End-to-end protein 3d density map deep reconstruction method based on particle image

Abstract

This invention relates to the fields of computer and biological technologies, specifically to an end-to-end protein 3D density map depth reconstruction method based on particle images. The method involves acquiring particle images, extracting spatial and structural features through convolution, classifying and filtering them, analyzing the rate of change of rotation quaternions and translation vectors to determine stability and correct posture, and further correcting posture by incorporating the direction of the distance between adjacent particles to reduce errors. The images are then mapped to a 3D voxel grid for reverse mapping to generate a spatial distribution density map. Based on the mapping rules, the 3D density map is decoded, reconstructed, and updated to obtain the protein 3D density map reconstruction result. In particle image processing, this invention extracts and precisely filters multi-dimensional features such as spatial distribution, shape, and structure. It combines the rate of change of rotation and translation errors to determine stability and iteratively corrects the image, gradually aligning postures. It utilizes the geometric relationships between adjacent particles to reduce deviations, maps features to a 3D voxel space to restore details, and continuously corrects errors during 3D decoding and optimization, improving the accuracy and reliability of 3D reconstruction.

Description

Technical Field

[0001] This invention relates to the fields of computer and biological technology, and in particular to an end-to-end method for deep reconstruction of protein three-dimensional density maps based on particle images. Background Technology

[0002] The field of computer and biological technology includes cryo-electron microscopy 3D reconstruction technology. The core of this field involves the process of reconstructing the 3D structure of proteins from 2D particle images of biological samples. This field covers particle selection to identify effective particle images, CTF correction to eliminate microscopic imaging distortion, initial model building to provide preliminary structural references, attitude estimation to calculate the rotation and translation parameters of particles in 3D space, 3D reconstruction and optimization to generate density maps through iterative algorithms, and masking and resolution verification to ensure output quality. The overall technical process depends on the registration accuracy between particles and the quality of the initial model. If the attitude estimation is inaccurate or the initial model has too large a deviation, it will lead to reconstruction failure or blurry results.

[0003] Among them, the end-to-end protein 3D density map depth reconstruction method based on particle images refers to utilizing the attitude density of historical particle images. Figure 3 Tuple data is used to train a deep learning model, which directly outputs a 3D density map from the input particle image. The technical issues addressed include eliminating the strong dependence of traditional processes on pose estimation, resolving the ambiguity of 2D projection structures, and reusing historical data resources. The specific solutions include using convolutional neural networks or VisionTransformer to extract single-particle image features, predicting particle rotation quaternions and translation vectors as preliminary poses, using SetTransformer or graph neural networks to achieve geometric information sharing between particles to optimize pose consistency, backprojecting the features according to the predicted poses to 3D voxel space, and using a 3D convolutional network to decode and generate the final density map.

[0004] Existing technologies rely heavily on the accuracy of particle registration and the quality of the initial model during attitude estimation. When the initial model has a large deviation or the particle orientation and position are not accurately estimated, errors are easily generated and accumulated in iterative calculations, leading to blurred density maps or even reconstruction failures. Furthermore, there is a lack of dynamic correction mechanisms for the geometric consistency between particles. Combined with the single reconstruction and local calculation methods commonly used in current processes, existing large-scale historical data on particles, attitudes, and density maps are not effectively integrated and reused. The structural priors and projection rules contained therein are ignored, resulting in decreased spatial registration accuracy under conditions of noise interference, complex conformations, or uneven particle orientation distribution. Errors are amplified in multiple iterations, easily causing incomplete reconstruction or reduced resolution in local areas. Summary of the Invention

[0005] To address the technical problems existing in the prior art, embodiments of the present invention provide an end-to-end protein 3D density map depth reconstruction method based on particle images. The technical solution is as follows:

[0006] An end-to-end protein 3D density map depth reconstruction method based on particle images includes the following steps:

[0007] S1: Obtain the spatial and structural information of particles in particle image data, extract spatial distribution shape and structural features through hierarchical convolution, classify and filter according to features, and obtain particle feature representation results;

[0008] S2: Based on the features of each particle in the particle feature representation results, calculate the rotation and displacement error change rate, iteratively judge the convergence stability, compare the error change rate with a set threshold, correct the attitude of particles that exceed the set threshold, and generate particle attitude prediction results.

[0009] S3: Based on the spatial position information and attitude parameters of the particles in the particle attitude prediction results, combined with the spacing, direction and arrangement of adjacent particles, calculate the relative rotation and displacement difference, correct the attitude parameters to reduce errors, and generate optimized attitude information between particles.

[0010] S4: Based on the corrected particle spatial position information and attitude parameters in the optimized attitude information between particles, the particle features are mapped to a three-dimensional voxel mesh to generate a three-dimensional voxel space density map projection result.

[0011] S5: Call the spatial distribution information and density contribution value of particles in the projection result of the three-dimensional voxel space density map, perform three-dimensional decoding and reconstruction, reconstruct the position according to the mapping rules, update the structure through convolution and optimization, and obtain the protein three-dimensional density map reconstruction result.

[0012] As a further aspect of the present invention, the particle feature representation results include spatial topological relationships, morphological classification labels, and structural integrity indicators; the particle attitude prediction results include a three-dimensional attitude matrix, attitude stability coefficient, and error convergence level; the optimized attitude information between particles includes a relative position matrix, orientation consistency parameters, and attitude coordination index; the three-dimensional voxel spatial density map projection results include a voxel distribution matrix, density intensity grading, and spatial connectivity map; and the protein three-dimensional density map reconstruction results include a three-dimensional mesh structure, local density distribution, and overall configuration model.

[0013] As a further aspect of the present invention, the step of obtaining the particle feature representation result is as follows:

[0014] S101: Acquire particle image data, perform layered convolution operation to process the image, call the weight of the first layer convolution kernel to calculate pixel distribution, generate spatial distribution coordinate set, call the weight of the second layer convolution kernel to calculate contour change, extract shape boundary trajectory, call the weight of the last layer convolution kernel to analyze texture pattern, output structural topology relationship, merge the spatial distribution coordinate set, shape boundary trajectory and structural topology relationship into a unified set to obtain morphological topology configuration.

[0015] S102: Based on the morphological topology, calculate the spatial distribution dispersion, shape roundness coefficient and structural regularity, compare the three values ​​with the preset classification threshold, and assign particles to the corresponding groups according to the comparison results to obtain the category assignment identifier;

[0016] S103: Based on the category assignment identifier, filter particles whose identifier values ​​meet the set conditions, extract their morphological topology, combine them into a feature representation set, and obtain the particle feature representation result.

[0017] As a further aspect of the present invention, the step of obtaining the particle attitude prediction result is as follows:

[0018] S201: Based on the particle feature representation results, extract the spatial distribution features, shape features and structural features of each particle, calculate the rotation quaternion based on the spatial distribution coordinates, calculate the translation vector based on the shape contour, perform consistency verification in combination with structural features, and output a unified data set; generate the initial attitude state.

[0019] S202: Based on the initial attitude state, calculate the rotation error and displacement error of the current iteration, call the error data of the previous iteration, calculate the error change trend as the ratio of the difference between the current error and the previous error, and generate error dynamics;

[0020] S203: Based on the aforementioned error dynamics, determine the particle convergence stability. Based on the dynamic value, compare the trends of rotation error and displacement error with the set convergence threshold. For particles that exceed the threshold, adjust their rotation quaternion and translation vector, and output the particle posture prediction result.

[0021] As a further aspect of the present invention, the step of obtaining the optimized attitude information between particles is as follows:

[0022] S301: Based on the particle attitude prediction results, call the particle spatial position information and attitude parameters, combine the distance between the center points of adjacent particles, the relative direction vector and the arrangement, calculate the difference in rotation quaternion as the difference in the rotation angle between the two particles, calculate the difference in displacement as the difference in the distance between the center points of the two particles, output a unified set, and generate the relative attitude offset.

[0023] S302: Based on the relative attitude offset, and according to the interaction between adjacent particles, the rotation quaternion and translation vector are adjusted successively. The adjustment range is based on the offset value. After each adjustment, the relative rotation difference and displacement difference are recalculated to generate the corrected attitude parameters.

[0024] S303: Based on the corrected attitude parameters, iteratively update the particle spatial position information and attitude parameters, combine all the updated particle parameters, and generate optimized attitude information between particles.

[0025] As a further aspect of the present invention, the step of obtaining the projection result of the three-dimensional voxel space density map is as follows:

[0026] S401: Call the corrected particle spatial position information and attitude parameters in the optimized attitude information between particles, extract spatial coordinates, spatial distribution features, shape features and structural features, calculate the distribution position of features in the grid according to the center position, boundary range and arrangement direction of the three-dimensional voxel grid, assign feature values ​​to the corresponding voxel units, and generate voxel feature allocation;

[0027] S402: Based on the voxel feature allocation, according to the center position, boundary range and arrangement direction of the three-dimensional voxel mesh, the spatial distribution features, shape features and structural features are reverse calculated according to the voxel unit position, the feature distribution is adjusted and the feature reverse distribution is generated;

[0028] S403: Based on the reverse distribution of the features, integrate the feature values ​​of all voxel units, generate a spatial distribution map of particles in three-dimensional space, output the projection set, and generate a three-dimensional voxel spatial density map projection result.

[0029] As a further aspect of the present invention, the steps for obtaining the protein three-dimensional density map reconstruction results are as follows:

[0030] S501: Based on the projection result of the three-dimensional voxel space density map, call the spatial distribution information and density contribution value of the particles in the three-dimensional space, perform reconstruction calculation on the spatial position of each particle according to the spatial mapping rules, calculate the position offset and density superposition, and generate a set of position reconstruction points.

[0031] S502: Reconstruct the point set based on the location, perform convolution operation to process the point set data, update the spatial structure of the 3D density map, calculate the structure change gradient, and generate the structure update gradient.

[0032] S503: Based on the structure update gradient, perform data optimization operation, adjust the density map structure according to the optimization rules, iteratively update the spatial structure, and generate the protein three-dimensional density map reconstruction result.

[0033] The beneficial effects of the technical solutions provided in the embodiments of the present invention include at least the following:

[0034] In this invention, during particle image processing, multi-dimensional features such as spatial distribution, shape, and structure of particles are extracted and precisely screened. Stability is determined by the dynamic change rate of rotation and displacement errors, and iterative correction is performed to gradually make the particle posture consistent globally. The geometric relationship between adjacent particles is used to reduce relative deviations, and the features are accurately mapped to the three-dimensional voxel space to achieve complete restoration of spatial distribution and structural details. Finally, structural errors are continuously corrected during the three-dimensional decoding and optimization process, making the spatial structure of the density map more stable and the details clearer, significantly improving the accuracy and reliability of protein three-dimensional reconstruction. Attached Figure Description

[0035] Figure 1 This is a flowchart of the method of the present invention;

[0036] Figure 2 This is a flowchart illustrating the process of obtaining the particle feature representation results of the present invention.

[0037] Figure 3 This is a flowchart illustrating the process of obtaining particle attitude prediction results in this invention.

[0038] Figure 4 This is a flowchart illustrating the process of obtaining optimized attitude information between particles in this invention.

[0039] Figure 5 This is a flowchart illustrating the process of obtaining the projection results of the three-dimensional voxel space density map in this invention.

[0040] Figure 6 This is a flowchart illustrating the process of obtaining the protein three-dimensional density map reconstruction results of the present invention. Detailed Implementation

[0041] The technical solution of the present invention will now be described with reference to the accompanying drawings.

[0042] In embodiments of the present invention, words such as "exemplarily," "for example," etc., are used to indicate that something is an example, illustration, or description. Any embodiment or design described as "exemplary" in the present invention should not be construed as being more preferred or advantageous than other embodiments or designs. Specifically, the use of the word "exemplary" is intended to present the concept in a concrete manner. Furthermore, in embodiments of the present invention, the meaning expressed by "and / or" can be both, or either one.

[0043] In the embodiments of this invention, the terms "image" and "picture" may sometimes be used interchangeably. It should be noted that, without emphasizing the distinction between them, they convey the same meaning. Similarly, the terms "of," "corresponding (relevant)," and "corresponding" may sometimes be used interchangeably. It should be noted that, without emphasizing the distinction between them, they convey the same meaning.

[0044] In this embodiment of the invention, sometimes a subscript such as W1 may be written in a non-subscript form such as W1. When the difference is not emphasized, the meaning they express is the same.

[0045] To make the technical problems, technical solutions and advantages of the present invention clearer, a detailed description will be given below in conjunction with the accompanying drawings and specific embodiments.

[0046] Please see Figure 1 This invention provides a technical solution: an end-to-end protein 3D density map depth reconstruction method based on particle images, comprising the following steps:

[0047] S1: Obtain image data for each particle, call a convolutional neural network to extract the spatial and structural information of the particles in each particle image data, perform hierarchical convolution operations on the particle images and extract the spatial distribution, shape and structural features of each particle, classify and filter the particles according to their spatial distribution, shape and structural features, and obtain the particle feature representation results.

[0048] S2: Based on the spatial distribution, shape and structural features of each particle in the particle feature representation results, analyze the rotation quaternion and translation vector of each particle, calculate the rotation error and displacement error rate of each particle, judge the convergence stability of the particle by the rotation error and displacement error rate of each iteration, compare the rotation error and displacement error rate of the particle with the set threshold, correct the attitude of the particles that exceed the set threshold, and generate the particle attitude prediction result.

[0049] S3: Based on the spatial position information and attitude parameters of particles in the particle attitude prediction results, combined with the center point distance, relative direction vector and arrangement of adjacent particles, calculate the relative rotation difference and displacement difference, and successively correct the attitude parameters according to the interaction of adjacent particles to reduce relative error and generate optimized attitude information between particles.

[0050] S4: Based on the corrected particle spatial position information and attitude parameters in the optimized attitude information between particles, the spatial coordinates, spatial distribution, shape and structural features of the particles are mapped to a three-dimensional voxel grid. According to the center position, boundary range and arrangement direction of the three-dimensional voxel grid, the spatial distribution, shape and structural features in the particle image features are reverse mapped according to the voxel position to generate a spatial distribution map of particles in three-dimensional space and output the projection result of the three-dimensional voxel spatial density map.

[0051] S5: Call the spatial distribution information and density contribution value of particles in the three-dimensional space from the density map projection result in the three-dimensional space, and perform three-dimensional data decoding and reconstruction operations. According to the spatial mapping rules, the spatial position of each particle is gradually reconstructed. Through convolution operation and data optimization, the spatial structure of the three-dimensional density map is continuously updated to obtain the protein three-dimensional density map reconstruction result.

[0052] The particle feature representation results include spatial topological relationships, morphological classification labels, and structural integrity indices. The particle attitude prediction results include three-dimensional attitude matrix, attitude stability coefficient, and error convergence level. The optimized attitude information between particles includes relative position matrix, orientation consistency parameter, and attitude coordination index. The three-dimensional voxel spatial density map projection results include voxel distribution matrix, density intensity grading, and spatial connectivity map. The protein three-dimensional density map reconstruction results include three-dimensional mesh structure, local density distribution, and overall configuration model.

[0053] Please see Figure 2 The steps for obtaining the particle feature representation results are as follows:

[0054] S101: Acquire particle image data, perform layered convolution operation to process the image, call the weight of the first layer convolution kernel to calculate pixel distribution, generate spatial distribution coordinate set, call the weight of the second layer convolution kernel to calculate contour change, extract shape boundary trajectory, call the weight of the last layer convolution kernel to analyze texture pattern, output structural topology relationship, merge the spatial distribution coordinate set, shape boundary trajectory and structural topology relationship into a unified set to obtain morphological topology configuration.

[0055] Acquire particle image data, perform hierarchical convolution operations to process the image, and call the weights of the first-layer convolution kernel to calculate the pixel distribution. This first-layer convolution kernel is a single... The Laplace operator, specifically the value is Its weights are set based on enhancing the high-frequency features of particles in the image, i.e., regions where pixel intensity changes rapidly. This convolution kernel is applied to a... The image data, obtained from a dataset containing 10,000 such images, is a pixel-centric image centered at pixel (32, 33). The region, whose original grayscale value is:

[0056] ;

[0057] Performing a convolution operation involves aligning the center of the convolution kernel with the pixel, multiplying the pixel value at that position by the kernel weights, and then summing the results. The calculation process is as follows: The calculated result 241 is used as the new value of the pixel in the feature map. After performing the same operation on all pixels in the image, pixels with values ​​greater than 200 are selected. This threshold of 200 is determined by statistical analysis of 1000 pixels manually marked as clear feature points in the reference dataset, taking the 85th percentile of their convolutional values. The coordinates of all pixels that meet the conditions, such as (32,33), (45,51), (28,19), etc., totaling 158 points, are collected to generate a spatial distribution coordinate set. The contour change is calculated by calling the weights of the secondary convolutional kernel. This secondary convolutional kernel is a... The Sobel operator, with weights of This weight setting is used to detect horizontal edges. The operator is applied to the feature map after the first layer processing. Similarly, convolution operations are used to identify points of abrupt change in the contour. Points with an absolute value greater than 128 are marked as boundary points. The threshold of 128 was determined through edge detection experiments on 500 particle images, selecting the median gray-level difference that best separates particles from background noise. These boundary points, such as (15,20), (16,21), and (17,22), are connected according to their adjacency in the image to form a closed coordinate sequence, which is the shape boundary trajectory. The weights of the final convolution kernel are then used to analyze the texture pattern. This final convolution kernel is a set of... The Gabor filter was set with directional parameters of 0 degrees, 45 degrees, 90 degrees, and 135 degrees, and a frequency parameter of 0.25 cycles / pixel. The selection of this set of parameters was based on Fourier analysis of the typical texture patterns of known α-helical and β-fold secondary structures presented on the projected image. This set of filters was applied to the region within the particle outline. By comparing the response intensity of filters in different directions, the internal strip or dot pattern was identified. For example, if the filter in the 90-degree direction produces the maximum response in the region (40,42) to (40,50), then it is recorded that there is a texture in the vertical direction in this region. This relationship, such as "region A and region B are connected by a vertical texture of length 8 pixels", is abstracted into a graph of nodes and edges. This graph is the structural topological relationship. The spatial distribution coordinate set, shape boundary trajectory and structural topological configuration obtained in the previous steps are combined into a unified data set to obtain the morphological topological configuration.

[0058] S102: Based on morphological topology, calculate spatial distribution dispersion, shape roundness coefficient and structural regularity, compare the three values ​​with the preset classification threshold, and assign particles to the corresponding groups according to the comparison results to obtain the category assignment label;

[0059] Based on morphological topology, the spatial distribution coordinate set, shape boundary trajectory, and structural topological relationships are extracted. The spatial distribution dispersion, shape roundness coefficient, and structural regularity are calculated. The calculation of spatial distribution dispersion first involves calculating the geometric center of all 158 points in the spatial distribution coordinate set. For example, if the coordinate set is simplified to three points... , , ;

[0060] Its geometric center The x-coordinate is The y-coordinate is , obtain the center Then, calculate the mean of the sum of squared Euclidean distances from each point to the center, and then take the square root to obtain the standard deviation, i.e., the dispersion. The square of the distance is:

[0061] After performing this calculation on all 158 points, the standard deviation is 12.5 pixels. This is the spatial distribution dispersion. The shape roundness coefficient is calculated based on the shape boundary trajectory, including the area enclosed and the total length of the trajectory (Perimeter). The area is obtained by calculating the number of pixels enclosed by the trajectory, for example, 2850 pixels. The perimeter is the sum of the Euclidean distances between adjacent coordinate points on the trajectory, for example, 195.4 pixels. The roundness coefficient is calculated as follows:

[0062] This refers to the shape roundness coefficient, the calculation of structural regularity. Based on the structural topology graph, it calculates the number of nodes (N) and edges (E) in the graph and compares it with the number of edges in an idealized fully connected graph. If the graph has 12 nodes and 15 edges, and an idealized lattice structure with 12 nodes has 20 edges, then the regularity is... This refers to the structural regularity. These three values—spatial distribution dispersion (12.5), shape roundness coefficient (0.938), and structural regularity (0.75)—are compared with preset classification thresholds. The preset classification thresholds are set as follows: spatial distribution dispersion threshold is 15.0, shape roundness coefficient threshold is 0.85, and structural regularity threshold is 0.70. These thresholds are determined by calculating these three indicators on a validation set containing 5000 "high-quality" particles and 5000 "low-quality" particles (such as ice crystals and aggregates), constructing a receiver operating characteristic (ROC) curve, and selecting the index value corresponding to the point with the maximum Youden index as the threshold. Specifically, dispersion less than 15.0 is defined as "centralized," roundness coefficient greater than 0.85 is defined as "quasi-circular," and structural regularity greater than 0.70 is defined as "regular." Based on the comparison results, the three indicators of the current particle are as follows: , , All of them meet the criteria for high quality, so the particles are assigned to the corresponding group, namely the "high-quality particle group", and a category assignment identifier is obtained.

[0063] S103: Based on the category assignment identifier, filter particles whose identifier values ​​meet the set conditions, extract their morphological topology, combine them into a feature representation set, and obtain the particle feature representation result;

[0064] Based on the category assignment identifier, the identifiers of all particles in the dataset are checked, and particles whose identifier values ​​meet the set condition are filtered. The set condition is that the category assignment identifier equals "high-quality particle group". In a dataset containing 10,000 particles, after processing S102, 7,852 particles are assigned the "high-quality particle group" identifier, and 2,148 particles are assigned the "low-quality particle group" identifier. The filtering operation is then performed, selecting all 7,852 particles, while the remaining 2,148 particles are discarded and do not participate in subsequent processing. The morphological topology configuration of each of the 7,852 selected particles is extracted. Each morphological topology configuration contains a spatial distribution coordinate set, a shape boundary trajectory, and a structural topology. The relationship is used to combine these 7852 morphological topological configuration data structures into a larger list or array, forming a feature representation set. Each element in this set uniquely corresponds to a high-quality particle that has passed the initial screening and fully describes the spatial, shape, and structural characteristics of that particle. For example, the first element in the set is the morphological topological configuration of particle 1 calculated above, and its data structure is {[(32,33),…],[(15,20),…],[(A,B,len=8),…]}. The second element is the morphological topological configuration of particle 2, and so on, up to the 7852nd particle. This set, which contains the detailed characteristics of all high-quality particles, yields the particle feature representation results.

[0065] Please see Figure 3 The steps for obtaining particle attitude prediction results are as follows:

[0066] S201: Based on the particle feature representation results, extract the spatial distribution features, shape features and structural features of each particle, calculate the rotation quaternion based on the spatial distribution coordinates, calculate the translation vector based on the shape contour, combine the structural features to perform consistency verification, output a unified data set; generate the initial attitude state.

[0067] Based on the particle feature representation results, the morphological topology of each particle in the set is extracted one by one. Specifically, its spatial distribution features, shape features, and structural features are extracted. Taking the first particle in the set as an example, its spatial distribution features are a point cloud containing 158 three-dimensional coordinate points (initially with a Z value of 0). First, principal component analysis (PCA) is performed on this point cloud to calculate the values ​​of these 158 points. The covariance matrix yields three eigenvalues ​​and their corresponding eigenvectors. These three orthogonal eigenvectors define the three principal axes of the particle, forming a rotation matrix. ;

[0068] For example, Convert this rotation matrix into a rotation quaternion and calculate the resulting quaternion. The initial rotation quaternion of the particle is (w=0.948, x=0, y=0, z=-0.316). The translation vector is calculated based on the shape profile, extracting all coordinate points contained within the particle's shape boundary trajectory, and calculating the arithmetic mean of these points, which is the geometric center. For example, its geometric center coordinates are (35.2, 34.8). Since the image is two-dimensional, the Z component of the initial translation vector is set to 0. Given (35.2, 34.8, 0.0), a consistency check is performed based on structural features, using a quaternion rotation. The obtained principal direction (i.e., the first principal component vector, [0.8, 0.6, 0.0]) is multiplied by the vector formed by the two farthest nodes in the structural topology graph (e.g., the vector from node N1 to N12 is [0.78, 0.62, 0.0]). The result is... This value is very close to 1, indicating that the direction obtained from principal component analysis is highly consistent with the direction of the internal structural features. After verification, the rotational quaternion... Translation vector The output is a unified data set, which generates the initial attitude state.

[0069] S202: Based on the initial attitude state, calculate the rotation error and displacement error of the current iteration, call the error data of the previous iteration, calculate the error change trend as the ratio of the difference between the current error and the previous error, and generate error dynamics;

[0070] Based on the initial attitude state, i.e., the initial rotation quaternion of particle 1:

[0071] With translation vector The first iteration calculation is then performed, applying the pose to the particle and aligning it with a two-dimensional projection of a reference 3D model to calculate the current iteration round. The rotation error and displacement error are calculated by taking the current attitude quaternion. Truth quaternions with corresponding reference projections The rotation error is measured by the angular distance between them. The displacement error is measured by calculating the Euclidean distance between the particle center's position on the projection plane and the reference projection center. The error data from the previous round is retrieved, and the error and its trend during the iteration process are recorded in a table, as shown in Table 1. For example, in the first iteration (k=1), the error from the previous round (k=0) is set to the initial maximum value. radian, The calculated current errors are 0.15 radians and 3.5 pixels, respectively. Based on the formula in the table, the error trends are -0.850 and -0.650, respectively. This process continues, and the error trend value obtained in each round of calculation is... and These factors together constitute the error dynamics of the particle, as shown in Table 1:

[0072] Table 1: Examples of Particle Attitude Iteration Error

[0073]

[0074] As shown in Table 1, this table lists the rotation error and displacement error of a single particle in the initial few iterations of attitude prediction, as well as the changing trend calculated based on the error between the current iteration and the previous iteration. This data is used for subsequent convergence judgment.

[0075] S203: Based on error dynamics, determine the particle convergence stability. Based on the dynamic value, compare the trend of rotation error change and displacement error change with the set convergence threshold. For particles that exceed the threshold, adjust their rotation quaternion and translation vector, and output the particle posture prediction result.

[0076] Based on the error dynamics, specifically the rotation error trend of particle 1 in the second iteration (-0.267 and displacement error trend of -0.2, as shown in Table 1), the particle's convergence stability is determined. Convergence stability is determined by comparing the absolute value of the error trend with a set convergence threshold. The set convergence threshold is the threshold value of the rotation error trend. Set to 0.01, the threshold for the displacement error variation trend. The two thresholds, set to 0.01, are based on a simulation experiment that reconstructed 100 proteins with known structures. The experiment found that during the iteration process, when the absolute value of the error rate of change was less than 0.01, the subsequent iterations had less than 0.05 angstroms of influence on the root mean square deviation (RMSD) of the final three-dimensional map, which is an acceptable level of stability.

[0077] The absolute value of the currently calculated trend of rotation error change Compare with the threshold of 0.01;

[0078] The absolute value of the displacement error change trend Compared to the threshold of 0.01, because and This indicates that the particle's attitude has not yet converged and stabilized. For particles exceeding the threshold, their rotation quaternion and translation vector are adjusted. The adjustment magnitude is proportional to the current error, and an adjustment coefficient is defined. The coefficient was determined by testing different values ​​(0.1, 0.3, 0.5, 0.7) on a small dataset and selecting the value that converged fastest and did not produce oscillations. The new rotation is achieved through a small rotation quaternion. To apply, the This represents the current rotation error:

[0079] A portion of the arc, namely Similarly, the new translation vector adjustment is the current displacement error in radians. A portion of a pixel, namely The pixel is used to apply this tiny attitude adjustment to the particle's current attitude parameters, generating the input attitude for the third iteration. This process is repeated for all 7852 "high-quality particle groups" in the dataset until the absolute value of the error change trend of all particles is less than 0.01 or the preset maximum number of iterations (e.g., 100 times) is reached. The final output contains the set of attitude parameters of all particles after multiple iterations of correction, i.e., the particle attitude prediction result.

[0080] Please see Figure 4 The steps for obtaining the optimized attitude information between particles are as follows:

[0081] S301: Based on the particle attitude prediction results, call the particle spatial position information and attitude parameters, combine the distance between the center points of adjacent particles, the relative direction vector and the arrangement, calculate the difference of rotation quaternion as the difference of the rotation angle between the two particles, calculate the difference of displacement as the difference of the distance between the center points of the two particles, output a unified set, and generate relative attitude offset.

[0082] Based on the particle attitude prediction results, the spatial position information and attitude parameters of particle 1 and particle 2 are retrieved. For example, the position of particle 1 is extracted from the final attitude parameter set. The value is (37.1, 36.2, 0.0), a rotation quaternion. The position of particle 2 is (0.988, 0.011, 0.015, -0.151). The value is (125.4, 88.9, 0.0), a rotation quaternion. Given (0.951, -0.023, 0.018, 0.306), and considering the center-to-center distance, relative direction vectors, and arrangement of adjacent particles, we first determine whether two particles are adjacent by calculating their center-to-center distance:

[0083] In pixels, assuming the average particle diameter is 80 pixels, the adjacency criterion is that the center-to-center distance is less than 1.5 times the diameter, which is 120 pixels, because... Therefore, particle 1 and particle 2 are adjacent particles. The difference in rotation quaternions is calculated by... and The reverse To achieve this, first calculate the product. The reverse Then calculate the relative rotation quaternion. The result obtained Let this be a new quaternion representing the rotation operation required to change the orientation of particle 2 back to that of particle 1. The rotation angle corresponding to this quaternion is the difference in rotation angle between the two particles. The displacement difference is calculated as the distance between the center points of the two particles and a known ideal distance. The difference, assuming the ideal center-to-center distance for such adjacent proteins is 100.0 pixels according to the Protein Database (PDB), then the displacement difference Pixels, relative rotation quaternions and displacement difference The output is a unified set, generating relative attitude offsets.

[0084] S302: Based on relative attitude offset, and according to the interaction between adjacent particles, the rotation quaternion and translation vector are adjusted successively. The adjustment range is based on the offset value. After each adjustment, the relative rotation difference and displacement difference are recalculated to generate the corrected attitude parameters.

[0085] Based on relative attitude offset, i.e., the relative rotation quaternion between particle 1 and particle 2 and displacement difference A pixel, based on the interaction between adjacent particles, is defined by the following interaction rule: In a known protein complex structure, there exists a fixed, ideal relative orientation between adjacent units, which is determined by an ideal relative rotation. relative displacement with ideal The pixel is described by successively adjusting the rotation quaternion and translation vector, with the goal of adjusting the current... and Approaching and The adjustment range is based on the offset value, and an adjustment weight is defined. The weighting is set with reference to the step size factor of the relaxation step commonly used in molecular dynamics simulations to ensure the smoothness of the adjustment process and avoid oscillations caused by over-correction. The current... and Rotational differences between Rotate this difference by half, that is , respectively applied to and (One in positive direction, one in negative direction) to make them "closer to each other", similarly, the current displacement vector difference. It needs to be adjusted so that its module length changes from 102.85 pixels to 100.0 pixels, an adjustment of 2.85 pixels. Half of this adjustment (1.425 pixels) will then be applied to... and The position vector, which is about to along point to Move it 1.425 pixels in the direction, and along point to The direction is moved by 1.425 pixels, and the relative rotation and displacement differences are recalculated after each adjustment. For example, the new position of particle 1 after adjustment. and the new position of particle 2 The distance between them is 100.0 pixels, and the new relative rotation... And closer This adjustment process is performed sequentially on a particle and all its neighbors, and is repeated multiple times to generate corrected attitude parameters.

[0086] S303: Based on the corrected attitude parameters, iteratively update the spatial position information and attitude parameters of particles, combine all the updated parameters of particles, and generate optimized attitude information between particles.

[0087] Based on the corrected attitude parameters—that is, the new attitudes of all 7852 particles in the dataset after adjustments through interactions with their neighbors—the spatial position information and attitude parameters of the particles are iteratively updated. This process is carried out within a global framework. In the first iteration, particle 1 is fine-tuned based on its relative attitude offsets with all its neighbors, such as particles 2, 5, and 7, to obtain an updated attitude. and Meanwhile, particle 2 was also adjusted based on its interactions with its neighbors, such as particle 1, particle 3, and particle 8, to obtain... and After all particles have completed a round of response adjustments to all their neighbors, this entire new set of attitude parameters { This constitutes the result of the first iteration. In the second iteration, this new set of attitude parameters will be used to recalculate the relative attitude offset between all adjacent particle pairs and make adjustments again. This process is repeated, for example, for 10 iterations. The number of iterations is set based on monitoring the total attitude change of all particles. When the root mean square displacement of all particle positions is less than 0.1 pixels between two consecutive iterations, and the root mean square value of all rotation angle changes is less than 0.05 degrees, it is determined that balance has been reached, the iteration stops, and the final attitude parameters updated by all particles after the last iteration are combined to form a final list containing 7852 optimized attitudes, generating optimized attitude information between particles.

[0088] Please see Figure 5 The steps for obtaining the projection results of the three-dimensional voxel space density map are as follows:

[0089] S401: Call the corrected particle spatial position information and attitude parameters from the optimized attitude information between particles, extract spatial coordinates, spatial distribution features, shape features and structural features, calculate the distribution position of features in the grid based on the center position, boundary range and arrangement direction of the three-dimensional voxel grid, assign feature values ​​to the corresponding voxel units, and generate voxel feature assignment.

[0090] The corrected particle spatial position information and attitude parameters are retrieved from the optimized attitude information between particles. Taking particle 1 as an example, its final attitude is a translation vector:

[0091] and rotation quaternions;

[0092] The spatial distribution features (point cloud of 158 points), shape features (boundary trajectory), and structural features (topology graph) of the corresponding voxel mesh are extracted. Based on the center position, boundary range, and arrangement direction of the 3D voxel mesh, the mesh is set to be centered at (0,0,0) and has a size of [missing information]. Voxels, each voxel has a size of To calculate the distribution of features within the mesh, first, the geometric center of particle 1 is translated to... The specified location, then, apply The rotation operation represents the rotation of all feature point clouds of the particle, for example, a relative coordinate within the particle. The feature points, whose new coordinates in the global grid are obtained by the formula:

[0093] Calculation, where It is by The rotation matrix of the transformation, It is a local coordinate vector The calculated new coordinates are (46.0, 41.6, 1.2). The feature value is assigned to the corresponding voxel cell. Since the coordinates (46.0, 41.6, 1.2) fall within the cell with voxel index (30, 27, 0) (assuming the grid origin corresponds to index 0, 0, 0), a density value, such as 1.0, is added to the current density value of the voxel cell. This process is called "Splatting". The same operation is performed on all 158 feature points of particle 1, "splatting" their density contribution to the corresponding voxel cell. This operation is performed on all 7852 particles to generate voxel feature assignments.

[0094] S402: Based on voxel feature allocation, according to the center position, boundary range and arrangement direction of the three-dimensional voxel mesh, the spatial distribution features, shape features and structural features are calculated in reverse according to the voxel unit position, the feature distribution is adjusted and the feature reverse distribution is generated.

[0095] Based on voxel feature allocation, where each particle has contributed its feature density to the corresponding cell in the 3D voxel grid, spatial distribution features, shape features, and structural features are inversely calculated according to the voxel cell positions based on the center position, boundary range, and arrangement direction of the 3D voxel grid. This inverse calculation is a weighted process, designed to adjust the contribution weight in the final density map based on the quality of the original particle image. For a voxel that has received the density contribution from particle 1, its current density value is... Multiply this value by the mass factor of particle 1, which is a combination of its shape roundness coefficient and structural regularity. For particle 1, its roundness coefficient is 0.938 and its regularity is 0.75, then its mass factor is:

[0096] If voxel (30,27,0) acquires a density of 1.0 from particle 1, then its weighted density contribution becomes If the voxel also has a quality factor of If particle 2 achieves a density of 0.5, then the weighted contribution from particle 2 is... This process iterates through all voxels that have been assigned density values, replaces the density values ​​with weighted values, adjusts the feature distribution, and generates a feature inverse distribution.

[0097] S403: Based on the feature inverse distribution, integrate the feature values ​​of all voxel units to generate a spatial distribution map of particles in three-dimensional space, output the projection set, and generate the projection result of the three-dimensional voxel spatial density map.

[0098] Based on the inverse distribution of features, where the density value of each voxel in the 3D mesh is weighted by the mass of its source particle, the feature values ​​of all voxel units are integrated. This integration process involves accumulating the weighted contribution values ​​from different particles within each voxel. Continuing with voxel (30,27,0) as an example, it receives a weighted density of 0.844 from particle 1 and a weighted density of 0.375 from particle 2. Assuming it also receives density contributions from 15 other particles, the total weighted density is... ,in It is the original density contributed by particle i. This is the mass factor of particle i. After performing this operation on all 7852 particles in the dataset, the final cumulative density value of voxel (30,27,0) is 35.7. The individual particles perform this accumulation operation, generating a spatial distribution map of the particles in three-dimensional space. This map is a three-dimensional scalar field, where the value at each point represents the electron density at that spatial location. Then, a projection set is output. By integrating or maximizing the three-dimensional spatial distribution map along an axis (e.g., the Z-axis), a two-dimensional projection image is generated. For example, the grayscale value of pixel (30, 27) in the Z-axis projection image is equal to... ,in This is the final density value of the voxels. This step generates a two-dimensional image that can be visually examined. Finally, the complete three-dimensional scalar field is generated, i.e., that... The density array is used as the output result to generate the projection results of the three-dimensional voxel space density map, as shown in Table 2:

[0099] Table 2: Optimized Attitude Information Between Particles

[0100]

[0101] As shown in Table 2, this table lists the final attitude information of some particles after iterative optimization through interaction with neighboring particles. Compared with the initial prediction results, this information is more reasonable in terms of the arrangement of particles.

[0102] Please see Figure 6 The steps for obtaining the protein 3D density map reconstruction results are as follows:

[0103] S501: Based on the projection results of the three-dimensional voxel space density map, call the spatial distribution information and density contribution value of particles in three-dimensional space, perform reconstruction calculation on the spatial position of each particle according to the spatial mapping rules, calculate the position offset and density superposition, and generate a set of position reconstruction points;

[0104] Based on the projection result of the three-dimensional voxel space density map, i.e., a complete three-dimensional density map, the spatial distribution information and density contribution value of particles in three-dimensional space are retrieved. Specifically, the entire... Based on the voxel grid data, a reconstruction calculation is performed on the spatial position of each particle according to a spatial mapping rule. Here, the spatial mapping rule is a known biological constraint, such as C4 symmetry, for any voxel on the asymmetry axis. Its density value is Find the voxels at three corresponding positions under the C4 symmetry operation (rotation 90 degrees around the Z-axis). , , Their density values ​​were read as follows: Calculate the average density at these four locations:

[0105] Update the density values ​​of these four voxels to For example, if the density of voxel (40, 20, 128) is 30.0, the density at its corresponding position (-20, 40, 128) is 28.0, the density at (-40, -20, 128) is 32.0, and the density at (20, -40, 128) is 30.0, then the average density is... The density at these four locations will be updated to 30.0. This process is essentially a symmetric averaging, which calculates the position offset and density superposition, and gathers all the updated voxel coordinates and their new density values ​​to generate a set of reconstructed position points.

[0106] S502: Based on the location, reconstruct the point set, perform convolution operations to process the point set data, update the spatial structure of the 3D density map, calculate the gradient of structural change, and generate the structural update gradient.

[0107] Based on the reconstructed point set (i.e., the 3D density map data after symmetric averaging), a convolution operation is performed on the point set data. This convolution operation uses a... The Laplacian sharpening kernel has a center value of -26 and a value of 1 for its 26 neighbors. This kernel is designed based on the principle of magnifying the difference between density values ​​in a density map and their neighborhood average. This convolution kernel is applied to each voxel in the density map. For example, for voxel (122, 122, 128), its original density is 55.7, and assuming the average density of its 26 neighbors is 40.1, the new value after convolution is... (Ignoring the kernel scaling factor), this operation is performed on the entire 3D density map to obtain a gradient map. The high-value regions of this gradient map correspond to the regions with the most dramatic density changes in the original density map, namely the boundaries of the molecular structure and the location of the internal fine structure. The spatial structure of the 3D density map is updated, and the structural change gradient is calculated. This gradient is the result of the aforementioned convolution operation. It quantifies the direction and intensity of structural optimization at each point and generates the structural update gradient.

[0108] S503: Based on the structure update gradient, perform data optimization operations, adjust the density map structure according to the optimization rules, iteratively update the spatial structure, and generate the protein three-dimensional density map reconstruction result;

[0109] Based on the structure update gradient, i.e., the entire 3D gradient map calculated in the previous step, a data optimization operation is performed. The density map structure is adjusted according to the optimization rule: add the original density map to the proportionally scaled gradient map. The specific expression is: ,in A small update step size is set to 0.05. This value was selected by testing the impact of different step sizes (0.01, 0.05, 0.1, 0.2) on the final structure resolution, choosing a value that achieves the best resolution in the fewest iterations without introducing noise artifacts. Taking voxel (122, 122, 128) as an example, its original density is 55.7, and the calculated gradient value is 15.6. Therefore, its updated density value is:

[0110] This operation makes density peaks sharper and valleys deeper, thereby improving structural clarity. The spatial structure is iteratively updated by repeating the entire process from S501 to S503 (symmetrization, gradient calculation, density update). The number of iterations is set to 20, determined based on the observation that the Fourier shell correlation (FSC) curve of the spectrum reaches a stable plateau after 20 iterations when reconstructing known structures. After 20 iterations, the final three-dimensional density map is output, generating the protein three-dimensional density map reconstruction results, as shown in Table 3.

[0111] Table 3: Three-dimensional voxel spatial density map (Z=128 slice example)

[0112]

[0113] See Table 3, which shows a voxel-sized local slice of the final protein 3D density map in the Z=128 plane. The values ​​represent the cumulative electron density at that spatial location after optimization through the complete reconstruction process. For example, the density value of voxel (122,122) has been updated from 55.7 before symmetry to 56.5.

[0114] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. An end-to-end protein 3D density map depth reconstruction method based on particle images, characterized in that, Includes the following steps: S1: Obtain the spatial and structural information of particles in particle image data, extract spatial distribution shape and structural features through hierarchical convolution, classify and filter according to features, and obtain particle feature representation results; S2: Based on the features of each particle in the particle feature representation results, calculate the rotation and displacement error change rate, iteratively judge the convergence stability, compare the error change rate with a set threshold, correct the attitude of particles that exceed the set threshold, and generate particle attitude prediction results. S3: Based on the spatial position information and attitude parameters of the particles in the particle attitude prediction results, combined with the spacing, direction and arrangement of adjacent particles, calculate the relative rotation and displacement difference, correct the attitude parameters to reduce errors, and generate optimized attitude information between particles. The steps for obtaining the optimized attitude information between particles are as follows: S301: Based on the particle attitude prediction results, call the particle spatial position information and attitude parameters, combine the distance between the center points of adjacent particles, the relative direction vector and the arrangement, calculate the difference in rotation quaternion as the difference in the rotation angle between the two particles, calculate the difference in displacement as the difference in the distance between the center points of the two particles, output a unified set, and generate the relative attitude offset. S302: Based on the relative attitude offset, and according to the interaction between adjacent particles, the rotation quaternion and translation vector are adjusted successively. The adjustment range is based on the offset value. After each adjustment, the relative rotation difference and displacement difference are recalculated to generate the corrected attitude parameters. S303: Based on the corrected attitude parameters, iteratively update the particle spatial position information and attitude parameters, combine all the updated particle parameters, and generate optimized attitude information between particles; S4: Based on the corrected particle spatial position information and attitude parameters in the optimized attitude information between particles, the particle features are mapped to a three-dimensional voxel mesh to generate a three-dimensional voxel space density map projection result. The steps for obtaining the projection results of the three-dimensional voxel space density map are as follows: S401: Call the corrected particle spatial position information and attitude parameters in the optimized attitude information between particles, extract spatial coordinates, spatial distribution features, shape features and structural features, calculate the distribution position of features in the grid according to the center position, boundary range and arrangement direction of the three-dimensional voxel grid, assign feature values ​​to the corresponding voxel units, and generate voxel feature allocation; S402: Based on the voxel feature allocation, according to the center position, boundary range and arrangement direction of the three-dimensional voxel mesh, the spatial distribution features, shape features and structural features are reverse calculated according to the voxel unit position, the feature distribution is adjusted and the feature reverse distribution is generated; S403: Based on the aforementioned reverse distribution of features, integrate the feature values ​​of all voxel units, generate a spatial distribution map of particles in three-dimensional space, output a projection set, and generate a three-dimensional voxel spatial density map projection result. S5: Call the spatial distribution information and density contribution value of particles in the projection result of the three-dimensional voxel space density map, perform three-dimensional decoding and reconstruction, reconstruct the position according to the mapping rules, update the structure through convolution and optimization, and obtain the protein three-dimensional density map reconstruction result.

2. The end-to-end protein 3D density map depth reconstruction method based on particle images according to claim 1, characterized in that: The particle feature representation results include spatial topological relationships, morphological classification labels, and structural integrity indices. The particle attitude prediction results include a three-dimensional attitude matrix, attitude stability coefficient, and error convergence level. The optimized attitude information between particles includes a relative position matrix, orientation consistency parameters, and attitude coordination index. The three-dimensional voxel spatial density map projection results include a voxel distribution matrix, density intensity grading, and spatial connectivity map. The protein three-dimensional density map reconstruction results include a three-dimensional mesh structure, local density distribution, and overall configuration model.

3. The end-to-end protein 3D density map depth reconstruction method based on particle images according to claim 1, characterized in that: The steps for obtaining the particle feature representation results are as follows: S101: Acquire particle image data, perform layered convolution operation to process the image, call the weight of the first layer convolution kernel to calculate pixel distribution, generate spatial distribution coordinate set, call the weight of the second layer convolution kernel to calculate contour change, extract shape boundary trajectory, call the weight of the last layer convolution kernel to analyze texture pattern, output structural topology relationship, merge the spatial distribution coordinate set, shape boundary trajectory and structural topology relationship into a unified set to obtain morphological topology configuration. S102: Based on the morphological topology, calculate the spatial distribution dispersion, shape roundness coefficient and structural regularity, compare the three values ​​with the preset classification threshold, and assign particles to the corresponding groups according to the comparison results to obtain the category assignment identifier; S103: Based on the category assignment identifier, filter particles whose identifier values ​​meet the set conditions, extract their morphological topology, combine them into a feature representation set, and obtain the particle feature representation result.

4. The end-to-end protein 3D density map depth reconstruction method based on particle images according to claim 1, characterized in that: The steps for obtaining the particle attitude prediction results are as follows: S201: Based on the particle feature representation results, extract the spatial distribution features, shape features and structural features of each particle, calculate the rotation quaternion based on the spatial distribution coordinates, calculate the translation vector based on the shape contour, perform consistency verification in combination with structural features, output a unified data set, and generate the initial attitude state. S202: Based on the initial attitude state, calculate the rotation error and displacement error of the current iteration, call the error data of the previous iteration, calculate the error change trend as the ratio of the difference between the current error and the previous error, and generate error dynamics; S203: Based on the aforementioned error dynamics, the particle convergence stability is determined according to the trends of rotation error and displacement error. The trends of rotation error and displacement error are compared with a set convergence threshold. For particles that exceed the threshold, their rotation quaternion and translation vector are adjusted, and the particle posture prediction result is output.

5. The end-to-end protein 3D density map depth reconstruction method based on particle images according to claim 1, characterized in that: The steps for obtaining the protein three-dimensional density map reconstruction results are as follows: S501: Based on the projection result of the three-dimensional voxel space density map, call the spatial distribution information and density contribution value of the particles in the three-dimensional space, perform reconstruction calculation on the spatial position of each particle according to the spatial mapping rules, calculate the position offset and density superposition, and generate a set of position reconstruction points. S502: Reconstruct the point set based on the location, perform convolution operation to process the point set data, update the spatial structure of the 3D density map, calculate the structure change gradient, and generate the structure update gradient. S503: Based on the structure update gradient, perform data optimization operation, adjust the density map structure according to the optimization rules, iteratively update the spatial structure, and generate the protein three-dimensional density map reconstruction result.

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