Method and system for reconstructing three-dimensional structure of cryoelectron microscope based on Gaussian sputtering

Abstract

The invention relates to the technical field of structural biology and computational imaging, and discloses a method and a system for reconstructing a three-dimensional structure of a cryoelectron microscope based on Gaussian sputtering, and the method comprises the following steps: representing the structural information of biomacromolecules by using a three-dimensional Gaussian function; projecting a three-dimensional Gaussian function to a two-dimensional image for imaging according to the structural information, simulating a cryoelectron microscope imaging process, and optimizing imaging positions, shapes and features through a neural network; in the neural network training process, distribution of a Gaussian function is optimized through progressive pruning and a densification process, and three-dimensional structure reconstruction of the cryoelectron microscope is carried out by optimizing the distribution and the shape of the Gaussian function. The system comprises a representation unit, an imaging unit and a three-dimensional structure reconstruction unit. The method is used for solving the limitations of an existing cryoelectron microscope three-dimensional structure reconstruction method in the aspects of insufficient resolution, poor robustness to attitude estimation errors and high noise, high dependence on limited data, low calculation efficiency, insufficient isotropy and the like.

Description

Technical Field

[0001] The present invention relates to the fields of structural biology and computational imaging technology, and in particular to a method and system for three-dimensional structure reconstruction using a cryo-electron microscope based on Gaussian sputtering, which is used to address the limitations of existing three-dimensional structure reconstruction methods using cryo-electron microscopes, such as insufficient resolution, poor robustness to pose estimation errors and high noise, high dependence on limited data, low computational efficiency, and insufficient isotropy. Background Art

[0002] Cryo-electron microscopy (Cryo-EM) is a core technology in structural biology, used to reconstruct the three-dimensional structure of complex biomolecules from two-dimensional projection images. In recent years, Cryo-EM technology has made significant progress in resolving the structure of biomolecules, but it still faces the following key challenges: the reconstruction resolution of existing methods is still far below the theoretical limit under conditions such as high noise, uneven particle orientation distribution, and sample heterogeneity. For example, on the EMPIAR-10492 dataset, the best resolution of existing methods is The theoretical limit is Traditional Fourier transform methods and deep learning-based methods are prone to distortion when dealing with high noise and pose estimation errors. Existing methods struggle to maintain the integrity of structural details, especially when pose estimation errors are large. Biological samples are often dynamic and heterogeneous, and existing methods often fail to accurately reconstruct 3D models of different conformations when dealing with heterogeneous structures. Existing methods also suffer from significant deficiencies in computational efficiency. For example, on the EMPIAR-10076 dataset, CryoNeFEN required 1606 hours and 53GB of memory, making efficient reconstruction difficult on standard hardware. When dealing with complex structures, existing methods suffer from poor isotropy in reconstruction results, resulting in large variations in resolution across different directions. In summary, existing cryo-EM 3D structure reconstruction methods still have significant limitations in terms of resolution, robustness, heterogeneity handling capabilities, and computational efficiency. New approaches that can overcome these challenges are urgently needed.

[0003] The present invention provides a method and system, equipment, and medium for three-dimensional structure reconstruction of cryo-electron microscopy based on Gaussian sputtering, aiming to address the limitations of existing three-dimensional structure reconstruction methods for cryo-electron microscopy, such as insufficient resolution, poor robustness to posture estimation errors and high noise, high dependence on limited data, low computational efficiency, and insufficient isotropy. Summary of the Invention

[0004] This invention provides a cryo-electron microscopy 3D structure reconstruction method, system, equipment, and medium based on Gaussian sputtering. These methods address the limitations of existing cryo-electron microscopy 3D structure reconstruction methods, including insufficient resolution, poor robustness to pose estimation errors and high noise, high dependence on limited data, low computational efficiency, and insufficient isotropy. This method offers advantages such as strong targeting, diverse methods, advanced technology, comprehensive considerations, and a balanced approach, thereby improving reconstruction quality and efficiency.

[0005] The present invention is achieved through the following technical solution: a method for reconstructing three-dimensional structures using a cryo-electron microscope based on Gaussian sputtering, comprising the following steps:

[0006] Step S1, using a three-dimensional Gaussian function to represent the structural information of the biomacromolecule;

[0007] Step S2, projecting the three-dimensional Gaussian function onto a two-dimensional image for imaging based on the structural information, simulating the cryo-electron microscopy imaging process, and optimizing the imaging position, shape, and features through a neural network;

[0008] Step S3, during the training of the neural network, optimizing the distribution of the Gaussian function through a progressive pruning and densification process, and reconstructing the cryo-electron microscopy three-dimensional structure by optimizing the distribution and shape of the Gaussian function

[0009] In order to better implement the present invention, further, step S1 includes:

[0010] The three-dimensional Gaussian function is defined as: G(x)=exp(-0.5(xu) T Σ -1 (xu));

[0011] in, and represents the coordinates in three-dimensional space, And represents the center position of the Gaussian function, is the covariance matrix, which describes the shape and direction of the Gaussian function;

[0012] The covariance matrix ∑ can be decomposed into a scale matrix and the rotation matrix And expressed as ∑=QSS T Q T .

[0013] In order to better implement the present invention, further, step S2 includes:

[0014] Step S21, projecting the three-dimensional Gaussian function into the two-dimensional space, the process is expressed as: and in, is the corresponding angle The rotation matrix below represents the posture of the particle image. P and J are the projection transformation and the corresponding Jacobian matrix, which are used to map the three-dimensional information to the two-dimensional plane and are defined as:

[0015] In step S22, after obtaining the two-dimensional parameters in the two-dimensional space, a rendered image is obtained according to a volume rendering formula; the volume rendering formula is expressed as: Where r′ is the angle The spatial position of the projection ray under i (r′) is the Gaussian weight calculated based on u′ and ∑′, where α i d i is the output of the neural network θ, whose input is the center u of each Gaussian function.

[0016] In order to better implement the present invention, further, step S3 includes:

[0017] Define the learnable parameters of each Gaussian function as: Θ = (u, θ, Q, S);

[0018] Given images taken at different angles by cryo-electron microscopy, The image is defined as Define the loss function as The loss function is used to train Gaussian parameters, and the Gaussian function is voxelized according to the trained Gaussian parameters to reconstruct 3D information and perform cryo-electron microscopy three-dimensional structure reconstruction.

[0019] The present invention also provides a cryo-electron microscopy three-dimensional structure reconstruction system based on Gaussian sputtering, comprising a representation unit, an imaging unit and a three-dimensional structure reconstruction unit, wherein:

[0020] A representation unit for representing the structural information of biological macromolecules using a three-dimensional Gaussian function;

[0021] An imaging unit, configured to project the three-dimensional Gaussian function onto a two-dimensional image for imaging based on the structural information, simulate the cryo-electron microscopy imaging process, and optimize the imaging position, shape, and features through a neural network;

[0022] The three-dimensional structure reconstruction unit optimizes the distribution of the Gaussian function through a progressive pruning and densification process during the training of the neural network, and performs cryo-electron microscopy three-dimensional structure reconstruction by optimizing the distribution and shape of the Gaussian function.

[0023] The present invention also provides an electronic device, which includes a processor and a memory; the processor includes the Gaussian sputtering-based cryo-electron microscopy three-dimensional structure reconstruction system described in the second aspect above.

[0024] The present invention also provides a computer-readable storage medium, which includes instructions; when the instructions are executed on the electronic device described in the third aspect, the electronic device executes the method described in the first aspect.

[0025] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0026] (1) The present invention provides a method and system for three-dimensional structure reconstruction using cryo-electron microscopy based on Gaussian sputtering, which is used to address the limitations of existing three-dimensional structure reconstruction methods using cryo-electron microscopy, such as insufficient resolution, poor robustness to pose estimation errors and high noise, high dependence on limited data, low computational efficiency, and insufficient isotropy.

[0027] (2) The present invention provides a method and system for reconstructing three-dimensional structures using a cryo-electron microscope based on Gaussian sputtering, which has the advantages of strong targeting, diverse methods, advanced technology, comprehensive considerations, and emphasis on balance, thereby improving the quality and efficiency of reconstruction. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] The present invention is further described in conjunction with the following drawings and embodiments, and all concepts and innovations of the present invention should be regarded as disclosed contents and the protection scope of the present invention.

[0029] Figure 1 A flowchart of a method and system for reconstructing three-dimensional structures using a cryo-electron microscope based on Gaussian sputtering provided in an embodiment of the present application;

[0030] Figure 2 A schematic diagram of a cryo-electron microscopy three-dimensional structure reconstruction method based on Gaussian sputtering and an image captured by a cryo-electron microscope in the system provided in an embodiment of the present application;

[0031] Figure 3 A schematic diagram showing different data effects in a cryo-electron microscopy 3D structure reconstruction method based on Gaussian sputtering and a system provided in an embodiment of the present application a;

[0032] Figure 4 A schematic diagram b showing different data effects in a cryo-electron microscopy three-dimensional structure reconstruction method based on Gaussian sputtering and a system provided in an embodiment of the present application;

[0033] Figure 5 A schematic diagram c showing different data effects in a cryo-electron microscopy three-dimensional structure reconstruction method based on Gaussian sputtering and a system provided in an embodiment of the present application;

[0034] Figure 6 Schematic diagram d showing a method for reconstructing three-dimensional structures using a cryo-electron microscope based on Gaussian sputtering and different data effects in the system provided in an embodiment of the present application. DETAILED DESCRIPTION

[0035] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. It should be understood that the described embodiments are only part of the embodiments of the present invention, not all of the embodiments, and therefore should not be regarded as limiting the scope of protection. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technical personnel in this field without making creative work are within the scope of protection of the present invention.

[0036] In the description of the present invention, it should be noted that, unless otherwise expressly specified or limited, the terms "disposed," "connected," and "connected" should be understood in a broad sense. For example, they may refer to fixed, detachable, or integral connections; mechanical or electrical connections; direct or indirect connections through an intermediate medium; and internal communication between two components. Those skilled in the art will understand the specific meanings of the above terms in the present invention.

[0037] Example 1:

[0038] A Gaussian sputtering-based cryo-electron microscopy three-dimensional structure reconstruction method and system of this embodiment, such as Figure 1 As shown in the figure, a three-dimensional Gaussian function is used to represent the structural information of biological macromolecules. The three-dimensional Gaussian function is projected onto a two-dimensional image, and its position, shape, and features are optimized through a neural network. The distribution of the Gaussian function is optimized through a progressive pruning and densification process, which reduces the computational cost. By optimizing the distribution and shape of the Gaussian function, the isotropy of the reconstruction results is improved. Compared with existing methods, CryoGS has significant advantages in many aspects: Figure 3-Figure 6 As shown, it approaches the theoretical limit on multiple datasets, for example, it reaches Approaching the theoretical limit It exhibits excellent robustness under conditions of pose estimation errors, limited data, and high noise; significantly reduces computational time and memory consumption. For example, on the EMPIAR-10076 dataset, CryoGS only requires 11.3 hours and 4.3GB of memory, while existing methods require 1606 hours and 53GB of memory; the resolution of the reconstruction results in different directions is more uniform, significantly improving the integrity of the structure.

[0039] This figure shows the optimization process of the 3D Gaussian distribution, including coordinate adjustment and iterative update of the Gaussian kernel position in 3D space.

[0040] Increase or decrease the number of Gaussian kernels: adjust the number of Gaussian kernels through adaptive splitting or merging operations (such as density control).

[0041] Shape evolution: The Gaussian kernel changes dynamically with optimization. This part intuitively reflects the densification process of the model from coarse-grained to fine-grained.

[0042] Top right - Mathematical and neural network representation of 3D Gaussian including:

[0043] Mathematical modeling: The 3D Gaussian function is defined by a parameter set \(\Theta=(x,S,Q,\alpha)\) (position, scale, rotation, density).

[0044] Neural network assistance: It is possible to predict or optimize Gaussian parameters through deep learning networks (such as MLP) to enhance the ability to characterize complex molecular structures.

[0045] Projection rendering and loss calculation include:

[0046] 3D to 2D projection: The optimized 3D Gaussian model is used to generate a 2D image through differentiable rendering (such as splatting).

[0047] Loss function optimization: The rendered image is compared with the experimental electron microscopy image of the protein molecule at the pixel level, and the error is back-propagated to iteratively adjust the Gaussian parameters to ultimately achieve high-fidelity reconstruction.

[0048] Example 2:

[0049] This embodiment is further optimized based on the first embodiment, and the three-dimensional Gaussian function is defined as: G(x) = exp(-0.5(xu) T Σ -1 (xu));

[0050] in, and represents the coordinates in three-dimensional space, And represents the center position of the Gaussian function, is the covariance matrix, which describes the shape and direction of the Gaussian function;

[0051] The covariance matrix ∑ can be decomposed into a scale matrix and the rotation matrix And expressed as ∑=QSS T Q T .

[0052] This decomposition allows us to independently adjust the magnitude and orientation of the Gaussian function.

[0053] The rest of this embodiment is the same as that of embodiment 1, so it will not be described again.

[0054] Example 3:

[0055] This embodiment further optimizes the above embodiment 1 or 2 by projecting the three-dimensional Gaussian function into the two-dimensional space. The process is expressed as follows: and in, is the corresponding angle The rotation matrix below represents the posture of the particle image. P and J are the projection transformation and the corresponding Jacobian matrix, which are used to map the three-dimensional information to the two-dimensional plane and are defined as:

[0056] After obtaining the two-dimensional parameters in the two-dimensional space, the rendered image is obtained according to the volume rendering formula; the volume rendering formula is expressed as: Where r′ is the angle The spatial position of the projection ray under i (r′) is the Gaussian weight calculated based on u′ and Σ′, where α i d i is the output of the neural network θ, whose input is the center u of each Gaussian function.

[0057] The position, shape, and features are defined by these parameters (Q, S, u, a, d). a and d are optimized through a neural network, while the other parameters are optimized directly without the need for a neural network.

[0058] The rest of this embodiment is the same as any of the above embodiments 1-2, so it will not be repeated here.

[0059] Example 4:

[0060] This embodiment further optimizes any of the above embodiments 1-3. During training, the distribution of Gaussian functions is optimized through pruning and densification. Pruning refers to removing Gaussian functions that contribute less to the reconstruction result to reduce the computational burden; densification refers to subdividing larger Gaussian functions to improve resolution. In the above system, we can define the learnable parameters of each Gaussian function as: Θ = (u, θ, Q, S);

[0061] Given images taken at different angles by cryo-electron microscopy, The image is defined as Define the loss function as According to images from different angles, Gaussian parameters are trained to reconstruct 3D information. Figure 2 Shown are images taken at different angles for training cryo-electron microscopy.

[0062] The loss function is used to train the Gaussian parameters. According to the trained Gaussian parameters, the Gaussian function is voxelized to reconstruct the 3D information and perform cryo-electron microscopy 3D structure reconstruction.

[0063] According to the trained parameters, the Gaussian function is voxelized to obtain 3D information.

[0064] 3D information can be represented by a 3D matrix, such as a D×D×D matrix. For each element in the matrix, we can calculate it using the following formula:

[0065] Where W i (x v ) is the Gaussian weight calculated based on Σ and u, x v Represents the coordinates of the vth voxel.

[0066] The rest of this embodiment is the same as any of the above embodiments 1-3, so it will not be repeated here.

[0067] Example 5:

[0068] The present invention also provides a Gaussian sputtering-based cryo-electron microscopy three-dimensional structure reconstruction system that matches the method, including a representation unit, an imaging unit and a three-dimensional structure reconstruction unit.

[0069] The present invention also provides an electronic device, which includes a processor and a memory; the processor includes the above-mentioned Gaussian sputtering-based cryo-electron microscopy three-dimensional structure reconstruction system.

[0070] Example 6:

[0071] The present invention also provides a computer-readable storage medium comprising instructions; when the instructions are executed on the electronic device described in the above embodiment, the electronic device executes the method described in the above embodiment. Optionally, the computer-readable storage medium may be a memory.

[0072] The processor involved in the embodiments of the present application may be a chip. For example, it may be a field programmable gate array (FPGA), an application specific integrated circuit (ASIC), a system on chip (SoC), a central processor unit (CPU), a network processor (NP), a digital signal processor (DSP), a microcontroller unit (MCU), a programmable logic device (PLD), or other integrated chips.

[0073] The memory involved in the embodiments of the present application may be a volatile memory or a non-volatile memory, or may include both volatile and non-volatile memories. Among them, the non-volatile memory may be a read-only memory (ROM), a programmable read-only memory (PROM), an erasable programmable read-only memory (EPROM), an electrically erasable programmable read-only memory (EEPROM), or a flash memory. The volatile memory may be a random access memory (RAM), which is used as an external cache. By way of example and not limitation, many forms of RAM are available, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDR SDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), and direct RAM bus RAM (DR RAM). It should be noted that the memory of the systems and methods described herein is intended to include, but is not limited to, these and any other suitable types of memory.

[0074] It should be understood that in the various embodiments of the present application, the size of the serial numbers of the above-mentioned processes does not mean the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of the present application.

[0075] Those skilled in the art will appreciate that the modules and algorithm steps of each example described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professional and technical personnel can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0076] Those skilled in the art will clearly understand that, for the convenience and brevity of description, the specific working processes of the systems, devices and modules described above can refer to the corresponding processes in the aforementioned method embodiments and will not be repeated here.

[0077] In the several embodiments provided in this application, it should be understood that the disclosed systems, devices, and methods can be implemented in other ways. For example, the device embodiments described above are merely illustrative. For example, the division of the modules is merely a logical function division. In actual implementation, there may be other division methods, such as multiple modules or components can be combined or integrated into another device, or some features can be ignored or not executed. Another point is that the mutual coupling or direct coupling or communication connection shown or discussed can be through some interfaces, indirect coupling or communication connection of devices or modules, which can be electrical, mechanical or other forms.

[0078] The modules described as separate components may or may not be physically separate, and the components shown as modules may or may not be physical modules, that is, they may be located on a single device or distributed across multiple devices. Some or all of the modules may be selected to achieve the purpose of this embodiment based on actual needs.

[0079] In addition, the functional modules in the various embodiments of the present application may be integrated into one device, or each module may exist physically separately, or two or more modules may be integrated into one device.

[0080] In the above embodiments, it can be implemented in whole or in part by software, hardware, firmware or any combination thereof. When implemented using a software program, it can be implemented in whole or in part in the form of a computer program product. The computer program product includes one or more computer instructions. When loading and executing computer program instructions on a computer, the process or function described in the embodiment of the present application is generated in whole or in part. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable devices. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another computer-readable storage medium. For example, the computer instructions can be transmitted from a website, computer, server or data center by wired (such as coaxial cable, optical fiber, digital subscriber line (DSL)) or wireless (such as infrared, wireless, microwave, etc.) mode to another website, computer, server or data center. The computer-readable storage medium can be any available medium that a computer can access or a data storage device such as a server or data center that contains one or more media that can be integrated. The available medium may be a magnetic medium (eg, a floppy disk, a hard disk, a magnetic tape), an optical medium (eg, a DVD), or a semiconductor medium (eg, a solid state disk (SSD)).

[0081] The above description is only a preferred embodiment of the present invention and does not limit the present invention in any form. Any simple modification or equivalent change made to the above embodiment based on the technical essence of the present invention falls within the scope of protection of the present invention.

Claims

1. A method for three-dimensional structure reconstruction using cryo-electron microscopy based on Gaussian sputtering, characterized in that: The following steps are involved: Step S1, using a three-dimensional Gaussian function to represent the structural information of the biomacromolecule; Step S2, projecting the three-dimensional Gaussian function onto a two-dimensional image for imaging based on the structural information, simulating the cryo-electron microscopy imaging process, and optimizing the imaging position, shape, and features through a neural network; Step S3: During the training of the neural network, the distribution of the Gaussian function is optimized through a progressive pruning and densification process, and the cryo-electron microscopy three-dimensional structure is reconstructed by optimizing the distribution and shape of the Gaussian function.

2. The method for three-dimensional structure reconstruction using cryo-electron microscopy based on Gaussian sputtering according to claim 1, wherein: The step S1 comprises: The three-dimensional Gaussian function is defined as: G(x)=exp(-0.5(xu) T ∑ -1 (xu)) in, and represents the coordinates in three-dimensional space, And represents the center position of the Gaussian function, is the covariance matrix, which describes the shape and direction of the Gaussian function; The covariance matrix ∑ can be decomposed into a scale matrix and the rotation matrix And expressed as QSS T Q T .

3. The method for three-dimensional structure reconstruction using cryo-electron microscopy based on Gaussian sputtering according to claim 1, wherein: The step S2 comprises: Step S21, projecting the three-dimensional Gaussian function into the two-dimensional space, the process is expressed as: and in, is the corresponding angle The rotation matrix below represents the posture of the particle image. P and J are the projection transformation and the corresponding Jacobian matrix, which are used to map the three-dimensional information to the two-dimensional plane and are defined as: In step S22, after obtaining the two-dimensional parameters in the two-dimensional space, a rendered image is obtained according to a volume rendering formula; the volume rendering formula is expressed as: Where r′ is the angle The spatial position of the projection ray under i (r′) is the Gaussian weight calculated based on u′ and ∑′, where α i d i is the output of the neural network θ, whose input is the center u of each Gaussian function.

4. The method for three-dimensional structure reconstruction using cryo-electron microscopy based on Gaussian sputtering according to claim 1, wherein: The step S3 comprises: Define the learnable parameters of each Gaussian function as: Θ = (u, θ, Q, S); Given images taken at different angles by cryo-electron microscopy, The image is defined as Define the loss function as The loss function is used to train Gaussian parameters, and the Gaussian function is voxelized according to the trained Gaussian parameters to reconstruct 3D information and perform cryo-electron microscopy three-dimensional structure reconstruction.

5. A cryo-electron microscopy 3D structure reconstruction system based on Gaussian sputtering, characterized in that: It includes a representation unit, an imaging unit and a three-dimensional structure reconstruction unit, wherein: A representation unit for representing the structural information of biological macromolecules using a three-dimensional Gaussian function; An imaging unit, configured to project the three-dimensional Gaussian function onto a two-dimensional image for imaging based on the structural information, simulate the cryo-electron microscopy imaging process, and optimize the imaging position, shape, and features through a neural network; The three-dimensional structure reconstruction unit optimizes the distribution of the Gaussian function through a progressive pruning and densification process during the training of the neural network, and performs cryo-electron microscopy three-dimensional structure reconstruction by optimizing the distribution and shape of the Gaussian function.

6. An electronic device, characterized in that: It comprises a processor and a memory; the processor is used to run the Gaussian sputtering-based cryo-electron microscopy three-dimensional structure reconstruction system as described in claim 8.

7. A computer-readable storage medium, characterized in that The computer-readable storage medium includes instructions; when the instructions are executed on the electronic device according to claim 6, the electronic device is caused to execute the method according to any one of claims 1 to 7.

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