A protein structure-density map fitting method based on feature point matching

Abstract

A protein structure-density map fitting method based on feature point matching belongs to the field of bioinformatics and structural biology, constructs a protein complex structure dataset, converts the structure into a unified resolution point set through voxelization and uniform sampling, and adopts the farthest point sampling to construct a multi-resolution point set to depict scale geometry; a deep learning network is adopted to learn the rotation equivariant and invariant features of the structure and the density map under multi-resolution, and a geometric self-attention mechanism based on nearest neighbor layer-by-layer expansion is introduced at the neck to enhance the representation; a coarse-to-fine feature point matching strategy is adopted in the training stage, combined with a superpoint matching loss, a point-level matching loss and a contrast rotation loss optimization; in the inference stage, multi-scale and hybrid sampling are adopted, and candidate poses are generated through translation mask, the candidate poses are screened and optimized according to the structure-density map fitting score, and the final fitting result is output. The present application can realize high-precision and high-efficiency structure-density map fitting under complex conditions.

Description

Technical Field

[0001] This invention belongs to the fields of bioinformatics, structural biology, and computer applications, and in particular relates to a protein structure-density map fitting method based on feature point matching. Background Technology

[0002] In recent years, the rapid development of cryo-electron microscopy has made it possible to resolve the three-dimensional density maps of macromolecular complexes at near-atomic resolution, significantly advancing structural bioinformatics. Atomic structure modeling methods for density maps can be mainly classified into two categories: de novo modeling and structure fitting assembly. The accuracy of de novo modeling methods is highly dependent on the overall resolution and local quality of the density map. Under high-resolution density map conditions, this type of method can achieve relatively accurate main chain tracing and sequence recovery; however, in medium- and low-resolution density maps or regions with low signal-to-noise ratios, its modeling accuracy often decreases significantly, limiting its applicability. In contrast, fitting assembly methods are less dependent on the quality of the density map. Especially in recent years, the development of high-precision protein structure prediction models based on sequences has provided high-quality atomic-level initial structures for fitting assembly, resulting in substantial improvements in the modeling accuracy and stability of this type of method. Against this backdrop, fitting assembly based on predicted or template structures has gradually become one of the important means of resolving complex macromolecular complexes. However, the performance ceiling of fitting assembly methods essentially depends on the performance of the structure-density map fitting algorithm; its accuracy and robustness will largely determine the overall quality of the final complex model. Therefore, the design and optimization of fitting algorithms remain the core issues in this field.

[0003] In existing technologies, structure-density map fitting methods can be mainly divided into image-based fitting methods and sampling point-based fitting methods, depending on the data mode used. Image-based fitting methods typically voxelize the structure model to be fitted, generate a corresponding simulated density map, and combine optimization algorithms such as Fast Fourier Transform to perform an exhaustive search in the discrete pose space to maximize the correlation score or other similarity evaluation indicators of the structure-density map, thereby achieving the fitting of the structure-density map. Theoretically, this type of method can make full use of continuous density information and has high fitting accuracy. However, its search space increases rapidly with the size of the density map and the scale of the structure, resulting in low computational efficiency when processing large density maps or multiple structural units. In addition, under high-resolution density map conditions, indicators such as correlation scores are sensitive to small pose perturbations, easily getting trapped in local optima and struggling to converge stably to the global optimum. Sampling point-based fitting methods, on the other hand, typically preprocess the source and target density maps using clustering algorithms such as mean shift after voxelizing the structure into a density map, and perform point sampling according to a preset threshold, while introducing additional information such as density direction vectors to the sampling points. Building upon this foundation, optimization algorithms are used to search within a discrete pose space, typically aiming to maximize the overlap rate of sampling points or minimize the vector angle between density directions to achieve the matching of structure and density maps. This type of method significantly compresses the search space through point-level representation, offering a clear advantage in computational efficiency. However, compared to continuous density representation, the sampling point approach inevitably loses some density information; furthermore, its fitting method still primarily relies on exhaustive search, limiting overall efficiency and robustness. In addition, some methods in recent years have introduced manually designed geometric or density descriptors based on sampling point representation, directly registering structure and density maps in the feature space. However, these methods are highly sensitive to the design of the manual descriptors and the setting of hyperparameters. When the initial overlap rate between the structure and density maps is low or the local density quality is poor, the discriminative ability of the descriptors easily decreases, thus affecting the stability and reliability of the fitting results. Summary of the Invention

[0004] To overcome the shortcomings of existing protein structure-density map fitting methods in terms of accuracy, computational efficiency, and robustness, this invention proposes a protein structure-density map fitting method based on feature point matching. This method effectively adapts to different scale conditions and initial pose differences through learnable feature representations and feature point matching mechanisms. Compared with traditional methods, this invention reduces the dependence on exhaustive search and manual descriptors, making the fitting process more robust and significantly improving computational efficiency while ensuring accuracy.

[0005] The technical solution adopted by this invention to solve its technical problem is:

[0006] A protein structure-density map fitting method based on feature point matching is proposed. First, a non-redundant, non-homologous structure-density map dataset is constructed. Then, after splitting the structure by chain, preprocessing operations such as voxelization, uniform voxel size, and uniform point sampling are performed to form a standardized input representation suitable for training deep learning models.

[0007] Before training, a series of data augmentations were performed on the two point sets, including random rotation, random shuffling of point order, and random pruning under high overlap. At the same time, multi-resolution downsampling was performed using the farthest point sampling.

[0008] Secondly, a deep learning network architecture suitable for fitting structure and density maps was designed. A geometric self-attention mechanism based on nearest neighbor layer-by-layer expansion was added to the neck of the network structure, and the conventional cross-attention mechanism was removed.

[0009] Based on this, the model extracts features at different resolutions to complete coarse-to-fine feature matching, and performs pose estimation based on the matching points and their corresponding isovariant features to achieve end-to-end training.

[0010] During the inference phase, a translation masking operation is performed on the target density map based on the spatial scale of the input structure, decomposing the global structure-density map fitting problem into multiple local candidate regions, and using the trained model to quickly estimate the relative pose between the structure and each local density map; at the same time, a multi-scale voxel downsampling strategy is introduced, and hybrid sampling is performed at the superpoint level.

[0011] Finally, based on the multiple initial pose candidates obtained, the initial poses with high matching degree are selected by the preset structure-density map fitting evaluation index, and they are continuously fine-tuned and optimized to achieve high-precision, high-efficiency structure-density map fitting that is insensitive to initial conditions.

[0012] Furthermore, the method includes the following steps:

[0013] 1) Download all protein complex structures from the PDB library, perform redundancy removal based on sequence similarity and structural similarity, remove inter-chain homologous complexes based on structural similarity, and randomly divide the processed dataset into training set, validation set and test set according to a set ratio.

[0014] 2) The complete protein complex structure is split into chains, and the split structures are randomly rotated and translated to obtain the source structure. The original complete complex structure is used as the target structure. A resolution parameter is randomly sampled, and the source structure and target structure are voxelized using a Gaussian kernel function to generate corresponding simulated density maps. The voxel sizes of the two are unified. The density map is uniformly sampled using three times the standard deviation of the density values ​​in the entire density map as a threshold to generate source point sets and target point sets respectively.

[0015] Furthermore, the method also includes the following steps:

[0016] 3) At the beginning of training, data augmentation is performed on the two input point sets, including random rotation transformation, random shuffling of point order, spatial clipping under high overlap conditions, and small-scale random perturbation. The point sets are downsampled step by step according to the preset point ratio, and point sets of different resolutions are generated by sampling the farthest point.

[0017] 4) Using the PARECONV backbone network, extract rotation-equivalent and rotation-invariant features from the source and target point sets obtained in step 3) at different resolution levels. Remove the cross-attention module in the traditional deep learning framework from the network structure, and introduce a geometric self-attention mechanism based on nearest neighbor layer-by-layer expansion at the network neck to enhance the rotation-invariant features. The enhanced rotation-invariant features are then passed up the network layers one by one.

[0018] Furthermore, the method also includes the following steps:

[0019] 5) Based on the rotation invariance feature in step 4), the feature matching method in GeoTransformer is used from coarse to fine to perform matching. The pose change is estimated by the mutual matching points and their corresponding rotation isovariant features. A composite loss function is constructed by super-point matching loss, point-level matching loss and comparative rotation loss. The network parameters are updated by backpropagation.

[0020] 6) During the inference phase, based on the rotation radius of the source point set structure to be processed, a translation mask operation is performed on the target point set to generate multiple partially overlapping target sub-point sets in the target point set, and sub-point sets with too few points are deleted; multi-scale voxel downsampling is performed on the two point sets simultaneously, and hybrid sampling is performed at the neck, i.e., superpoint level; the model parameters obtained in step 5) are used for inference to generate multiple candidate initial poses.

[0021] 7) Based on the overlap rate and correlation score, select the top five candidate poses obtained in step 6) and further refine them: calculate the fitting score of all current candidate poses on the target density map, estimate the corresponding gradient information using the difference method, and optimize using the gradient descent method; during the optimization process, alternately update the rotation and translation parameters, and adaptively adjust the optimization step size according to the change of the density fitting score, and finally select the pose with the highest correlation score as the final fitting result.

[0022] The technical concept of this invention is as follows: First, a non-redundant structure-density map dataset is constructed, and the structure is split into chains and preprocessed using uniform voxel size and uniform point sampling to form a standardized input representation suitable for deep learning model training. Second, a deep learning network architecture suitable for fitting the structure and density map is designed. A geometric self-attention mechanism based on nearest neighbor layer-by-layer expansion is added to the neck of the network structure, and the conventional cross-attention mechanism is removed. At the same time, the farthest point sampling strategy is uniformly adopted during the training phase. Furthermore, data augmentation strategies such as rotation perturbation, spatial pruning, and adding Gaussian noise are introduced. Based on this, features extracted by the model at different resolutions are used to complete coarse-to-fine feature matching, and based on the matching points... The model performs pose estimation based on the corresponding isomorphic features to achieve end-to-end training. During the inference phase, a translation mask operation is performed on the target density map according to the spatial scale of the input structure, decomposing the global structure-density map fitting problem into multiple local candidate regions. The trained model is then used to quickly estimate the relative pose between the structure and each local density map. Simultaneously, a multi-scale voxel downsampling strategy is introduced, and hybrid sampling is performed at the superpoint level. Finally, based on the obtained multiple initial pose candidates, the initial poses with high matching degree are selected through preset structure-density map fitting evaluation indicators, and they are continuously fine-tuned and optimized to achieve high-precision, high-efficiency structure-density map fitting that is insensitive to initial conditions.

[0023] The beneficial effects of this invention are as follows: First, by introducing a pose estimation mechanism based on deep learning feature point matching, this invention avoids the dependence on discrete exhaustive search in traditional structure-density map fitting methods, significantly improving overall computational efficiency and effectively reducing the sensitivity of the fitting process to the initial pose setting, thereby enhancing the stability and robustness of the method in complex scenarios. Second, through a series of data augmentation and training strategies, combined with multi-scale voxel downsampling, superpoint hybrid sampling, and translation masking, this invention enhances the model's ability to represent geometric structural features, significantly improving the model's generalization ability under different scale conditions, making it applicable to protein structure-density map data with complex structures and significant scale variations. Finally, this invention jointly utilizes sampling point information and density map information for feature learning and pose estimation during the fitting process. Compared to fitting methods based solely on point representations, this invention can more fully utilize the continuous spatial constraints contained in the density distribution, thereby obtaining more reliable structure-density map matching results while ensuring computational efficiency. Attached Figure Description

[0024] Figure 1 This is a basic flowchart of a protein structure-density map fitting method based on feature point matching.

[0025] Figure 2 This is the resolved structure of the A chain in the protein complex 8sqa.

[0026] Figure 3 This is a simulated density plot of the protein complex 8sqa.

[0027] Figure 4 This is the cryo-electron microscopy density map (EMD-40700) corresponding to the protein complex 8sqa.

[0028] Figure 5 It is the result of a protein structure-density map fitting method based on feature point matching. Detailed Implementation

[0029] The invention will now be further described with reference to the accompanying drawings.

[0030] Reference Figures 1-5 A protein structure-density map fitting method based on feature point matching includes the following steps:

[0031] 1) Download all publicly available protein structure data up to January 22, 2025 from the PDB (https: / / www.rcsb.org) database. First, the initial data was filtered using the sequence clustering method in MMseqs2 (https: / / github.com / soedinglab / MMseqs2): when the sequence similarity between any two protein chains exceeded 80%, they were grouped into the same cluster. Then, Foldseek (https: / / search.foldseek.com / search) was used for further clustering based on the similarity of three-dimensional structures. If the structural similarity between any two chains in two complexes exceeded 50%, the corresponding structures were grouped into the same structural cluster. Finally, US-align (https: / / www.aideepmed.com / US-align / ) was used to remove homology between the obtained structures, eliminating homologous complexes with a structural similarity between any two chains exceeding 70%, thus constructing a non-redundant, non-homologous complex structure dataset. Finally, the training set, validation set, and test set were randomly divided in a ratio of 7:1.5:1.5.

[0032] 2) The complete protein complex structure is dissected chain by chain. Random rotation and translation transformations are applied to the dissected structures, which are then used as the source structures. The original complete complex structure is used as the target structure. Subsequently, resolution parameters are randomly and uniformly sampled within the range of 2 Å to 10 Å. Voxelization is then performed on both the source and target structures based on a Gaussian kernel function to generate corresponding simulated density maps. The voxel size for both is uniformly set to 2 Å. Finally, uniform point sampling is performed on the simulated density maps using three times the standard deviation of the density values ​​in each simulated density map as a threshold, constructing source point sets for each. With target point set ;

[0033] 3) During the training phase, data augmentation is performed on the input source and target point sets, including random rotation, point shuffling, spatial clipping with high overlap, and small-scale random perturbations; rotation transformation is achieved by generating a rotation matrix through random sampling and applying it to the source or target point set with a preset probability; uniformly distributed random perturbations are randomly added to the 3D coordinates, with an amplitude range of [missing value]. σ is preferably 0.05 Å; high overlap rate point sets trigger random pruning: randomly generate direction vectors, calculate projection values, determine the pruning threshold based on the projection distribution, remove points at the high or low percentiles, and retain a preset proportion of points. Simultaneously, a farthest point sampling strategy is used for downsampling to obtain point sets at different resolutions. Downsampling is performed three times at preset proportions, set to 0.75, 0.25, and 0.5 respectively; where the overlap rate is defined as follows: If the overlap rate is greater than or equal to 0.7, it is considered a high overlap rate. This represents the number of interior points that originally overlapped between the source and target point sets. This represents the number of source and target point sets; the method for determining interior points is as follows: ,in The value is 1.5 Å;

[0034] 4) Scale normalization is performed on the point set at each resolution level. A three-layer PARECOnov-backbone (https: / / github.com / yaorz97 / PARENet) is used to extract rotation-equivalent and rotation-invariant features of the source and target point sets at different resolution levels. In the neck structure of the PARECOnov-backbone, six geometric self-attention modules based on nearest neighbor layer-by-layer expansion are cascaded to enhance the feature modeling capability by expanding the attention perception range of the feature point set layer by layer. The nearest neighbor ratios for each layer are set to 0.5, 0.75, and 1.0, respectively. At the same time, the cross-attention module in the traditional deep learning framework is removed, and the rotation-invariant features enhanced by the geometric self-attention module are passed down step by step along the network layers towards higher resolution.

[0035] 5) Utilizing the rotation-invariant features extracted by the model at various resolutions, a coarse-to-fine feature matching approach using GeoTransformer (https: / / github.com / qinzheng93 / GeoTransformer) is employed. First, in the coarse matching stage, based on the source point set... With target point set Matching is performed on the corresponding superpoint-level rotation-invariant features. Point-level invariant feature matching is then performed within the surrounding neighborhood of the matched superpoints. Using successfully matched point pairs, referencing the pose estimation methods of GeoTransformer and PARE-Net, multiple pose hypothesis estimates are generated sequentially using the matched points and their corresponding rotational isovariant features. Singular value decomposition is then used for efficient solution, followed by statistical analysis of the inlier ratio to select the optimal pose change. The source point set is then subjected to pose change, utilizing the superpoint matching loss (…). Point-level matching loss ), and compared rotational loss ( Construct a composite loss function The network parameters are updated via backpropagation. The learning rate is automatically decayed using the cosine annealing strategy in the Adam optimizer, with an initial learning rate set to 1e-3 and a minimum learning rate set to 1e-5. Training is performed for 30 epochs, and the model with the lowest relative rotation error on the validation set is selected as the final model. The superpoint matching loss (…) The following represents the source point set. For example:

[0036] ;

[0037] in, Points representing the source point set at the superpoint scale. Similarly, this represents the points at the super-point scale within the target point set; represent and The overlap rate; and These represent the point sets for positive and negative samples, respectively. The boundary for positive samples is set to 2.5; The boundary for negative samples is set to 6. and Euclidean distance representing the rotational invariance characteristics of two points at the superpoint level; and These represent the weights of the positive and negative samples, respectively. , , Set the temperature overparameter to 2; similarly, It can be obtained through symmetry, ultimately Point-level matching loss ( It is represented as follows:

[0038] ;

[0039] in, and This represents the interior point under actual pose changes; and Represents the predicted interior points; and Represents the predicted pose change; Matching score matrix (row normalized) representing point-level rotation invariant features; Matching score matrix (column normalized) representing point-level rotation invariance features; contrasting rotation loss ( It is represented as follows:

[0040] ;in, Represents a point-level point. Represents a point at the super-point level; Represents rotational invariance characteristics at the superpoint level; Represents actual changes in posture; and Distinguish between the source point and the target point;

[0041] 6) During the inference phase, the mask radius is set to 1.45 times the rotation radius of the source point set structure. A translation mask operation with a step size of 0.45 times the mask radius is performed on the target point set to generate multiple partially overlapping target sub-point sets. If the number of points in a sub-point set is less than 20% of the number of points in the source point set, it is deleted and no inference is performed. Multi-scale voxel downsampling is performed on the two point sets, and farthest point sampling (sampling ratio of 0.5) and voxel sampling are performed simultaneously at the superpoint level. The trained model parameters are used for inference to obtain the candidate initial pose.

[0042] 7) Based on the overlap rate and correlation scores, the top five candidate initial poses are selected and finely optimized. During the optimization process, the fitting score of the structure on the target density map is calculated by trilinear interpolation, and the gradient is estimated by difference. The rotation and translation parameters are updated alternately using the gradient descent method, and the step size is adaptively adjusted according to the changes in the fitting score. At the beginning of each evaluation segment (10 steps), the current parameters are recorded and the preset number of iterations is executed. At the end of the evaluation segment, the step size is adjusted according to the comparison between the actual movement distance and the theoretical movement distance. If the movement distance is less than the threshold, the step size is reduced, and otherwise it is increased appropriately. The optimization is terminated when the step size is less than the minimum value, the maximum number of iterations is reached, or no better solution is found after 400 consecutive steps. Finally, the optimal pose is selected based on the structure-density map correlation score.

[0043] Taking the protein complex PDB ID: 8sqa as an example, the corresponding cryo-electron microscopy density map is EMD-40700, which has a resolution of 4.2 Å. Chain A of the protein complex was selected, and starting from three different initial poses, the above steps were followed for processing and fitting. The fitting results are as follows... Figure 5 As shown, the average TM-score of the fitted chain is 1.00, the RMSD is 0.02 Å, and the average running time for a single fit is approximately 2 minutes. The obtained fitting results are highly consistent with the experimental analysis results.

[0044] The embodiments described in this specification are merely examples of implementations of the inventive concept and are for illustrative purposes only. The scope of protection of this invention should not be considered limited to the specific forms described in these embodiments; rather, it extends to equivalent technical means conceived by those skilled in the art based on the inventive concept.

Claims

1. A protein structure-density map fitting method based on feature point matching, characterized in that, First, a non-redundant, non-homogeneous structure-density graph dataset is constructed. After splitting the structure by chain, preprocessing operations are performed to obtain the source point set and the target point set, thereby forming a standardized input representation suitable for training deep learning models. Before training, perform data augmentation on the source and target point sets; Simultaneously, multi-resolution downsampling is performed on the source point set and the target point set using the farthest point sampling method; Secondly, a deep learning network architecture suitable for fitting structure and density maps was designed. A geometric self-attention mechanism based on nearest neighbor layer-by-layer expansion was added to the neck of the network structure, and the conventional cross-attention mechanism was removed. Based on this, the model extracts features at different resolutions to complete coarse-to-fine feature matching, and performs pose estimation based on the matching points and their corresponding isovariant features to achieve end-to-end training. During the inference phase, a translation masking operation is performed on the target density map based on the spatial scale of the input structure, decomposing the global structure-density map fitting problem into multiple local candidate regions, and using the trained model to quickly estimate the relative pose between the structure and each local density map; at the same time, a multi-scale voxel downsampling strategy is introduced, and hybrid sampling is performed at the superpoint level. Finally, based on the multiple initial pose candidates obtained, the initial poses with high matching degree are selected by the preset structure-density map fitting evaluation index, and they are continuously fine-tuned and optimized to achieve high-precision, high-efficiency structure-density map fitting that is insensitive to initial conditions.

2. The protein structure-density map fitting method based on feature point matching as described in claim 1, characterized in that, The method includes the following steps: 1) Download all protein complex structures from the PDB library, perform redundancy removal based on sequence similarity and structural similarity, remove inter-chain homologous complexes based on structural similarity, and randomly divide the processed dataset into training set, validation set and test set according to a set ratio. 2) The complete protein complex structure is split into chains, and the split structures are randomly rotated and translated to obtain the source structure. The original complete complex structure is used as the target structure. A resolution parameter is randomly sampled, and the source structure and target structure are voxelized using a Gaussian kernel function to generate corresponding simulated density maps. The voxel sizes of the two are unified. The density map is uniformly sampled using three times the standard deviation of the density values ​​in the entire density map as a threshold to generate source point sets and target point sets respectively.

3. The protein structure-density map fitting method based on feature point matching as described in claim 2, characterized in that, The method further includes the following steps: 3) At the beginning of training, data augmentation is performed on the two input point sets, including random rotation transformation, random shuffling of point order, spatial clipping under high overlap conditions, and small-scale random perturbation. The point sets are downsampled step by step according to the preset point ratio, and point sets of different resolutions are generated by sampling the farthest point. 4) Using the PARECONV backbone network, extract rotation-equivalent and rotation-invariant features from the source and target point sets obtained in step 3) at different resolution levels. Remove the cross-attention module in the traditional deep learning framework from the network structure, and introduce a geometric self-attention mechanism based on nearest neighbor layer-by-layer expansion at the network neck to enhance the rotation-invariant features. The enhanced rotation-invariant features are then passed up the network layers one by one.

4. The protein structure-density map fitting method based on feature point matching as described in claim 3, characterized in that, The method further includes the following steps: 5) Based on the rotation invariance feature in step 4), the feature matching method in GeoTransformer is used from coarse to fine to perform matching. The pose change is estimated by the mutual matching points and their corresponding rotation isovariant features. A composite loss function is constructed by super-point matching loss, point-level matching loss and comparative rotation loss. The network parameters are updated by backpropagation. 6) During the inference phase, based on the rotation radius of the source point set structure to be processed, a translation mask operation is performed on the target point set to generate multiple partially overlapping target sub-point sets in the target point set, and sub-point sets with too few points are deleted; multi-scale voxel downsampling is performed on the two point sets simultaneously, and hybrid sampling is performed at the neck, i.e., superpoint level, and inference is performed using the model parameters obtained in step 5) to generate multiple candidate initial poses.

5. The protein structure-density map fitting method based on feature point matching as described in claim 4, characterized in that, The method further includes the following steps: 7) Based on the overlap rate and correlation score, select the top five candidate poses obtained in step 6) and further refine them: calculate the fitting score of all current candidate poses on the target density map, estimate the corresponding gradient information using the difference method, and optimize using the gradient descent method; during the optimization process, alternately update the rotation and translation parameters, and adaptively adjust the optimization step size according to the change of the density fitting score, and finally select the pose with the highest correlation score as the final fitting result.

6. The protein structure-density map fitting method based on feature point matching as described in claim 2, characterized in that, In step 1), the process of constructing the training dataset is as follows: collect all protein complex PDB structures; use clustering methods in MMseqs2 and Foldseek to cluster the initial dataset and select the cluster center structure; use US-align to remove homologous complexes between chains, and finally obtain a non-redundant non-homologous structure dataset.

7. The protein structure-density map fitting method based on feature point matching as described in claim 3, characterized in that, In step 3), data augmentation is performed on the input source and target point sets by randomly rotating the source or target point sets with a preset probability; a uniformly distributed random perturbation is added to the three-dimensional coordinates, with an amplitude range of [missing value]. σ is 0.05 Å; for point sets with overlap > 0.7, direction vectors are randomly generated, projection values ​​are calculated, and the clipping threshold is determined according to the projection distribution. Points at the high or low percentile are removed, and points at a preset ratio are retained; during the training phase, downsampling at different resolutions uses the farthest point sampling, and each layer of point sets is downsampled step by step according to a preset ratio.

8. The protein structure-density map fitting method based on feature point matching as described in claim 3, characterized in that, In step 4), a three-layer PARECOnov-backbone is used to extract rotation-equivalent and rotation-invariant features of the source and target point sets at different resolution levels, and scale normalization is performed on the point sets at each resolution level. Six geometric self-attention modules based on neighborhood-level expanding masks are cascaded in the neck structure of the PARECOnov-backbone to expand the attention range of the feature point set layer by layer. At the same time, the cross-attention modules in the traditional deep learning framework are removed, and the rotation-invariant features enhanced by the geometric self-attention modules are propagated step by step along the network layers towards the high resolution direction.

9. The protein structure-density map fitting method based on feature point matching as described in claim 4, characterized in that, In step 6), the rotation radius is calculated based on the input structure, and 1.45 times the rotation radius is taken as the radius of the translation mask. The translation mask operation is performed on the target point set with a step size of 0.45 times the translation mask radius. Multiple partially overlapping target sub-point sets are generated in the target point set, and sub-point sets with too few points are deleted. At the same time, the point set at super-resolution adopts a hybrid sampling method of voxel sampling and farthest point sampling.

Images