comprises two processes: a forward noising process indicated by the blue solid line, in which Gaussian noise is progressively added to the input structure, and a reverse denoising process indicated by the green dashed line. B Distribution of adjacent C4’ distances of conformation ensembles generated by DynaRNA(blue) compared to PDB experimental structures(orange). C EGNNs are utilized to predict the noise and denoise. D Distribution of C4’ hyper bond angles of conformation ensembles generated by DynaRNA (blue) compared to PDB experimental structures (green).

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In our implementation of DynaRNA, we employed partial noising and denoising instead of a conventional fully noising process. This approach aimed to balance efficient sampling and the preservation of essential initial structural information of RNA conformation generation. With the complete diffusion process of 1024 steps, we systematically evaluated truncated versions at 200, 400, 600, 800, 1000, and 1024 steps for RNA conformation generation of U40. These generated conformational ensembles were rigorously compared against reference ensembles obtained from molecular dynamics simulations using the D. E. SHAW force field26. As shown in Fig. 2, we conducted a comprehensive analysis of distance map comparisons and Jensen–Shannon (JS) divergence calculations between DynaRNA-generated ensembles across different denoising steps and the MD reference ensemble for the U40 system. Our quantitative evaluation revealed that the 800-step implementation achieved the optimal trade-off between structural fidelity and computational efficiency, demonstrating superior agreement with the MD reference while maintaining reasonable sampling speed. Therefore, we implemented a partial noising process where the forward diffusion process, as well as the backward denoising process, spans 800 steps instead of the full 1024 steps in inference. The flexibility introduced by partial noising allows users to control how much structural prior is retained during sampling, enabling tailored conformational generation based on the desired balance between fidelity and diversity. This makes our approach particularly suitable for modeling RNA molecules, as RNA conformation ensembles are often more diverse than proteins. Further architectural and training details are provided in the “Materials and methods” section.

Fig. 2: JS divergence between MD simulation conformations (green) and generated conformations of different steps with DynaRNA (blue).
figure 2

The first panel shows the nucleotide–nucleotide distance contact map of the MD simulation ensemble. The following panels present contact maps of ensembles generated by adding noise and denoising from 200 to 1024 steps. Each panel is annotated with the JS divergence relative to the MD ensemble distribution, with the ensemble at 800 steps showing the smallest JS divergence.

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General validation of DynaRNA

We first assessed the geometric fidelity of RNA conformations generated by DynaRNA by examining two key structural features: the distance between adjacent nucleotides and the hyper bond angles formed by three consecutive nucleotide C4’ atoms. These metrics serve as important indicators of RNA backbone integrity. We computed the distributions of these features in the DynaRNA-generated conformations and compared them with reference distributions derived from high-resolution RNA structures in the Protein Data Bank (PDB)27, as shown in Fig. 1B, D. The results demonstrated that the adjacent C4’–C4’ distances in the DynaRNA-generated ensemble are highly consistent with those observed in experimental structures, both peaking around 6 Å. Besides, the hyper bond angles defined by three consecutive C4’ atoms are centered around 40 degrees in both datasets, reinforcing the model’s ability to reproduce the local backbone geometry of native RNA conformations.

Moreover, we have systematically generated conformational ensembles for all RNA structures in the PDB training set and performed a comprehensive structural evaluation, including both fundamental geometric properties, such as bond lengths and bond angles, and global structural features, such as the radius of gyration (Rg). As shown in Table 1, The average bond lengths of C5′–C4′, C3′–C4′, and C4′–O4′ in the DynaRNA-generated ensembles are 1.509 Å, 1.520 Å, and 1.450 Å, respectively, whereas those in the PDB ensembles are 1.478 Å, 1.512 Å, and 1.467 Å, respectively. The mean absolute errors (MAEs) between the two ensembles are 0.031 Å, 0.008 Å, and 0.017 Å. Similarly, the average bond angles of C5′–C4′–C3′, C5′–C4′–O4′, and C3′–C4′–O4′ in the DynaRNA-generated ensembles are 115.73°, 109.80°, and 104.29°, respectively, compared with 113.57°, 111.12°, and 104.05° in the PDB ensembles, yielding MAEs of 2.16°, 1.32°, and 0.24°, respectively. These results indicate that the basic geometric features of the DynaRNA-generated ensembles are highly consistent with those of experimental PDB structures, supporting the geometric plausibility of our generated conformations. As shown in the new Fig. 3, the predicted and experimental Rg values exhibit a very strong correlation (R² = 0.982), with the regression line closely following the y = x reference, indicating that DynaRNA accurately reproduces the global structural properties of RNA.

Fig. 3: Correlation between the experimental and DynaRNA-predicted Rg for RNAs in the PDB training set.
figure 3

Green point represents RNA entries, with the experimental Rg on the x-axis and the ensemble-averaged Rg from DynaRNA-generated conformations on the y-axis. The blue line is the linear fit (R²  = 0.982), which closely follows the black dashed line (y = x), indicating that DynaRNA accurately reproduces global structural properties.

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Table 1 Comparison of bond length and bond angle between experimental PDB and DynaRNA-generated conformation ensembles
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Taken together, these observations suggest that DynaRNA is capable of generating RNA conformations with high geometric plausibility, closely matching the statistical features of experimentally resolved RNA structures. This level of agreement underscores the model’s fidelity and its potential utility in RNA structure modeling and related computational studies.

DynaRNA can capture the conformation ensemble of tetranucleotides

Tetranucleotide, consisting of four nucleotides, serves as a key benchmark system for RNA computational structure research5. Existing computational methods, such as molecular dynamics simulations, generate a large number of RNA intercalated conformations, which are in serious disagreement with the results of solution NMR experiments17. We systematically compared the performance of DynaRNA with MD simulations employing three distinct force fields (OL328, BSFF111, and BSFF210) initialized from canonical A-form structures and intercalated conformations. Quantitative analysis of intercalation propensity in the generated conformational ensembles is presented in Fig. 4. Notably, DynaRNA-predicted tetranucleotide ensembles exhibited substantially lower intercalation ratios compared to MD simulations with OL3. This improvement was particularly evident when starting from the intercalated conformation. For CAAU and CCCC systems, simulations with OL3 became trapped in the intercalated conformation, with intercalation rates of 97.3% and 90.7%, respectively. In contrast, DynaRNA yielded a conformation ensemble with intercalation rates of only 9.2% and 4.7%. Regardless of whether the simulations started from the A-form or the intercalated conformation, the intercalation rates in DynaRNA-generated ensembles remained below 10%, effectively demonstrating the robustness of DynaRNA. Besides, we conducted direct and quantitative comparisons of tetranucleotide ensembles with experimental data. Specifically, the radius of gyration (Rg) of tetranucleotide ensembles generated with DynaRNA and OL3 was calculated and compared with the previous experimental fit results29 (Rg = 10−10 × (4.06 ± 0.47) × N(0.38 ± 0.03), N represents the number of nucleotides). Results shown in Supplementary Table 1 demonstrate that the DynaRNA-generated tetranucleotide ensembles are in closer agreement with experimental measurements, thereby providing more objective validation of the model. These additional comparisons based on experimental observables strengthen the validation of DynaRNA. However, DynaRNA still has room for improvement. The Rg of the DynaRNA-generated ensembles for tetranucleotides remains partially underestimated. This discrepancy stems from the fact that DynaRNA’s training set is derived from the PDB database, in which the vast majority of experimentally resolved RNA structures are compact. Consequently, DynaRNA may have limited exposure to short, single-stranded RNA conformations that are largely unstructured, such as UUUU. This limitation could be addressed by expanding the training set to include more diverse RNA dynamic datasets for model training.

Fig. 4: DynaRNA captures the experimental conformation ensemble of tetranucleotides.
figure 4

A Intercalation ratio of conformation ensembles generated with molecular dynamics simulations and DynaRNA initialized from A-form structures. B Intercalation ratio of conformation ensembles generated with molecular dynamics simulations and DynaRNA initialized from intercalated structures.

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Furthermore, we performed detailed structural analysis of the conformational ensembles. Previous studies have shown significant differences in the ζ/α dihedral distributions between intercalated and non-intercalated conformations11. Our results, shown in Fig. 5 revealed that in the ensemble simulated with OL3, the ζ/α dihedrals were predominantly concentrated in the intercalated conformation region (+30° to +90°). In contrast, DynaRNA-generated ensembles exhibited ζ/α dihedrals concentrated in the non-intercalated region (−30° to −90°), which was closer to experimental results.

Fig. 5: Results of ζ/α dihedral distributions analysis.
figure 5

A Dihedral statistical distribution of PDB experimental structures. B, C Dihedral statistical distribution of conformation ensemble generated by molecular dynamics simulations with OL3 initialized from A-form structures and intercalated structures. D, E Dihedral statistical distribution of conformation ensemble generated with DynaRNA initialized from A-form structures and intercalated structures. F–J Dihedral statistical distribution of conformation ensemble generated by molecular dynamics simulations with OL3 of AAAA, CAAU, CCCC, GACC, UUUU, respectively. K–O Dihedral statistical distribution of conformation ensemble generated by molecular dynamics simulations with DynaRNA of AAAA, CAAU, CCCC, GACC, UUUU, respectively.

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Structural clustering analysis shown in Supplementary Figs. 1 and 2 further confirmed that the major conformation in DynaRNA-generated ensembles was the non-intercalated A-form, whereas OL3 force field simulations predominantly yielded intercalated conformations. Besides, we also analyzed the dihedral distribution of the conformation ensemble generated by molecular dynamics simulations with BSFF1 and BSFF2. Results shown in Supplementary Figs. 3–6 demonstrated that DynaRNA attains accuracy on par with, or exceeding, that of MD simulations in RNA conformation ensemble generation, while also offering significantly faster computational speed due to its innovative approach of bypassing the need for step-by-step sampling.

DynaRNA can capture the excited state of RNA conformation

The HIV-1 trans-activation response (TAR) element has emerged as a highly promising therapeutic target30. Its structure, consisting of two helical regions connected by a bulge and a hairpin loop motif at the apex, has attracted extensive research attention31. Previous studies have revealed that besides the dominating GS, HIV-1 TAR also adopts low-populated excited states (ES)20,21. These ES play essential roles in biochemical reactions, disease mechanisms, and therapeutic development32. However, due to their richness in non-canonical mismatches and energetically unfavorable nature, they are sparse and short-lived, posing significant challenges for structural characterization. Conventional experimental techniques struggle to capture the RNA excited state33. Traditional computational techniques, such as molecular dynamics simulations, face difficulties in overcoming the high energy barriers required to sample ES34. DynaRNA provides a unique technique to overcome the energy barrier and directly explore the ensemble of conformational space. Recently, Ainan Geng et al determined an HIV-1 TAR ES termed ES2 with a population of about 0.4% and a lifetime of ~2.1 ms21.

We herein generated the HIV-1 TAR conformation ensemble with DynaRNA initialized from both GS and ES2. The GS starting structure is taken from the PDB entry 8THV, and the ES2 starting structure from the PDB entry 8U3M. As shown in Fig. 6A, GS differed from ES2 of secondary structure, involving six base pairings and over fifteen nucleotides. Transitions between these states necessitate crossing multiple conformational potential energy barriers, presenting a formidable computational challenge for molecular dynamics simulations. This challenge is particularly serious for ES2, which exists at a higher potential energy level, making it especially difficult to access from GS. DynaRNA has successfully bridged this gap with the bidirectional conformation generation capability shown in Fig. 6B, C. When initiated from GS, DynaRNA generated conformational ensembles that effectively captured ES2. Conversely, when initiated from ES2, DynaRNA also successfully sampled GS. Results of principal component analysis (PCA) for conformation ensemble generated by DynaRNA initialized from GS and ES2 were respectively represented in Fig. 6D, E. Conformational landscapes exhibit two distinct clusters, corresponding to the ground state (GS) and the excited state 2 (ES2). Notably, initiated from either GS or ES2, DynaRNA could capture the alternate conformations, highlighting its ability to traverse the complex conformational landscape of RNA. We performed clustering analysis for the conformation ensemble generated by DynaRNA from both states. Specifically, for the ensemble initiated from GS, the clustering analysis identified a GS population of 48% and an ES2 population of 11%. Conversely, for the ensemble initiated from ES2, clustering yielded an ES2 population of 59% and a GS population of 16%. These results underscore DynaRNA as a powerful tool for discovering and characterizing rare, transient RNA conformational states and imply the potential of DynaRNA as a valuable method for RNA structural plasticity and its functional implications.

Fig. 6: Results of HIV-1 TAR conformation generation with DynaRNA.
figure 6

A Secondary structure of HIV-1 TAR GS and ES2. B Tertiary structure of GS and ES2 generated by DynaRNA initialized from the other state. C Structural annotation for GS and ES2 generated by DynaRNA initialized from the other state. D PCA results of conformation ensemble generated by DynaRNA initialized from GS. E PCA results of the conformation ensemble generated by DynaRNA initialized from ES2.

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DynaRNA can capture de novo folding of RNA tetraloops

Tetraloops, comprising a Watson–Crick base-paired stem and a loop of four nucleotides, represent one of the most ubiquitous and well-characterized RNA secondary structure motifs35. Tetraloops play critical roles in RNA folding, stability, and function, and often serve as nucleation sites in tertiary interactions36. De novo folding of tetraloops remains a challenge for RNA computational research. This challenge is further exacerbated by the inaccuracies of RNA force fields37. Recent RNA force fields such as gHBfix9, tHBfix8, and DE Shaw’s RNA force field26 partially revised these inaccuracies and can sample folded states with extensive simulations. Previous studies38 have shown that RNA hairpin folding is a hierarchical process, which makes it computationally expensive to de novo capture the tetraloop folded state using molecular dynamics simulations39. Despite these challenges, DynaRNA successfully generated native-like folded conformations of tetraloops starting from fully extended, single-stranded RNA sequences without any structural restraints or prior knowledge. Results of alignment between experimental structure and DynaRNA-predicted structure are shown in Fig. 7. DynaRNA achieved the minimum atom root-mean-square deviation (RMSD) of 0.9 Å and eRMSD of 1.01 for the UUCG tetraloop (PDB ID: 2KOC) and RMSD of 1.3 Å with eRMSD of 1.13 for the GAAA tetraloop (PDB ID: 8CLR) compared with the corresponding native structures, which recapitulated all of the Watson-Crick base pairs with no prior knowledge. We performed clustering analysis of the generated conformational ensembles, which showed native state cluster populations of 20.6% and 18%, respectively. DynaRNA is a generative model, and thus its ensemble distributions are not expected to converge to a single dominant conformation as in MD simulations. DynaRNA can serve as a complementary tool to molecular dynamics, for example, by generating near-native states that can then be refined through MD simulations to achieve converged sampling, thereby combining reduced computational cost with accurate convergence.

Fig. 7: Results of alignment of tetraloops structures.
figure 7

The green color represents experimental structure and the blue color represents the  conformation generated by DynaRNA with structural annotation by DSSR and VARNA51.

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Discussion

Deciphering the complex hierarchical structural dynamics of RNA is crucial for understanding its functional mechanisms40, but this remains highly challenging for both traditional experimental and computational approaches41. To bridge this gap, we employed a neural generator to directly sample RNA dynamic conformation (DynaRNA). DynaRNA represents a paradigm shift in computational modeling of RNA conformational dynamics by leveraging the power of diffusion-based generative models. Unlike traditional molecular dynamics simulations that rely on step-by-step sampling with physics-based force fields and are often limited by sampling inefficiencies and force field inaccuracies, DynaRNA efficiently generates diverse and physically plausible RNA conformations.

DynaRNA successfully reproduced experimental geometries (e.g., C4’–C4’ distances, hyper bond angles) and predicted folded tetraloop structure de novo from fully unfolded initial conformation. Besides, DynaRNA outperformed MD simulations in generating tetranucleotide conformation ensembles, achieving intercalation rates below 10% compared to >90% for OL3 force fields, and demonstrated orders-of-magnitude faster computational efficiency. While conventional MD simulations typically require weeks of intensive sampling to explore conformational landscapes (often hindered by energy barriers and force field inaccuracies), DynaRNA generates physically plausible ensembles in mere minutes to hours on a single GPU. Notably, DynaRNA achieved high efficiency in capturing rare excited states, capturing the HIV TAR’s low-population (~0.3%) conformation, highlighting its robustness in escaping energy traps—a critical limitation of physics-based simulations. These results underscore the ability of DynaRNA to accurately and efficiently resolve RNA’s intrinsic heterogeneity.

Furthermore, the framework of DynaRNA holds substantial potential for expansion through strategic avenues. First, the artificial intelligence generative network of RNA can be integrated with a physics-based model (e.g., force field). Refining generated conformations with short MD simulations for local energy minimization could reconcile data-driven efficiency with physical realism. Second, incorporating richer training data, including RNA molecular dynamics trajectories and multi-resolution atomic representations (e.g., explicit backbone atoms beyond C4’), would enhance the model’s ability to capture subtle conformational nuances. Third, the framework of DynaRNA can be expanded to model DNA dynamics42, enabling comparative studies of nucleic acid flexibility. Besides, we observed that DynaRNA still has room for improvement in faithfully reproducing certain RNA secondary structure features, particularly canonical Watson–Crick base pairs. One promising direction is to enhance the granularity of the coarse-grained representation—from the current C4′-only model to incorporating additional backbone and base atoms, or even transitioning to an all-atom representation—combined with improved back-mapping methods to recover full-atom detail. Another avenue is to incorporate secondary structure recovery, specifically the preservation of canonical Watson–Crick base pairs, directly into the loss function to guide model optimization. Furthermore, expanding the training dataset beyond static PDB structures to include dynamic molecular data, such as RNA molecular dynamics trajectories, could further improve DynaRNA’s performance in challenging systems, including short single-stranded RNA systems such as the UUUU tetranucleotide.

DynaRNA bridges critical gaps in RNA research by complementing both experimental and computational techniques, such as molecular dynamics simulations, accelerating RNA therapeutic development, and expanding the scope of AI-driven structural analysis. DynaRNA can combine traditional methods like NMR and simulations, enabling cost-efficient, rapid, and accurate resolution of RNA conformational ensembles and also capturing rare excited and transient states, which are critical for function yet elude experimental and computational detection due to their low populations or short lifetimes. Future applications of DynaRNA will range from contributing to current molecular dynamics simulations, RNA-enhanced sampling, interpreting RNA experiments, RNA-targeted drug binding site identification, and RNA-protein binding mechanisms. These capabilities make DynaRNA a powerful tool for paving the way for future advancements in RNA-targeted drug discovery and RNA therapy development, such as mRNA vaccine design. Last but not least, DynaRNA breaks through the static structure prediction paradigm exemplified by AlphaFold3, pioneering the generative modeling of RNA dynamic ensembles—a framework that inherently aligns with RNA’s flexible nature, where biological functions emerge from continuous conformational transitions. By bridging RNA structure and dynamics, DynaRNA offers a scalable foundation for decoding the full complexity of RNA’s dynamic universe.

Materials and methods

Dataset

DynaRNA was trained on high-quality RNA PDB crystal structures. We extracted 14,632 experimentally determined 3D RNA structures from the RNAsolo database43. The training dataset was curated by removing entries that included non-RNA elements (e.g., DNAs and proteins), non-standard RNA elements (modified bases), or incomplete nucleotides. Structures containing 5–200 nucleotides were retained, producing 6,820 curated structures as the final training dataset. For the test dataset, MD trajectories of five tetranucleotides were derived from previous REST2 simulations10,11, which were extensively sampled starting from both the experimental A-form conformations and the intercalated conformations. MD trajectories of U40 were derived from DE Shaw’s research26.

Model

DynaRNA takes a single RNA structure as input, and does not rely on sequence features like MSA. Each nucleotide is coarse-grained into one particle located at the C4’ atom, providing a minimal yet informative encoding of the RNA backbone geometry. The resulting representations are subsequently integrated into downstream modeling pipelines to facilitate structural learning. DDPM44 is utilized in RNA conformation generation, which can be partitioned into a forward noising process and a symmetric backward denoising process. Both processes are defined on a discrete time space. The forward process gradually perturbs the original data with Gaussian noise, which is define by the following Itâ stochastic differential equation (SDE):

$${x}_{t}=\sqrt{1-{\beta }_{t}}\cdot {x}_{t-1}+\sqrt{{\beta }_{t}}\cdot {{\epsilon }}_{t}$$
(1)
$${\beta }_{t}={\beta }_{0}+\frac{t}{T-1}\cdot ({\beta }_{T}-{\beta }_{0}),t=0,1,\ldots ,T-1$$
(2)

where xt represents the noised data at the t-th step, βt represents the noise level at step t which is defined by Eq. (2), β0 is set as 0.0001, βT is set as 0.02, \({\epsilon }_{t}{{\mathscr{\sim }}}{{\mathscr{N}}}\left(0,I\right)\) is Gaussian noise.

To reverse the noising process and recover original structures, we train an EGNN45 to predict the noise \({\epsilon }_{\theta }\left({x}_{t},t\right)\) given data xt at the time step t. The EGNN architecture is specifically designed to respect geometric symmetries such as translation and rotation equivariance, making it highly suitable for molecular or geometric data. Each layer of EGNN incorporates both node and edge updates to capture intricate geometric relationships among nucleotides. The node features consist of the 3D positions of C4’ atoms along with time-step embeddings, while edge features encode both the molecular connectivity and spatial distances. We used a hidden dimension of 128 across all layers, with LayerNorm and SiLU activation functions to enhance training stability and non-linearity. Temporal information is encoded using sinusoidal embeddings, following the standard approach in diffusion models. To reduce overfitting, dropout with a rate of 0.1 is applied after each EGNN layer. The final output of the network predicts the noise vector added at each time step, conditioned on both geometry and graph topology. During inference, the reverse (denoising) process is approximated by integrating the following formulation:

$${\hat{x}}_{t-1}=\frac{1}{\sqrt{{\alpha }_{t}}}\left({x}_{t}-\frac{1-{\alpha }_{t}}{\sqrt{1-{\bar{\alpha }}_{t}}} \, {\cdot } \, {\epsilon }_{\theta }\left({x}_{t},t\right)\right)+z \, {\cdot } \, \sqrt{{\beta }_{t}}$$
(3)

where \({\hat{x}}_{t-1}\) represents predicted data at the previous timestep t − 1, αt = 1 − βt represents the signal retention rate, \({\bar{\alpha }}_{t}={\prod }_{s=1}^{t}{\alpha }_{s}\) represents the cumulative signal retention, \({\epsilon }_{\theta }\left({x}_{t},t\right)\) represents the noise predicted by EGNN, \(z\sim {{\mathscr{N}}}(0,I)\) represents, the fresh Gaussian noise used during sampling.

In DDPM framework pursues a distinct training objective compared to other neural networks. Instead of directly fitting RNA coordinates, the network is designed to estimate noise in the perturbed data. We utilized L2 loss on noise defined as follows:

$$L={{\mathbb{E}}}_{{x}_{0},{\epsilon },t}[{\Vert {\epsilon }-{{\epsilon }}_{\theta }({x}_{t},t)\Vert }^{2}]$$
(4)

where \(\epsilon\) represents the real noise, \({\epsilon }_{\theta }\left({x}_{t},t\right)\) represents the noise predicted \({\epsilon }_{\theta }\left({x}_{t},t\right)\) given data xt at the time step t. \({{\mathbb{E}}}_{{x}_{0},\epsilon ,t}\) is used to calculate the mean square error (MSE) between them.

Training

DynaRNA was implemented utilizing PyTorch and PyTorch-Lightning. All training processes were conducted on one NVIDIA 4090D GPU, taking approximately 14 days. The Model parameters were optimized with the Adam optimizer46, using a learning rate of 0.0001. To prevent gradient explosion and maintain numerical stability, gradient clipping with a maximum norm of 1.0 is applied. A weight decay of 1e-4 serves as a regularization mechanism to mitigate overfitting. Training procedure loss was shown in Supplementary Fig. 7.

Statistics and reproducibility

We generated 1000 RNA conformations for each system of tetranucleotides, tetraloops, and HIV TAR states, and calculated structural features for analysis. The random number of the generation was provided in the model for reproducibility.

Analysis

DSSR47 software was used for RNA structure analysis. Arena48 was used for converting the RNA coarse-grained model to an all-atom structure. Pymol was used for visualization and alignment. Intercalation conformation was defined with nucleotide j positioned between nucleotides i and i + 1 and forms stacking interactions with them, where j < i or j > i + 1. The DBSCAN algorithm was used for clustering based on the RMSD of all heavy atoms, where epsilon was set as 1.2 and the minimum number was set as 10. GS and ES2 conformations were obtained from the PDB(8U3M). Initial structures of de novo folding tetraloop were constructed with the NAB module, producing fully extended single-stranded conformations devoid of base pairing. Experimental structures from the PDB (2KOC and 8CLR) served as reference models for tetraloops.

Reporting summary

Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.