A structure-driven sequence design method for RNA inverse folding task

Abstract

The application belongs to the technical field of RNA reverse folding, and relates to a structure-driven sequence design method for an RNA reverse folding task. A low-frequency modal data enhancement method is used to enhance and correct RNA structure data to obtain structure samples. Feature maps are constructed by extracting backbone atom coordinates in the structure samples. Features extracted from each node and edge are divided into scalar and vector features, and the vector features are mapped to a local coordinate system. Meanwhile, scalar and vector features are fused through GVP-GNN, the fused features are embedded in hyperbolic space, a learnable curvature parameter is introduced in each layer of the hyperbolic message passing network, and local and global structures are adaptively modeled. After hyperbolic space message passing, feature fusion and hyperbolic-Euclidean mapping conversion, the RNA prediction sequence is input into a Transformer decoder to generate the RNA prediction sequence. The problems of insufficient structural diversity, limited feature representation and insufficient geometric modeling capability in RNA reverse folding are solved.

Description

Technical Field

[0001] This invention belongs to the field of RNA reverse folding technology, specifically relating to a structure-driven sequence design method for RNA reverse folding tasks. Background Technology

[0002] RNA inverse folding, the design of RNA sequences that fold into a given three-dimensional structure, is a core issue in RNA structure design, functional RNA construction, and RNA drug design. Inverse folding technology allows for the automatic generation of RNA sequences with the desired folding and functional characteristics from a target spatial structure, thereby significantly improving the efficiency of RNA engineering and synthetic biology.

[0003] Traditional RNA backfolding methods are primarily based on energy minimization and heuristic search, such as algorithms like RNAinverse, RNA-SSD, and INFO-RNA. These methods rely on secondary structure energy models (e.g., the Turner energy parameter set) to iteratively optimize sequences to match the target secondary structure. However, these methods can only handle relatively short RNA molecules, have limited consideration for three-dimensional spatial structural constraints, and struggle to guarantee the stability and biological functional consistency of the generated sequences at the three-dimensional structural level. With the accumulation of RNA three-dimensional structure databases (such as PDB and RNAcentral) and the development of deep learning technology, a series of deep learning RNA backfolding models based on three-dimensional structural constraints have emerged in recent years. Examples include R3Design, gRNAde, RhoDesign, RiboDiffusion, and RIDiffusion.

[0004] Existing RNA reverse folding methods are mainly divided into two categories: physical principle-based search and optimization methods and data-driven deep learning methods. The former relies on thermodynamic models and heuristic search, which is suitable for short sequences but has limited efficiency in long sequences and complex tertiary structure scenarios; the latter can learn the high-dimensional structure-sequence relationships implicit in the data, but still has shortcomings in three-dimensional modeling and structural fidelity control.

[0005] While R3Design uses 3D coordinate input, it only represents local geometric relationships through a standard graph neural network, failing to achieve true geometric equivariance. Therefore, the model struggles to guarantee rotation and translation invariance, resulting in unstable performance of the same structure in different coordinate systems. RhoDesign, while using predicted RNA 3D coordinates as input, relies solely on simplified distance and orientation features, lacking complete all-atom geometric modeling and SE(3) equivariance. Consequently, it remains significantly inadequate in capturing the high-order 3D topology and physical constraints of real RNA. Although RiboDiffusion and RIDiffusion use diffusion models, their structural conditions are largely based on low-dimensional embedding features or distance matrices, failing to fully express the spatial orientation information of RNA. This leads to weak constraints on the 3D folding conformation of the generated sequences, potentially resulting in locally correct but globally foldable sequences.

[0006] Insufficient data augmentation and modal registration are problems; most current methods directly use single 3D structural samples for training. The lack of low-frequency modal augmentation or conformational sampling mechanisms makes it difficult for models to learn the influence of structural flexibility on sequence folding. The sequences generated by these models are often sensitive to folding perturbations in experiments and cannot stably form the target structure. The scale of structural data is also limited; RNA 3D structural data is far less than protein structural data, with fewer than 4000 high-quality RNA structures currently available in the PDB. Summary of the Invention

[0007] The purpose of this invention is to overcome the shortcomings of existing technologies and provide a structure-driven sequence design method for RNA reverse folding tasks, mainly solving three problems:

[0008] First, there is the issue of the dataset. Most current methods directly use a single three-dimensional structure sample for training. However, there is a natural many-to-many relationship between the three-dimensional structure of RNA and the one-dimensional sequence. This invention uses low-frequency modes of elastic network models (ENMs) to augment the data. Low-frequency modes can simulate biologically reasonable flexible movements. The most likely deformations that molecules will undergo and the lowest energy cost are selected. While expanding the dataset, the model can fully learn the structural information corresponding to the sequence.

[0009] This invention improves upon the feature extraction process. Traditional neural networks typically assume that data is embedded in Euclidean space, but RNA biomolecules have non-Euclidean geometric features. Furthermore, traditional hyperbolic GNNs usually assume a fixed curvature (typically -1), which is often not optimal for different data types or different feature levels. This invention proposes Adaptive Curvature Hyperbolic Neural Networks, which allow the model to learn the most suitable curvature during training. Adaptive curvature parameters can be assigned to different layers, nodes, or dimensions, enabling the network to automatically adjust its geometric shape.

[0010] Regarding data processing, most existing models neglect the problems caused by RNA structure rotation and translation. Previous models often yielded different predictions for the same structure after rotation and translation, which is clearly unreasonable. This invention proposes a solution to address rotation and translation by establishing a local coordinate system and projecting vector features into it, thus resolving the changes in vector features caused by rotation and translation. By using GVP-GNN (Geometric VectorPerceptron Graph Neural Network) to fuse scalar and vector features, the model can encode both topological properties (through scalars) and capture geometric orientation information (through vectors), maintaining physical consistency under rotation or translation operations.

[0011] To achieve the objectives of this invention, the following technical solutions are adopted.

[0012] A structure-driven sequence design method for RNA reverse folding tasks includes the following steps:

[0013] S1. While maintaining the geometric constraints and key pairing relationships of the nucleotide backbone, the low-frequency modal data augmentation method is used to enhance and correct the RNA three-dimensional structure data to obtain stable RNA three-dimensional structure samples, thereby expanding the RNA three-dimensional structure data. Furthermore, by training the RNA backfolding model, the RNA backfolding model learns the stability of sequence-structure mapping under small conformational perturbations.

[0014] S2. Extract the RNA backbone atomic coordinates from stable RNA 3D structure samples, construct feature maps of nodes and edges, divide the extracted features into scalar features and vector features, and map the vector features to a local coordinate system to achieve invariance to rotation and translation of the RNA 3D structure; simultaneously, fuse the extracted scalar features and vector features using GVP-GNN to obtain fused features; wherein: the local coordinate system is a rotation matrix constructed at each node through Gram-Schmidt orthogonalization; the features include distance, direction, angle, and quaternion features;

[0015] S3. Embed the fused features into the hyperbolic space and initialize the curvature and define the message passing operator. Introduce learnable curvature parameters in each layer of the hyperbolic message passing network to adaptively model the local and global structures. After hyperbolic space message passing, feature fusion and hyperbolic-Euclidean mapping transformation, input the results into the Transformer decoder to generate the RNA prediction sequence.

[0016] Furthermore, the low-frequency modal data enhancement method includes the following specific steps:

[0017] S21. Data preparation: Download the structure files from the PDB website and the RNAsolo website, and extract the spatial atomic coordinates of the RNA backbone atoms from the structure files to construct conformational samples;

[0018] S22. Select the modal calculation method:

[0019] S221. If multiple conformational samples exist in the structure file, then the PCA method should be selected:

[0020] Assuming there are M conformational samples in an RNA molecule, we can perform eigenvalue decomposition by constructing a covariance matrix C:

[0021]

[0022] In the formula: , is the covariance matrix. This is an operation that unfolds a coordinate matrix into a one-dimensional vector by rows; This refers to the modal direction; This refers to the eigenvalues, which correspond to the modal variance. The low-frequency modes are the directions of the first K largest eigenvalues.

[0023] Sampling perturbation:

[0024] ,

[0025] In the formula: for The first K components, ; This refers to the sampling coefficients in these modal directions;

[0026] Adjust s until the average disturbance reaches the target RMSD by setting the target RMSD;

[0027] Output enhanced structure samples:

[0028] ;

[0029] S222. If there is only one conformational sample in the RNA molecule, then choose the ENM method:

[0030] Set contact cutoff distance By constructing the Hessian matrix H, we can perform eigenvalue decomposition by finding its solution.

[0031] ;

[0032] Where: Hessian matrix :

[0033] ;

[0034] Due to low-frequency characteristic values Corresponding to the system's flexibility direction, the first K modes are selected to generate the disturbance:

[0035] ;

[0036] In the formula: for The first K components, ; for The first K components, ;

[0037] Output enhancement structure:

[0038] ;

[0039] S23, Projection or Energy Minimization Correction

[0040] To ensure that the enhancement structure is chemically acceptable and to avoid generating unreasonable samples that could mislead model training, X′ is modified to a chemical conformation.

[0041] First, the preliminary reinforcement structure must be calculated. With the original structure The structural differences RMSD; based on the RMSD calculation results, the correction schemes are divided into:

[0042] When A < 1 angstrom, a linearized constraint projection method is used for correction:

[0043] Coordinates after initial perturbation By performing linearization constraint corrections, we obtain the closest perturbation that satisfies the first-order linear constraints. and corrected coordinates ;

[0044] Construct constraint equation C(·), and perform a first-order Taylor expansion of constraint function C(X)=0 at the conformational sample:

[0045] ;

[0046] If the conformation sample satisfies the constraint C(X)=0, then we hope that the corrected perturbation δ satisfies Jδ=0; writing all linear constraints as Aδ=0, the projection is to find the vector with the smallest distance from the original perturbation ΔX in the subspace that satisfies the linear equation, which is to solve the least squares problem:

[0047] ;

[0048] ;

[0049] Its analytical solution is:

[0050] ;

[0051] This solution is the perturbation that best satisfies the linearization constraints and is closest to the original perturbation, where A is the constraint matrix;

[0052] When A ≥ 1 angstrom, a nonlinear energy minimization correction method is used for correction:

[0053] When the perturbation is large or there are obvious nonlinear constraints, the linear approximation is insufficient to maintain chemical rationality. In this case, by establishing an energy function E(Y) that includes physicochemical terms, the energy is minimized under constraints only for the affected subset of atoms, so that the corrected conformation sample can both maintain the original perturbation direction as much as possible and satisfy the nonlinear chemical / structural constraints.

[0054] Formal objective:

[0055] ,in:

[0056] Penalty for key length: ;

[0057] To ensure fidelity, the control correction should not deviate from the original disturbance. The larger, the closer It's simply a difference in coordinate values; The penalty for key corners, ;

[0058] This is a penalty term for base pairs, calculated using a method analogous to the penalty term for bond length.

[0059] Furthermore, the process of obtaining the fusion features includes the following steps:

[0060] S31. Extract the atomic coordinates of the RNA molecule backbone from stable three-dimensional RNA structure samples, and construct the feature graph G=(V,E) of node V and edge E, where: node V represents nucleotide, and edge E represents spatial adjacency or chemical connection relationship.

[0061] S32. Extract features from each node and edge, divide the extracted features into scalar features and vector features, and map the vector features to the local coordinate system; at the same time, perform feature fusion on the extracted scalar features and vector features through GVP-GNN.

[0062] Furthermore, the method for constructing the local coordinate system is as follows: each base of RNA has not only a spatial location but also directional information; to ensure that the model can understand and maintain geometric equivariance, a local coordinate system is established for each node; the local coordinate system is defined as a rotation matrix. , where: each column vector These are unit orthogonal basis vectors, describing the orientation of the local coordinate system of a node in the global space. A local coordinate system is constructed using Gram-Schmidt orthogonalization. Initial vectors are defined, starting with two principal direction vectors. Gram-Schmidt orthogonalization of these vectors yields a set of three-dimensional orthogonal unit bases.

[0063]

[0064] Where: each column is a 3-dimensional unit vector, therefore This is the local coordinate system.

[0065] Furthermore, the process of generating the predicted RNA sequence includes the following steps:

[0066] S51, Hyperbolic Embedding and Curvature Initialization

[0067] S511, Embedding fusion features into hyperbolic space ;

[0068]

[0069] in: It is an exponential mapping that maps Euclidean vectors to the origin neighborhood of a hyperbolic manifold;

[0070] S512. The initial curvature parameter c is obtained through network self-learning or estimation via the nucleotide density function; the geometry of the hyperbolic space is controlled by the curvature parameter c > 0, and the hyperbolic distance is:

[0071]

[0072] S513. Define message-passing operators on hyperbolic manifolds to maintain geometric consistency;

[0073] S52, Adaptive Curvature Adjustment Mechanism

[0074] Introduce learnable curvature parameters for each layer of the hyperbolic message passing network. ;

[0075]

[0076] in: For the hidden features of the l-th layer nodes, f(·) is a non-linear mapping to ensure positive curvature; σ is the activation function: ReLU function; when When the manifold is large, the manifold bends dramatically, indicating that the layer is focused on local structures; when When the manifold is small, it is nearly flat, which is suitable for modeling long-range interactions;

[0077] This mechanism model can adaptively adjust the geometric curvature in different layers and local regions of different nodes, thereby achieving adaptive modeling of local and global structural complexity.

[0078] S53, Hyperbolic Message Passing and Feature Fusion

[0079] S531. Perform message passing in hyperbolic space:

[0080]

[0081] in: For Möbius method, For the curvature is Möbius matrix multiplication under the following conditions Attention weights;

[0082] S532. In each layer, node updates are performed using the Möbius stripe and hyperbolic transformation:

[0083]

[0084] Use hyperbolic transformations to maintain the geometric consistency of the manifold;

[0085] S533, Finally, the multi-layer outputs are fused in a hyperbolic-Euclidean mapping layer;

[0086] The hyperbolic features are mapped back to Euclidean space via a logarithmic mapping:

[0087]

[0088] S54, Sequence Generation and Decoding

[0089] The obtained structural representation is input into the conditional decoder module, the Transformer model decoder:

[0090]

[0091] Through conditional probability distribution RNA sequences are generated, and finally, predicted sequences are obtained. .

[0092] Beneficial effects: This invention addresses the problems of insufficient structural diversity, limited feature representation, and insufficient geometric modeling ability in RNA reverse folding tasks by proposing a method that integrates low-frequency modality data augmentation, adaptive hyperbolic neural networks, and local coordinate system geometric invariance modeling.

[0093] This invention achieves significant improvements in data processing speed, model accuracy, generalization ability, structure preservation, and computational stability through comprehensive improvements in the data layer, feature layer, and geometric learning layer.

[0094] This invention can generate multiple structural samples while maintaining the topological structure and chemical constraints of RNA molecules. Compared with traditional modeling methods that rely on only a single static structure, the training set size is increased by an average of 3–5 times, and the data coverage is more comprehensive. The data distribution is more balanced. After using low-frequency modality augmentation, the training data includes the natural conformational fluctuations of RNA, avoiding overfitting of the model to a certain conformation, thereby obtaining better generalization performance on the test set.

[0095] Geometric consistency and coordinate independence are achieved by extracting features from each node and edge, dividing these features into scalar and vector features, and mapping the vector features to a local coordinate system. Simultaneously, GVP-GNN is used to fuse the extracted scalar and vector features. This ensures that the model produces consistent outputs from RNA structure inputs in different coordinate systems, overcoming the dependence on input coordinates inherent in traditional methods.

[0096] This invention embeds the topology of RNA molecules into hyperbolic space for information transmission. Each layer adaptively learns the curvature parameter c, enabling the model to automatically adjust the spatial curvature for different hierarchical structures (local stacking, secondary loops, tertiary interactions).

[0097] Information aggregation is more efficient, and geodesic distances in hyperbolic space can express complex structural hierarchical relationships with fewer dimensions. Compared with Euclidean GNNs of the same scale, this invention improves information fidelity with the same number of parameters. Attached Figure Description

[0098] Figure 1 Here is a flowchart of the method.

[0099] Figure 2 Flowchart for low-frequency modal data augmentation;

[0100] Figure 3 This is a diagram of the RNA structure.

[0101] Figure 4 Flowchart for RNA structural feature extraction;

[0102] Figure 5 This is a flowchart of the adaptive hyperbolic neural network module. Detailed Implementation

[0103] The present invention will be further described in conjunction with the embodiments and accompanying drawings.

[0104] The flowchart of the HyperRdesign software proposed in this invention is as follows: Figure 1 As shown, we first downloaded datasets from RDB and RNAsolo websites, and then augmented the data using low-frequency modalities to expand the originally limited dataset. In the feature extraction part, each nucleotide was treated as a node, and the nearest nucleotides to each nucleotide were treated as edges, resulting in a graph. Distance, direction, angle, and dihedral angle were used to represent nodes and edges. Local coordinates were established, and a GVP-GNN network was used to process the features of nodes and edges to ensure their rotation and translation invariance. Finally, we used an adaptive curvature hyperbolic neural network to extract features to overcome the limitations of Euclidean space.

[0105] I. Enhancing RNA 3D Structure Data with Low-Frequency Modal Analysis

[0106] To improve the robustness of inverse folding models to structural flexibility and measurement noise, this invention proposes an enhancement method based on low-frequency modes of the structure. This method, while maintaining the geometric constraints of the nucleotide backbone and key pairing relationships, generates a set of structural samples (conformation enhancement sets) that are globally similar to the original structure but have microscopic differences by applying physical displacements in the low-frequency mode subspace of the structure. These enhancement samples are used for training / data augmentation, enabling the model to learn the stability of sequence-structure mapping under small conformational perturbations, thereby improving generalization ability and the folding robustness of the generated sequences. Specific steps (e.g.) Figure 2 (as shown)

[0107] Step 1: Data Preparation

[0108] Available conformations were collected, and structural files were downloaded from the PDB and RNAsolo websites. The spatial atomic coordinates of the RNA backbone atoms were extracted from these files. This invention extracts the P, O5′, C5′, C4′, C3′, and O3′ atomic coordinates for each base. Note that some files contain multiple RNA conformations, while others can only extract one.

[0109] Step 2: Select Modal Calculation Method

[0110] For samples containing multiple conformations, we use the PCA method; for samples containing only one conformation, we use the ENM (Elastic Network Model) method.

[0111] If multiple conformational samples exist, then PCA is used:

[0112] Suppose that a certain RNA molecule has a total of M observed conformations;

[0113] Construct the covariance matrix C and perform eigenvalue decomposition:

[0114] ;

[0115] Sampling perturbation:

[0116] ;

[0117] During the data augmentation phase, set a target RMSD (e.g., 1.5 Å) and adjust s until the average perturbation reaches that RMSD;

[0118] Output enhancement structure:

[0119] ;

[0120] If only a single conformation exists, then use ENM (Elastic Network Model).

[0121] When we have only one reference structure and cannot statistically calculate the covariance of multiple samples, we use a physical model to approximate the flexibility of the molecule. The idea behind ENM is to treat RNA atoms as "point masses," connecting adjacent atoms or those within a threshold distance with springs, and obtaining the system's natural vibrational modes through the second derivative matrix (Hessian matrix) of the potential energy. We set the contact cutoff distance... (7-10 Amy).

[0122] Construct the Hessian matrix H and find its eigenvalue decomposition:

[0123] ;

[0124] Due to low-frequency characteristic values ​​( For the corresponding system flexibility direction, the disturbance can be generated by selecting the first K modes:

[0125] ;

[0126] Output enhancement structure:

[0127] ;

[0128] Step 3: Geometric and chemical constraint correction (projection or energy minimization)

[0129] To ensure that the enhanced structure is chemically acceptable (bond lengths are not disrupted and base pairing relationships are not arbitrarily broken) and to avoid generating unreasonable samples that could mislead model training, X′ is modified to a chemically reasonable conformation.

[0130] First, the preliminary reinforcement structure must be calculated. With the original structure The structural differences are analyzed using the RMSD (Restricted Energy Minimum Structural Difference). Based on the RMSD calculation results, our correction scheme is divided into two types: when A < 1 Å, we use the linearized constrained projection method, and when A ≥ 1 Å, we use the nonlinear energy minimization correction method.

[0131] (1) Linearized constrained projection

[0132] Coordinates after initial perturbation By performing linearization constraint corrections, we obtain the closest perturbation that satisfies the first-order linear constraints. and corrected coordinates The main atoms extracted in this invention are P, O5′, C5′, C4′, C3′, and O3′ (e.g., ...). Figure 3 (The atoms are labeled sequentially by the orange-yellow dots). In RNA, it is generally desirable to maintain the following characteristics after perturbation (low-frequency mode deformation):

[0133] Covalent bond length (the bonds between the main chain and the internal sugar ring cannot be broken);

[0134] Base pairing distance (Watson–Crick pairing cannot deviate significantly);

[0135] Planar and angular constraints (base planes maintain planarity, sugar ring angles are constrained);

[0136] Local continuity (the phosphate backbone is connected continuously, and the O3'-P-O5' structure is not disordered);

[0137] By constructing the constraint equation C(·), a first-order Taylor expansion of the constraint function C(X)=0 is performed at the reference configuration:

[0138] ;

[0139] If the reference conformation satisfies the constraint C(X) = 0, then we hope the corrected perturbation δ satisfies Jδ = 0. Representing all linear constraints as Aδ = 0, the projection involves finding the vector with the smallest distance to the original perturbation ΔX in the subspace satisfying these linear equations, which is essentially solving the least squares problem.

[0140] ;

[0141] ;

[0142] Its analytical solution is:

[0143] ;

[0144] This solution is the perturbation that best satisfies the linearization constraints and is closest to the original perturbation, where A is the constraint matrix.

[0145] (2) Nonlinear energy minimum constraint method

[0146] When the perturbation is large or there are obvious nonlinear constraints (bond length, directionality of base pairing), linear approximation is insufficient to maintain chemical rationality. In this case, by establishing an energy function E(Y) that includes physicochemical terms, constrained energy minimization is performed locally (only for the affected subset of atoms), so that the modified conformation can both maintain the original perturbation direction as much as possible and satisfy the nonlinear chemical / structural constraints.

[0147] Formal objective:

[0148] in:

[0149] The penalty term for bond length (usually a second-order or higher-order potential energy). ; To ensure fidelity, the correction should be controlled to avoid deviating too much from the original perturbation. The larger, the closer It's simply a difference in coordinate values; The penalty for key corners,

[0150] ; This is a penalty term for base pairs, calculated using a method analogous to the penalty term for bond length.

[0151] II. Feature Extraction

[0152] To reduce the computational complexity of subsequent models, feature information is extracted from the three-dimensional space of RNA. This part mainly involves constructing a feature map of nodes and edges based on the spatial atomic coordinates of the RNA backbone atoms.

[0153] The process includes the following steps:

[0154] 1. Extract the atomic coordinates of the RNA backbone and establish a feature graph of edges and nodes G=(V,E), where node V represents nucleotides and edge E represents spatial adjacency or chemical connection.

[0155] 2. Extract physicochemical features for each node and edge, and map the vector features to the local coordinate system to ensure the invariance of overall rotation and translation. The features are divided into two categories: scalar and vector. Here, we mainly extract distance, vector, angle, dihedral angle, and quaternion features.

[0156] Each base in RNA has not only a spatial location (position vector) It also possesses directional information (i.e., the orientation of bases in three-dimensional space). To ensure the model can understand and maintain geometric equivariance, a local coordinate system is established at each node. This local coordinate system is defined as a rotation matrix. , where: each column vector These are unit orthogonal basis vectors, describing the orientation of the local coordinate system of a node in the global space. A local coordinate system is constructed using Gram-Schmidt orthogonalization. Initial vectors are defined, starting with two principal direction vectors. Gram-Schmidt orthogonalization of these vectors yields a set of three-dimensional orthogonal unit basis vectors.

[0157] ;

[0158] Where: each column is a 3-dimensional unit vector, therefore This refers to the local coordinate system. Projecting the vector features of the current node onto the current local coordinate system solves the problems caused by the rotation and translation of the overall structure.

[0159] III. Hyperbolic Neural Network with Adaptive Curvature

[0160] The biological functions of RNA are highly dependent on its complex three-dimensional spatial structure. However, due to the non-Euclidean characteristics of RNA structural space (such as hierarchical dependence of secondary structures, multi-scale nesting of tertiary structures, and long-range pairing interactions), traditional Euclidean spatial neural networks (such as GCN, GAT, or E(3)-isovariant networks) suffer from insufficient accuracy and difficulty in convergence when capturing RNA geometric relationships.

[0161] In recent years, hyperbolic geometric spaces have shown potential in biological structure learning due to their natural suitability for modeling hierarchical and exponentially growing structural relationships. However, existing hyperbolic neural networks typically have fixed curvature parameters, which cannot adapt to the geometric differences in local substructures of different RNAs, resulting in limited expressive power in complex RNA topologies.

[0162] Therefore, we propose an adaptive curvature hyperbolic neural network that can dynamically adjust the geometric curvature according to the local complexity of RNA structure in order to better capture structural relationships at different scales and levels, thereby improving the performance of RNA reverse folding tasks.

[0163] Step 1: Hyperbolic embedding and curvature initialization

[0164] 1. Embed node and edge features into hyperbolic space ;

[0165] ;

[0166] in It is an exponential mapping that maps Euclidean vectors to the origin neighborhood of a hyperbolic manifold.

[0167] 2. The initial curvature parameter c is obtained through network self-learning or estimation via the nucleotide density function; the geometry of the hyperbolic space is controlled by the curvature parameter c > 0, and the hyperbolic distance is:

[0168] ;

[0169] 3. Define message-passing operators on hyperbolic manifolds to maintain geometric consistency.

[0170] Step 2: Adaptive Curvature Adjustment Mechanism (Core Innovation)

[0171] Introduce learnable curvature parameters for each layer of the hyperbolic message passing network. ;

[0172] ;

[0173] in: Let f(·) be the hidden feature for the l-th layer node, where f(·) is a non-linear mapping (such as softplus) to ensure positive curvature; σ is the ReLU function used as the activation function. When the manifold is large, the manifold bends dramatically, indicating that the layer is focused on local structures (e.g., base stacking regions); when When the size is small, the manifold is nearly flat, which is suitable for modeling long-range interactions (such as loop regions or bulge regions).

[0174] Through this mechanism, the model can adaptively adjust the geometric curvature in different layers and local regions of different nodes, thereby achieving adaptive modeling of local and global structural complexity.

[0175] Step 3: Hyperbolic Message Passing and Feature Fusion

[0176] 1. Perform message passing in hyperbolic space:

[0177] ;

[0178] in: For Möbius method, For the curvature is Möbius matrix multiplication under the following conditions Attention weights;

[0179] 2. In each layer, nodes are updated using the Möbius stripe and hyperbolic transformation:

[0180] ;

[0181] Use hyperbolic transformations to maintain the geometric consistency of the manifold.

[0182] 3. Finally, the multi-layer outputs are fused in a hyperbolic-Euclidean map layer (Exponential / Logarithmic map).

[0183] Mapping hyperbolic features back to Euclidean space using a logarithmic mapping:

[0184] ;

[0185] Step 4: Sequence Generation and Decoding

[0186] The obtained structural representation is input into the conditional decoder module, the Transformer model decoder:

[0187] ;

[0188] Through conditional probability distribution RNA sequences are generated, and finally, predicted sequences are obtained. .

[0189] This invention proposes a structure-driven sequence design method for RNA reverse folding tasks. Its core innovations include three aspects: low-frequency modality data augmentation, adaptive hyperbolic neural network structure design, and rotation- and translation-invariant geometric feature extraction. These modules work synergistically, enabling the model to effectively generate stable and functionally correct RNA sequences under complex three-dimensional RNA structural conditions.

[0190] (a) Low-frequency mode-driven data augmentation

[0191] The three-dimensional structure of RNA typically exhibits multi-scale geometric changes, with low-frequency modes describing the smooth deformation of the overall conformational changes. Traditional modeling uses only a single static structure and cannot reflect the flexible characteristics of RNA molecules.

[0192] To this end, the present invention introduces a structural perturbation generation mechanism based on low-frequency modes in the data augmentation stage. This augmentation method preserves the topological consistency and functionally relevant deformation of RNA while ensuring chemical rationality, making the model more robust and generalizable during the training stage.

[0193] (II) Hierarchical geometric modeling of adaptive hyperbolic neural networks

[0194] The spatial structure of RNA exhibits strong hierarchical and non-Euclidean characteristics, making simple Euclidean embeddings insufficient to accurately represent its multi-level folding relationships. To address this, this invention proposes an Adaptive Hyperbolic GNN, which performs information transfer and geometric embedding learning in hyperbolic space. Each layer adaptively learns the curvature parameter c, enabling the model to automatically adjust the spatial curvature for different hierarchical structures (local stacking, secondary loops, tertiary interactions).

[0195] 1. Hyperbolic embedding representation, embedding for each node Project it onto hyperbolic space :

[0196] 2. In each layer, nodes are updated using the Möbius stripe and hyperbolic transformation:

[0197] 3. Introduce learnable curvature parameters to each layer of the hyperbolic message passing network. ;

[0198] (III) Extraction of rotation- and translation-invariant geometric features

[0199] Some graph neural networks, such as GVP-GNN, only possess rotation-translation invariance, which is insufficient for our needs. This invention addresses this by modifying the feature extraction process. In feature extraction, we distinguish between scalar and vector features. Scalar features are inherently rotation-translation invariant, while vector features change with rotation and translation. This invention processes the vector features by using the spatial coordinates of the three atoms (P, O5′, C5′) of each nucleotide to obtain two linearly independent vectors. A local coordinate system Ei is then obtained through Gram-Schmidt orthogonalization. All vector features in the current nucleotide are projected onto this local coordinate system Ei to ensure overall rotation-translation invariance.

[0200] Table 1 Comparison of Method Effects

[0201] gRNAde 33.78 28.25 GVP-GNN 33.88 39.81 Grap Trans 38.89 37.48 PiFold 37.54 38.83 SructGNN 41.95 41.11 R3Design 43.27 45.41 RIdiffusion 45.80 45.71 HyperR Design 65.76 86.29

[0202] Experiments show that this mechanism improves the model in both sequence recovery rate and F1 score. Compared with R3Design and RIDiffusion, this invention improves the sequence recovery rate by 22.49% and 19.96%, and the F1 score by 40.88 and 40.58, respectively, with the sequence recovery rate and F1 score reaching 65.76% and 86.29, respectively.

[0203] In summary, this invention achieves substantial breakthroughs in three aspects: structural enhancement, multi-scale geometric modeling, and efficient feature expression. Compared with existing RNA reverse folding techniques, this invention not only significantly improves sequence prediction accuracy but also offers clear advantages in data efficiency, model stability, and computational cost. Therefore, this invention can provide a new, high-precision, and high-efficiency structure-driven design solution for RNA design, functional ribosome construction, and RNA drug development.

[0204] The preferred embodiments of the present application have been described above with reference to the accompanying drawings, but this does not limit the scope of the claims of the present application. Any modifications, equivalent substitutions, and improvements made by those skilled in the art without departing from the scope and substance of the embodiments of the present application shall be within the scope of the claims of the present application.

Claims

1. A structure-driven sequence design method for RNA backfolding tasks, characterized in that: Includes the following steps: S1. While maintaining the geometric constraints and key pairing relationships of the nucleotide backbone, the low-frequency modal data augmentation method is used to enhance and correct the RNA three-dimensional structure data to obtain stable RNA three-dimensional structure samples, thereby expanding the RNA three-dimensional structure data. Furthermore, by training the RNA backfolding model, the RNA backfolding model learns the stability of sequence-structure mapping under small conformational perturbations. S2. Extract RNA backbone atomic coordinates from stable RNA 3D structure samples, construct feature maps of nodes and edges, extract features from each node and edge, divide the extracted features into scalar features and vector features, and map the vector features to a local coordinate system; simultaneously, fuse the extracted scalar features and vector features using GVP-GNN to obtain fused features; wherein: the local coordinate system is a rotation matrix constructed at each node through Gram-Schmidt orthogonalization; the features include distance, direction, angle, and quaternion features; S3. Embed the fused features into hyperbolic space and initialize the curvature and define the message passing operator. Introduce learnable curvature parameters in each layer of the hyperbolic message passing network to adaptively model the local and global structures. After hyperbolic space message passing, feature fusion and hyperbolic-Euclidean mapping transformation, input the results into the Transformer decoder to generate the RNA prediction sequence. The process of generating the predicted RNA sequence includes the following steps: S51, Hyperbolic Embedding and Curvature Initialization S511, Embedding fusion features into hyperbolic space ; ； in: It is an exponential mapping that maps Euclidean vectors to the origin neighborhood of a hyperbolic manifold; S512. The initial curvature parameter c is obtained through network self-learning or estimation via the nucleotide density function; the geometry of the hyperbolic space is controlled by the curvature parameter c > 0, and the hyperbolic distance is: ； S513. Define message-passing operators on hyperbolic manifolds to maintain geometric consistency; S52, Adaptive Curvature Adjustment Mechanism Introduce learnable curvature parameters for each layer of the hyperbolic message passing network. ; ； in: For the hidden features of the l-th layer nodes, f(·) is a non-linear mapping to ensure positive curvature; σ is the activation function: ReLU function; when When the manifold is large, the manifold bends dramatically, indicating that the layer is focused on local structures; when When the manifold is small, it is nearly flat, which is suitable for modeling long-range interactions; The model using this mechanism can adaptively adjust the geometric curvature in different layers and local regions of different nodes, thereby achieving adaptive modeling of local and global structural complexity. S53, Hyperbolic Message Passing and Feature Fusion S531. Perform message passing in hyperbolic space: ； in: For Möbius method, For the curvature is Möbius matrix multiplication under the following conditions Attention weights; S532. In each layer, node updates are performed using the Möbius stripe and hyperbolic transformation: ； Use hyperbolic transformations to maintain the geometric consistency of the manifold; S533, Finally, the multi-layer outputs are fused in a hyperbolic-Euclidean mapping layer; The hyperbolic features are mapped back to Euclidean space via a logarithmic mapping: ； S54, Sequence Generation and Decoding The obtained structural representation is input into the conditional decoder module, the Transformer model decoder: ； Through conditional probability distribution RNA sequences are generated, and finally, predicted sequences are obtained. .

2. The structure-driven sequence design method for RNA reverse folding tasks according to claim 1, characterized in that: The low-frequency modal data enhancement method includes the following specific steps: S21. Data preparation: Download the structure files from the PDB and RNAsolo websites, and extract the spatial atomic coordinates of the RNA backbone atoms from the structure files to construct conformational samples; S22. Select the modal calculation method: S221. If multiple conformational samples exist in the structure file, then the PCA method should be selected: Assuming there are M conformational samples in an RNA molecule, eigenvalue decomposition is performed using the constructed covariance matrix C: ； In the formula: , The covariance matrix, This is an operation that unfolds a coordinate matrix into a one-dimensional vector by rows; This refers to the modal direction; This refers to the eigenvalues, which correspond to the modal variance. The low-frequency modes are the directions of the first K largest eigenvalues. Sampling perturbation: ； In the formula: This is a low-frequency mode basis, where each column represents a mode direction, indicating that the top K dominant low-frequency modes are selected to form a low-dimensional subspace. ; It refers to the sampling coefficients in the modal direction, indicating how far it travels; This refers to the perturbation of atomic coordinates; K is the number of low-frequency modes, which determines the degrees of freedom for sampling and reconstructing disturbances in the modal space; Is The eigenvalues ​​obtained from this calculation refer to the variance. Adjust s until the average disturbance reaches the target RMSD by setting the target RMSD; Output enhanced structure samples: ； S222. If there is only one conformational sample in the RNA molecule, then choose the ENM method: Set contact cutoff distance By constructing the Hessian matrix H, its solution is obtained for eigenvalue decomposition. ； Due to low-frequency characteristic values Corresponding to the system's flexibility direction, the first K modes are selected to generate the disturbance: ； In the formula: for The first K components, ; for The first K components, ; Output enhancement structure: ； S23, Projection or Energy Minimization Correction To ensure the enhancement structure is chemically acceptable and to avoid generating unreasonable samples that could mislead model training, X′ is modified to a chemical conformation here. First, the preliminary reinforcement structure must be calculated. With the original structure The structural differences RMSD; based on the RMSD calculation results, the correction schemes are divided into: When A < 1 angstrom, a linearized constraint projection method is used for correction: Coordinates after initial perturbation By performing linearization constraint corrections, we obtain the closest perturbation that satisfies the first-order linear constraints. and corrected coordinates ; Construct constraint equation C(·), and perform a first-order Taylor expansion of constraint function C(X)=0 at the conformational sample: ； If the conformation sample satisfies the constraint C(X)=0, then we hope that the corrected perturbation δ satisfies Jδ=0; writing all linear constraints as Aδ=0, the projection is to find the vector with the smallest distance from the original perturbation ΔX in the subspace that satisfies the linear equation, which is to solve the least squares problem: ； ； Its analytical solution is: ； This solution is the perturbation that best satisfies the linearization constraints and is closest to the original perturbation, where A is the constraint matrix; When A ≥ 1 angstrom, a nonlinear energy minimization correction method is used for correction: When the perturbation is large or there are obvious nonlinear constraints, the linear approximation is insufficient to maintain chemical rationality. In this case, by establishing an energy function E(Y) that includes physicochemical terms, the energy is minimized under constraints only for the affected subset of atoms, so that the corrected conformation sample can both maintain the original perturbation direction as much as possible and satisfy the nonlinear chemical / structural constraints. Formal objective: ,in: Penalty for key length: ; To ensure fidelity, the control correction should not deviate from the original disturbance. The larger, the closer It's simply a difference in coordinate values; This is a penalty for key corners. ; This is a penalty term for base pairs, calculated using a method analogous to the penalty term for bond length.

3. The structure-driven sequence design method for RNA reverse folding tasks according to claim 2, characterized in that: The process of obtaining the fusion feature includes the following steps: S31. Extract the atomic coordinates of the RNA molecule backbone from stable three-dimensional RNA structure samples, and construct the feature graph G=(V,E) of node V and edge E, where: node V represents nucleotide, and edge E represents spatial adjacency or chemical connection relationship. S32. Extract features from each node and edge, divide the extracted features into scalar features and vector features, and map the vector features to the local coordinate system to achieve the invariance of the three-dimensional structure of RNA rotation and translation; at the same time, fuse the extracted scalar features and vector features through GVP-GNN to obtain the fused features.

4. The structure-driven sequence design method for RNA reverse folding tasks according to claim 3, characterized in that: The method for constructing the local coordinate system: Each base in RNA has not only a spatial location but also directional information; to ensure the model can understand and maintain geometric equivariance, a local coordinate system is established for each node; the local coordinate system is defined as a rotation matrix. , where: each column vector These are unit orthogonal basis vectors, describing the orientation of the local coordinate system of a node in the global space. A local coordinate system is constructed using Gram-Schmidt orthogonalization. Initial vectors are defined, starting with two principal direction vectors. Gram-Schmidt orthogonalization of these vectors yields a set of three-dimensional orthogonal unit bases. ； Where: each column is a 3-dimensional unit vector, therefore This is the local coordinate system.

Images