Protein-ligand interaction prediction method and related device

Abstract

The embodiment of the invention discloses a protein-ligand interaction prediction method and a related device. Determining a prediction interaction pair formed by atoms of the protein and atoms of the ligand molecule according to the data of the protein and the data of the ligand molecule, establishing a loss function according to the node characteristics and the edge characteristics of the real interaction pair and the node characteristics and the edge characteristics of the prediction interaction pair, and adjusting model parameters according to the loss function, the target neural network model can be used for predicting the interaction between any protein and ligand molecules. Physical priori knowledge of protein-ligand interaction is fused in model training and prediction, so that the model can learn characteristics with more biological significance, and the predicted biological correlation is improved. According to the method, the advantages of deep learning are utilized, high-dimensional features are automatically extracted, complex pattern recognition is carried out, the complex relation in protein-ligand interaction is captured, and the stability and accuracy of protein-ligand interaction prediction are improved.

Description

Technical Field

[0001] This application relates to the field of bioinformatics, specifically to a method for predicting protein-ligand interactions, a computer device, and a computer storage medium. Background Technology

[0002] Accurate prediction of protein-ligand interactions is crucial in drug design and development. Traditional experimental methods, such as X-ray crystallography and nuclear magnetic resonance (NMR) spectroscopy, while providing high-precision structural information, are costly and time-consuming. In recent years, machine learning, particularly deep learning, has made significant progress in protein-ligand interaction prediction. Deep learning models can learn complex patterns in large-scale structural data, providing more accurate predictions of molecular properties.

[0003] However, existing machine learning or deep learning models are usually insensitive to geometric transformations of molecules. They require extensive adjustment of model parameters and preprocessing of molecular structure data to adapt to different molecular conformations. As a result, the model's prediction results for molecular properties are heavily dependent on the initial conformation of the molecular structure. It cannot make full use of biological background information during prediction, is prone to overfitting, cannot automatically extract high-dimensional features, and requires a lot of computing resources and time, resulting in poor model stability. Summary of the Invention

[0004] This application provides a protein-ligand interaction prediction method, computer device, and computer storage medium to better capture the complex relationships in protein-ligand interactions and improve the stability and accuracy of protein-ligand interaction prediction.

[0005] The first aspect of this application provides a method for predicting protein-ligand interactions, the method comprising:

[0006] An initial neural network model is obtained by inputting protein data and ligand molecule data into the initial neural network model, so that the initial neural network model performs the following steps based on the protein data and the ligand molecule data:

[0007] Based on the data of the protein and the data of the ligand molecule, a predicted interaction pair consisting of atoms of the protein and atoms of the ligand molecule is determined. The predicted interaction pair is used to indicate that the model predicts that there is an interaction between atoms of the protein and atoms of the ligand molecule.

[0008] Extract the node features and edge features of the predicted interaction pair. The node features are used to represent the features of each atom in the predicted interaction pair, and the edge features are used to represent the features of the interactions present in the predicted interaction pair.

[0009] Obtain the true interaction pairs between the protein and the ligand molecule, establish a loss function based on the node features and edge features of the true interaction pairs and the node features and edge features of the predicted interaction pairs, adjust the model parameters of the initial neural network model according to the loss function, and stop model training when the convergence condition is met to obtain the target neural network model;

[0010] The target neural network model is used to predict the interaction between proteins and ligand molecules.

[0011] A second aspect of this application provides a computer device including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the method of the first aspect described above.

[0012] A third aspect of this application provides a computer storage medium storing instructions that, when executed on a computer, cause the computer to perform the method described in the first aspect.

[0013] As can be seen from the above technical solutions, the embodiments of this application have the following advantages:

[0014] The initial neural network model determines predicted interaction pairs composed of protein atoms and ligand atoms based on protein and ligand molecule data, and extracts node and edge features of these predicted interaction pairs. A loss function is established by comparing the node and edge features of the actual protein-ligand interaction pairs with those of the predicted pairs. The model parameters of the initial neural network model are adjusted according to this loss function until a convergence condition is met, at which point training stops, resulting in the target neural network model. This target neural network model can be used to predict interactions between any protein and ligand molecules. Therefore, model training and prediction integrate prior physical knowledge of protein-ligand interactions, such as hydrogen bonds, hydrophobic interactions, and electrostatic interactions, enabling the model to learn more biologically meaningful features and improve the biological relevance of predictions. Furthermore, leveraging the advantages of deep learning, high-dimensional features are automatically extracted and complex pattern recognition is performed. Compared to traditional rule-based and feature engineering methods, this approach better captures the complex relationships in protein-ligand interactions, improving the stability and accuracy of protein-ligand interaction predictions. Attached Figure Description

[0015] Figure 1This is a flowchart illustrating the protein-ligand interaction prediction method in the embodiments of this application;

[0016] Figure 2 This is another flowchart illustrating the protein-ligand interaction prediction method in the embodiments of this application;

[0017] Figure 3 This is a schematic diagram of the model structure of the equivariant graph neural network in an embodiment of this application;

[0018] Figure 4 This is another schematic diagram of the structure of the computer device in the embodiments of this application. Detailed Implementation

[0019] This application provides a protein-ligand interaction prediction method, computer device, and computer storage medium to better capture the complex relationships in protein-ligand interactions and improve the stability and accuracy of protein-ligand interaction prediction.

[0020] The protein-ligand interaction prediction method in the embodiments of this application is described below:

[0021] Please see Figure 1 One embodiment of the protein-ligand interaction prediction method in this application includes:

[0022] 101. Obtain an initial neural network model, and input protein data and ligand molecule data into the initial neural network model so that the initial neural network model executes steps 102 to 104 based on the protein data and the ligand molecule data;

[0023] The method of this embodiment can be applied to computer devices, which can be servers, terminals, or other computer devices capable of performing data processing. When the computer device is a terminal, it can be a personal computer (PC), desktop computer, or other terminal device; when the computer device is a server, it can be an independent physical server, a server cluster or distributed system composed of multiple physical servers, or a cloud server that provides basic cloud computing services such as cloud databases, cloud computing, big data, and artificial intelligence platforms.

[0024] The computer device can acquire an initial neural network model, which can be any neural network model, such as a graph neural network, convolutional neural network, recurrent neural network, graph embedding-based model, energy function-based physical model, etc. The computer device can input protein data and ligand molecule data into the initial neural network model so that the initial neural network model can be trained based on the data and perform predictions of protein-ligand interactions. The protein data can be any data related to the protein, such as amino acid sequence information, molecular conformation information, elemental composition information, etc.; the ligand molecule data can be any data related to the ligand molecule, such as elemental composition information, molecular structure information, atomic charge information, etc. This embodiment does not limit the specific data included in the protein data and ligand molecule data, as long as the data can affect the prediction of protein-ligand interactions.

[0025] 102. Based on the data of the protein and the data of the ligand molecule, determine a predicted interaction pair consisting of atoms of the protein and atoms of the ligand molecule, wherein the predicted interaction pair is used to indicate that the model predicts that there is an interaction between atoms of the protein and atoms of the ligand molecule.

[0026] Upon receiving data on proteins and ligand molecules, the initial neural network model can determine predicted interaction pairs composed of atoms from both the protein and ligand molecules. These predicted interaction pairs are the atom pairs predicted by the initial neural network model that interact with each other; that is, the protein provides atoms, the ligand molecule provides atoms, and there is an interaction between the atoms provided by both. The number of atoms provided by each is not limited and can be one or more. For example, this interaction can be a hydrogen bond, a hydrophobic interaction, or an electrostatic interaction.

[0027] 103. Extract the node features and edge features of the predicted interaction pair, wherein the node features are used to represent the features of each atom in the predicted interaction pair, and the edge features are used to represent the features of the interactions present in the predicted interaction pair;

[0028] The initial neural network model can further extract the node features and edge features of the predicted interaction pair. The node features of the predicted interaction pair are used to represent the features of each atom in the predicted interaction pair, and the edge features are used to represent the features of the interactions present in the predicted interaction pair.

[0029] For example, if the predicted interaction pair is the hydrogen bond pair between the protein and ligand molecules predicted by the initial neural network model, then the node features of the predicted hydrogen bond pair can be the features of each atom in the hydrogen bond pair, such as information related to the atom, such as its element, charge, whether it is a hydrogen bond donor or a hydrogen bond acceptor; the edge features of the predicted hydrogen bond pair can be information related to the hydrogen bond interaction between the atoms in the hydrogen bond pair, such as a marker indicating the presence of the hydrogen bond interaction, information related to the hydrogen bond interaction, such as a marker indicating the atomic composition of the hydrogen bond interaction.

[0030] 104. Obtain the true interaction pairs between the protein and the ligand molecule, establish a loss function based on the node features and edge features of the true interaction pairs and the node features and edge features of the predicted interaction pairs, adjust the model parameters of the initial neural network model according to the loss function, and stop model training when the convergence condition is met to obtain the target neural network model;

[0031] The computer device can also input the actual interaction pair between the protein and the ligand molecule into the initial neural network model. This actual interaction pair can be obtained from experimental data, or obtained through high-precision calculations, or obtained from existing records in the literature, and there is no limitation here.

[0032] After predicting the interaction pairs, the initial neural network model establishes a loss function based on the node and edge features of the actual interaction pairs between the protein and the ligand molecule, and the node and edge features of the predicted interaction pairs. The model parameters of the initial neural network model are then adjusted according to this loss function until the convergence condition is met, at which point model training stops, resulting in the target neural network model. This target neural network model can be used to predict interactions between any protein and ligand molecule.

[0033] In this embodiment, the initial neural network model determines the predicted interaction pairs composed of protein atoms and ligand molecules based on protein and ligand molecule data, and extracts the node and edge features of the predicted interaction pairs. A loss function is established based on the node and edge features of the actual protein-ligand interaction pairs and the predicted interaction pairs. The model parameters of the initial neural network model are adjusted according to this loss function until the convergence condition is met, at which point model training stops, resulting in the target neural network model. This target neural network model can be used to predict interactions between any protein and ligand molecules. Therefore, model training and prediction integrate prior physical knowledge of protein-ligand interactions, such as hydrogen bonds, hydrophobic interactions, and electrostatic interactions, enabling the model to learn more biologically meaningful features and improve the biological relevance of the predictions. Moreover, leveraging the advantages of deep learning, high-dimensional features are automatically extracted and complex pattern recognition is performed. Compared to traditional rule-based and feature engineering methods, this approach better captures the complex relationships in protein-ligand interactions, improving the stability and accuracy of protein-ligand interaction predictions.

[0034] The following will be discussed in the preceding text. Figure 1 Based on the illustrated embodiments, embodiments of this application will be described in further detail. Please refer to [link / reference]. Figure 2 Another embodiment of the protein-ligand interaction prediction method in this application includes:

[0035] 201. Obtain an initial neural network model, and input protein data and ligand molecule data into the initial neural network model so that the initial neural network model executes steps 202 to 204 based on the protein data and the ligand molecule data;

[0036] In this embodiment, the training samples used for training the initial neural network model can be existing, known data on protein ligand complexes. This data can be derived from experimental data or from existing literature. Alternatively, the training samples can include existing, known data on protein ligand complexes, as well as sample data obtained by data augmentation based on the existing data on protein ligand complexes.

[0037] Specifically, sample data obtained after data augmentation based on existing protein-ligand complex data can be acquired in several ways. One method is to acquire the protein-ligand complex data and perform a geometric transformation on it to obtain geometric transformation data. Another method is to acquire the protein-ligand complex data and perform molecular dynamics simulations based on a preset force field model and simulation parameters to obtain dynamic simulation data. Another method is to acquire the protein-ligand complex data, move each atom, group, or molecule of the protein-ligand complex based on its initial spatial conformation and a preset energy function, calculate the energy of the protein-ligand complex after the movement, and determine the new spatial conformation of the protein-ligand complex based on the energy after the movement.

[0038] The geometric transformation data of the protein-ligand complex, the dynamic simulation data of the protein-ligand complex, and the new spatial conformation of the protein-ligand complex are used as training data for the initial neural network model.

[0039] Data augmentation techniques primarily generate new training samples by performing various geometric transformations and simulations on existing protein-ligand complexes. These techniques can include rotation, translation, mirror transformation, molecular dynamics simulations, Monte Carlo simulations, and more.

[0040] By generating protein-ligand complexes with different conformations through data augmentation techniques, the diversity of training data can be increased, thereby improving the generalization ability of the model and effectively alleviating the problem of data scarcity.

[0041] For example, data augmentation using geometric transformations can include rotation, translation, and mirror transformations, which can alter the spatial conformation of protein-ligand complexes. Rotation refers to randomly selecting a rotation axis and an angle to rotate the protein and ligand separately or simultaneously. For example, the rotation axis can be the x-axis, y-axis, or z-axis, and the rotation angle can be randomly selected between 0 and 360 degrees. Translation refers to randomly translating the protein or ligand to simulate different binding sites. For example, random translations can be performed in the x, y, and z directions, with the translation distance randomly selected within a reasonable range. Mirror transformation refers to mirroring the protein or ligand to simulate its symmetrical conformation. For example, mirroring any one of the x, y, or z directions.

[0042] Molecular dynamics simulations can model the motion of protein-ligand complexes in the natural environment, generating different conformations. Specifically, simulation parameters can be set, including selecting an appropriate force field model (such as AMBER or CHARMM force field models) and setting simulation parameters (such as temperature and pressure). Based on these settings, molecular dynamics simulations of the protein-ligand complex are performed, recording the conformations at different time steps. For example, simulations ranging from a few nanoseconds to tens of nanoseconds can be performed, recording the conformation at regular intervals.

[0043] Monte Carlo simulations can generate different protein-ligand conformations through random sampling. Specifically, an initial conformation and energy function can be set, such as defining an energy function (e.g., binding energy, total energy, etc.). Monte Carlo sampling is then performed based on this initial conformation and energy function, that is, randomly selecting an atom or molecule for a small-range random movement and calculating the energy change after the movement. The energy change is then used to determine whether to accept the new conformation. For example, the Metropolis criterion is commonly used to determine whether to accept the new conformation based on the energy change.

[0044] Of course, a variety of protein-ligand complex conformations can be generated by combining the geometric transformations, molecular dynamics simulations, and Monte Carlo simulations mentioned above.

[0045] For example, assuming a protein-ligand complex structure exists, different conformations can be generated using the various data augmentation techniques described above, increasing the diversity of the training data. Several examples are presented below:

[0046] 1. Examples of geometric transformations;

[0047] 1.1 Rotation:

[0048] The complex is randomly rotated, for example, by 45 degrees around the x-axis, 30 degrees around the y-axis, and 60 degrees around the z-axis.

[0049] A new conformation is generated: the rotated protein-ligand complex.

[0050] 1.2 Translation:

[0051] The complex is randomly translated, for example, translated in the x-direction. Translate in the y direction Translate in the z direction

[0052] A new conformation is generated: the translated protein-ligand complex.

[0053] 1.3 Mirror Transformation:

[0054] Perform a mirror transformation on the complex, such as mirroring the x-direction.

[0055] A new conformation is generated: the mirrored protein-ligand complex.

[0056] 2. Examples of molecular dynamics simulations;

[0057] 2.1 Setting simulation parameters:

[0058] Using the AMBER force field, the simulation temperature was set to 300K and the simulation time to 10ns.

[0059] 2.2 Run the simulation and record the conformation:

[0060] Run molecular dynamics simulations and record the conformation every 1 ns.

[0061] Ten different conformations were generated.

[0062] 3. Monte Carlo simulation example;

[0063] 3.1 Setting the initial conformation and energy function:

[0064] The initial conformation is the primitive protein-ligand complex, and the energy function is the binding energy.

[0065] 3.2 Perform Monte Carlo sampling:

[0066] Randomly select a ligand atom, move it within a small range, and calculate the new energy.

[0067] The decision on whether to accept a new conformation is made according to the Metropolis criterion, and the above steps are repeated multiple times.

[0068] Multiple different conformations are generated.

[0069] Therefore, data augmentation techniques such as geometric transformations, molecular dynamics simulations, and Monte Carlo simulations can generate protein-ligand complexes with various conformations. These augmented data increase the diversity of training data, thereby improving the model's generalization ability and effectively alleviating the data scarcity problem. Specific steps include: geometric transformations, generating different conformations through rotation, translation, and mirroring; molecular dynamics simulations, simulating the motion of protein-ligand complexes in their natural environment and recording the conformations at different time steps; and Monte Carlo simulations, generating different protein-ligand conformations through random sampling. Combining these methods can significantly increase the diversity of training data and improve the model's performance in predicting protein-ligand interactions.

[0070] In this embodiment, the initial neural network model can be any neural network model, such as an Equivariant Graph Neural Network (E-GNN), or other neural networks, such as a Convolutional Neural Network (CNN) that combines 3D structure with 3D convolution operations to extract local 3D structural features and processes the 3D structure of proteins and ligands through voxel representation. Its advantage is that it effectively captures local 3D structural features and directly processes proteins and ligands in 3D space. Alternatively, it can be a Recurrent Neural Network (RNN) that combines sequence features, using the sequence features of proteins and ligands as input, and using RNN or LSTM to capture sequence dependencies. Its advantage is that it excels at processing sequence data and can capture long-range dependencies.

[0071] The neural network can also be a graph embedding-based model, using graph embedding methods (such as DeepWalk and Node2Vec) to embed the graph structure of proteins and ligands into a low-dimensional vector space, and then using traditional machine learning algorithms for prediction. Its advantages include efficient processing of large-scale graph data and the ability to combine multiple graph embedding techniques. Alternatively, it can be a physical model based on energy functions, using molecular dynamics simulations or quantum mechanical calculations to predict protein-ligand interactions based on physical energy functions. Its advantages include a strong physical foundation and accurate reflection of intermolecular interactions.

[0072] 202. Based on the data of the protein and the data of the ligand molecule, determine a predicted interaction pair consisting of atoms of the protein and atoms of the ligand molecule, wherein the predicted interaction pair is used to indicate that the model predicts that there is an interaction between atoms of the protein and atoms of the ligand molecule;

[0073] 203. Extract the node features and edge features of the predicted interaction pair, wherein the node features are used to represent the features of each atom in the predicted interaction pair, and the edge features are used to represent the features of the interactions present in the predicted interaction pair;

[0074] In this embodiment, based on protein data and ligand molecule data, predicted interaction pairs consisting of atoms of the protein and atoms of the ligand molecule are determined. A preferred implementation may involve obtaining the three-dimensional structure of the protein and the three-dimensional structure of the ligand molecule; determining the hydrogen bond donor and hydrogen bond acceptor of the protein based on the three-dimensional structure of the protein; determining the hydrogen bond donor and hydrogen bond acceptor of the ligand molecule based on the three-dimensional structure of the ligand molecule; and identifying hydrogen bond acceptors and hydrogen bond donors whose geometric parameters satisfy preset geometric parameters as predicted hydrogen bond pairs. These predicted hydrogen bond pairs represent the model's prediction that hydrogen bonding exists between atoms of the protein and atoms of the ligand molecule.

[0075] The geometric parameter can be a parameter between the hydrogen bond donor and the hydrogen bond acceptor in two-dimensional or three-dimensional space. For example, it can be the distance between the hydrogen bond donor and the hydrogen bond acceptor, or the angle between the hydrogen bond donor and the hydrogen bond acceptor, etc.

[0076] Hydrogen bonds are formed by the interaction between a donor (hydrogen atom) and an acceptor (such as an oxygen or nitrogen atom). Information about potential hydrogen bond pairs can be extracted by analyzing protein and ligand structures and used as initial features. The specific steps are as follows:

[0077] Step 1: Analyze the structure of proteins and ligands;

[0078] First, the three-dimensional structures of the protein and ligands need to be obtained. This is typically achieved through experimental methods such as X-ray crystallography or nuclear magnetic resonance (NMR), or predicted through computational modeling (such as molecular docking or homology modeling).

[0079] Step 2: Identify hydrogen bond donors and acceptors;

[0080] In protein and ligand structures, the recognition of hydrogen bond donors and acceptors is a crucial step. Hydrogen bond donors are typically hydrogen atoms bonded to highly electronegative atoms (such as oxygen or nitrogen), while hydrogen bond acceptors are electronegative atoms with lone pairs of electrons. The specific recognition steps are as follows:

[0081] Identify hydrogen bond donors, including hydrogen atoms, i.e. hydrogen atoms bonded to atoms with high electronegativity such as oxygen (O), nitrogen (N), and sulfur (S); and donor atoms, i.e. oxygen, nitrogen, or sulfur atoms to which these hydrogen atoms belong.

[0082] It recognizes hydrogen bond acceptors, including acceptor atoms, namely oxygen (O), nitrogen (N), or sulfur (S) atoms with lone pairs of electrons.

[0083] Step 3: Calculate potential hydrogen bond pairs;

[0084] Geometric criteria are used to determine whether a hydrogen bond can form between a hydrogen bond donor and acceptor. Common geometric criteria include the distance criterion, where the distance between the hydrogen bond donor and acceptor is typically 2.5 to... Therefore, the distance from the hydrogen atom of the donor atom to the acceptor atom should be within the reasonable range mentioned above; the angle criterion is that when hydrogen bonds are formed, the angle between the donor atom, hydrogen atom and acceptor atom should be close to a straight line, usually between 150° and 180°.

[0085] Step 4: Construct hydrogen bond features;

[0086] After identifying potential hydrogen bond pairs, this information is encoded as initial features. The specific steps are as follows:

[0087] Hydrogen bond pairs are labeled by creating a binary feature for each pair, indicating whether a hydrogen bond is likely to form. A pair is labeled 1 if it meets both the distance and angle criteria, and 0 otherwise.

[0088] Adding features to the graph structure involves incorporating these hydrogen bond features into the nodes and edges of the graph neural network. For example, node features can contain information about hydrogen bond donors and acceptors, while edge features can contain information about donor-acceptor pairs.

[0089] For example, suppose there is a structure of a protein and a ligand that recognizes the following hydrogen bond donor and acceptor, including the following steps:

[0090] Identify hydrogen bond donors and acceptors. For proteins, hydrogen bond donors and acceptors include: hydroxyl groups (OH) on the side chains of amino acids (donors); amino groups (NH2) (donors); and carboxyl groups (COOH) (acceptors). For ligands, hydrogen bond donors and acceptors include: hydroxyl groups (OH) (donors); amino groups (NH2) (donors); and carboxyl groups (COOH) (acceptors).

[0091] Next, potential hydrogen bond pairs were calculated. The calculations revealed the following potential hydrogen bond pairs: one is between the protein's hydroxyl group (OH) and the ligand's carboxyl group (COOH), with a distance of [missing information]. The angle is 160°; secondly, the distance between the amino group (NH2) of the protein and the hydroxyl group (OH) of the ligand is... The angle is 150°. These hydrogen bond pairs conform to the geometric criteria for hydrogen bond formation and are therefore labeled as possible hydrogen bond pairs.

[0092] Next, hydrogen bond features are constructed, encoding these hydrogen bond pair information as initial features. For example, a binary feature with a value of 1 is added for the edge between the hydroxyl group of the protein and the carboxyl group of the ligand; a binary feature with a value of 1 is added for the edge between the amino group of the protein and the hydroxyl group of the ligand.

[0093] Assuming there is a potential hydrogen bond pair between protein node P1 and ligand node L1 (atoms in the protein molecule or ligand molecule are considered as nodes), the edge characteristics are as follows:

[0094] Edge (P1-L1): [1, 0, 0, ...] (The first feature represents a hydrogen bond with a value of 1).

[0095] Therefore, by analyzing the three-dimensional structure of proteins and ligands, hydrogen bond donor and acceptor atoms can be identified, and potential hydrogen bond pairs can be calculated using distance and angle criteria. The information of potential hydrogen bond pairs is encoded as binary features and added to the node and edge features of the initial neural network model.

[0096] Based on protein and ligand molecule data, predicted interaction pairs consisting of atoms from the protein and ligand molecules are determined. Another preferred implementation involves determining hydrophobic atoms in the protein based on the protein data and hydrophobic atoms in the ligand molecules based on the ligand molecule data, and identifying adjacent hydrophobic atoms among the hydrophobic atoms in the protein and ligand molecules. Therefore, when extracting node and edge features of the predicted interaction pairs, node feature labels can be assigned to the hydrophobic atoms of the protein and ligand molecules respectively. These node feature labels indicate that the labeled atoms are hydrophobic atoms. Furthermore, edge feature labels can be assigned to adjacent hydrophobic atoms, indicating that a hydrophobic interaction exists between these adjacent hydrophobic atoms.

[0097] Hydrophobic interactions occur between hydrophobic residues. By identifying hydrophobic atoms (such as carbon atoms) in proteins and ligands, these atoms can be labeled and associated with specific features, as follows:

[0098] Step 1: Identify hydrophobic atoms;

[0099] Hydrophobic atoms are typically carbon atoms and atoms in the side chains of hydrophobic amino acids. Common hydrophobic amino acids include leucine (Leu), isoleucine (Ile), valine (Val), and phenylalanine (Phe).

[0100] The specific identification steps are as follows: for hydrophobic residues in proteins, the amino acid sequence in the protein can be traversed to identify hydrophobic amino acids, and the side chain atoms (mainly carbon atoms) of these amino acids can be extracted; for hydrophobic atoms in ligands, the chemical structure of the ligands can be examined to identify carbon atoms in hydrophobic regions (such as alkyl chains, aromatic rings, etc.).

[0101] Step 2: Label hydrophobic atoms and add features;

[0102] The identified hydrophobic atoms are labeled as specific features, and these features are added to the node and edge features of the initial neural network model.

[0103] The labeling and characterization steps include adding a binary feature to the labeling of each hydrophobic atom node, indicating whether the atom is hydrophobic. This can be represented by a binary vector. For example, hydrophobic atoms are labeled as 1, and other atoms are labeled as 0.

[0104] In the edge feature labeling, for adjacent hydrophobic atom pairs, a specific edge feature is added to indicate that the edge connects the two hydrophobic atoms. This can be represented by a binary vector. For example, an edge connecting two hydrophobic atoms is labeled as 1, and other edges are labeled as 0.

[0105] For example, assuming a protein and a ligand structure, specific operations are used to identify and label hydrophobic atoms. When identifying hydrophobic atoms, for proteins, hydrophobic amino acids such as leucine (Leu) and phenylalanine (Phe) are identified, and the carbon atoms in the side chains of these amino acids are extracted; for ligands, the chemical structure of the ligand is examined, and the carbon atoms in the alkyl chain are identified.

[0106] Assuming the following hydrophobic atoms are identified, the hydrophobic atoms of proteins include:

[0107] Leucine (Leu): C1, C2, C3;

[0108] Phenylalanine (Phe): C4, C5, C6.

[0109] The hydrophobic atoms of the ligands include:

[0110] Alkyl chains: C7, C8, C9

[0111] Next, a labeling and characterization step is performed, whereby the identified hydrophobic atoms are labeled as specific features and added to the node and edge features of the initial neural network model. For example, for node features, each hydrophobic atom of a protein can be labeled as:

[0112] C1: [1,0,0,...] (The first feature represents a hydrophobic atom with a value of 1);

[0113] C2: [1,0,0,...];

[0114] C3: [1,0,0,...];

[0115] C4: [1,0,0,...];

[0116] C5: [1,0,0,...];

[0117] C6: [1,0,0,...].

[0118] The hydrophobic atoms of the ligand can be labeled as follows:

[0119] C7: [1,0,0,...];

[0120] C8: [1,0,0,...];

[0121] C9: [1,0,0,...].

[0122] For edge features, edges connecting hydrophobic atom pairs can be labeled as:

[0123] Edge (C1-C2): [1,0,0,...] (The first feature represents hydrophobic interaction, with a value of 1);

[0124] Edge (C2-C3): [1,0,0,...];

[0125] Edge (C4-C5): [1,0,0,...];

[0126] Edge (C5-C6): [1,0,0,...];

[0127] Edge (C7-C8): [1,0,0,...];

[0128] Edge (C8-C9): [1,0,0,...].

[0129] Therefore, in this embodiment, hydrophobic atoms can be identified by recognizing hydrophobic amino acids from the amino acid sequence of the protein and extracting carbon atoms from the side chains of these amino acids. Carbon atoms in hydrophobic regions are also identified from the chemical structure of the ligands. Subsequently, hydrophobic atoms are labeled and features are added: binary node features are added to hydrophobic atoms to indicate whether they are hydrophobic; binary edge features are added to the edges connecting hydrophobic atoms to indicate hydrophobic interactions. Furthermore, these features are incorporated into an initial neural network model. By inputting the node and edge features into the initial neural network model, the model can capture hydrophobic interactions, thereby learning more biologically meaningful features and improving the biological relevance of predictions.

[0130] In this embodiment, based on protein data and ligand molecule data, predicted interaction pairs consisting of atoms of the protein and atoms of the ligand molecule are determined. Another preferred embodiment may involve determining the partial charge of each atom in the protein based on the protein data, and determining the partial charge of each atom in the ligand molecule based on the ligand molecule data. Adjacent charged atom pairs are then identified among the partially charged atoms in the protein and the partially charged atoms in the ligand molecule. Therefore, when extracting the node features and edge features of the predicted interaction pairs, the partial charge of each atom in the protein and the partial charge of each atom in the ligand molecule can be used as the node features of that atom. Edge features are then assigned to the adjacent charged atom pairs, representing the electrostatic interaction strength between the two charged atoms in the adjacent charged atom pair.

[0131] Electrostatic interactions are formed between charged atoms (such as positively charged amino acid residues and negatively charged ligand atoms). The partial charge of each atom can be calculated and used as a node feature. Specifically, this may involve several steps:

[0132] Step 1: Calculate the partial charge of each atom;

[0133] Partial charge refers to the actual charge distribution of atoms within a molecule, and is usually not an integer. Partial charge can be calculated using the following methods: quantum chemical calculations, such as using quantum chemical software (e.g., Gaussian, ORCA) to perform electronic structure calculations to obtain the partial charge of each atom; commonly used methods include Mulliken charge analysis and ESP (Electrostatic Potential) charge analysis; and empirical methods, such as using force field-based calculations (e.g., AMBER, CHARMM force fields) to estimate the partial charge. These methods calculate the partial charge using known empirical parameters and molecular force fields.

[0134] Step 2: Label charged atoms and add features;

[0135] The calculated partial charge is added as a node feature to the initial neural network model, and the electrostatic interaction between charged atoms is reflected in the edge features. Specifically, in the labeling and characterization steps, for node features, a numerical feature can be added to each atomic node to represent the partial charge of that atom; for edge features, a specific edge feature can be added to adjacent pairs of charged atoms to indicate that the edge connects the two charged atoms, taking into account the strength of their electrostatic interaction.

[0136] For example, assuming a protein and a ligand structure, the electrostatic interactions are calculated and labeled through specific manipulations. When calculating partial charges, quantum chemical calculation software or force field methods are used to calculate the partial charge of each atom in the protein and ligand. Assume the following partial charges are obtained:

[0137] The charged atoms of a protein and their partial charges:

[0138] Positively charged amino groups (NH3+): Some have a charge of +0.3;

[0139] Negatively charged carboxyl group (COO-): Partial charge is -0.5.

[0140] The charged atoms of the ligands and their partial charges:

[0141] Negatively charged carboxyl group (COOH): partially charged with -0.4;

[0142] Positively charged amine group (NH2): Partial charge is +0.2.

[0143] In the labeling and characterization steps, the calculated partial charges are used as node features, and the electrostatic interactions between charged atoms are reflected in the edge features. For example, the node features of charged atoms in a protein can be represented as follows:

[0144] NH3+: [+0.3,...] (The first numerical characteristic indicates partial charge);

[0145] COO-: [-0.5,...].

[0146] The nodal characteristics of the charged atoms of the ligand can be represented as follows:

[0147] COOH: [-0.4,...];

[0148] NH2: [+0.2,...].

[0149] When labeling edges, a feature is added to edges connecting charged atoms to indicate the strength of the electrostatic interaction. This can be estimated based on the magnitude of the charges and their spatial distance. For example, suppose the following electrostatic interactions are identified:

[0150] NH3+ and COO-: There is a strong electrostatic attraction between the positively charged amino group and the negatively charged carboxyl group, so a feature is added to the edge connecting these two atoms to indicate this strong interaction.

[0151] COOH and NH2: There is also a significant electrostatic interaction between the negatively charged carboxyl group and the positively charged amine group in the ligand. Therefore, a feature is added to the edge connecting these two atoms to reflect this interaction.

[0152] For example, in equivariant graph neural networks, these electrostatic interaction features can be represented as edge features:

[0153] Edge (NH3+-COO-): [Strong electrostatic interaction,...] (The strength of the interaction can be represented by a numerical characteristic);

[0154] Edge (COOH-NH2): [moderate electrostatic interaction,...].

[0155] Therefore, in this embodiment, the partial charge of each atom can be calculated using quantum chemical calculations or force field methods to obtain the partial charge of each atom in the protein and ligand. When labeling charged atoms and adding features, partial charge features can be added to charged atom nodes, and electrostatic interaction features can be added to the edges connecting charged atoms to reflect the interaction strength between the two atoms. These features can also be incorporated into the initial neural network model. By inputting node features and edge features into the initial neural network model, the model can capture electrostatic interactions, thereby learning more biologically meaningful features and improving the biological relevance of predictions.

[0156] 204. Obtain the true interaction pairs between the protein and the ligand molecule, establish a loss function based on the node features and edge features of the true interaction pairs and the node features and edge features of the predicted interaction pairs, adjust the model parameters of the initial neural network model according to the loss function, and stop model training when the convergence condition is met to obtain the target neural network model;

[0157] During model training, a message-passing mechanism can be used to train the initial neural network model. During message passing, specific message functions and update rules can be designed to capture the various physical interactions mentioned above. For example, for hydrogen bond-related message passing, the mechanism can be designed to increase the weight of message passing when hydrogen bonds are likely to form between two atoms, thus making the model pay more attention to these interactions. Similarly, for hydrophobic interaction message passing, the frequency or intensity of message passing can be increased for identified hydrophobic atom pairs to better reflect the impact of hydrophobic interactions on the overall structure. For electrostatic interaction message passing, the influence of electrostatic interactions is considered during the message passing process, and the message passing weights between charged atoms are adjusted to ensure these interactions are appropriately reflected in the model.

[0158] In designing the loss function, specific physical interaction constraints can be added to further incorporate prior physical knowledge to ensure that the model can correctly capture and predict these interactions.

[0159] The following are the specific operating steps and examples.

[0160] 1. Hydrogen bond constraint;

[0161] The hydrogen bond constraint term aims to encourage the model's predicted hydrogen bonds to be close to the actual hydrogen bonds. This can be achieved by adding an extra term to the loss function that penalizes the difference between the model's predicted hydrogen bonds and the actual hydrogen bonds.

[0162] Detailed operation steps:

[0163] Step 1: Identify real hydrogen bonds:

[0164] Obtain real hydrogen bond information, including hydrogen bond donor and acceptor pairs, from experimental data or high-precision calculations.

[0165] Step 2: Hydrogen bonds predicted by the model.

[0166] The model outputs predicted hydrogen bond information, including predicted hydrogen bond donor and acceptor pairs.

[0167] Step 3: Calculate hydrogen bond loss:

[0168] Add a hydrogen bond constraint term to the loss function, which can be defined as the difference between the hydrogen bonds predicted by the model and the actual hydrogen bonds. A common approach is to calculate the sum of squared differences between predicted and actual hydrogen bond pairs.

[0169] For example, suppose we have the following hydrogen bond pairs:

[0170] Real hydrogen bond pairs: [(donor 1, acceptor 1), (donor 2, acceptor 2)];

[0171] The model predicts the following hydrogen bond pairs: [(donor 1', acceptor 1'), (donor 2', acceptor 2')].

[0172] The hydrogen bond constraint term in the loss function can be expressed as:

[0173] Hydrogen bond loss = Σ[(donor i - donor i')^2 + (acceptor i - acceptor i')^2];

[0174] The aforementioned hydrogen bond loss can be calculated using the nodal characteristics of hydrogen bond donors and acceptors. The nodal characteristics of hydrogen bond donors and acceptors have been described previously and will not be repeated here.

[0175] 2. Hydrophobic interaction constraint;

[0176] The hydrophobic interaction constraint ensures that the model correctly captures the interactions between hydrophobic atoms. This constraint can be added to the loss function to reflect the differences in the interaction strength between pairs of hydrophobic atoms.

[0177] Detailed operation steps:

[0178] Step 1: Identify the actual hydrophobic interactions:

[0179] Obtain real information about hydrophobic atom pairs from experimental data or high-precision calculations.

[0180] Step 2: Model-predicted hydrophobic interactions:

[0181] The model outputs predicted information about hydrophobic atom pairs.

[0182] Step 3: Calculate the hydrophobic interaction loss:

[0183] Add a hydrophobic interaction constraint term to the loss function, which can be defined as the difference between the predicted hydrophobic atom pairs and the actual hydrophobic atom pairs.

[0184] For example, suppose we have the following hydrophobic atom pairs:

[0185] True hydrophobic atom pairs: [(atom 1, atom 2), (atom 3, atom 4)];

[0186] The model predicts the hydrophobic atom pairs: [(atom 1', atom 2'), (atom 3', atom 4')].

[0187] The hydrophobic interaction constraint term in the loss function can be expressed as:

[0188] Hydrophobic interaction loss = Σ[(atom i - atom i')^2 + (atom j - atom j')^2].

[0189] The hydrogen bond loss mentioned above can be calculated using the nodal characteristics of hydrophobic atoms. The nodal characteristics of hydrophobic atoms have been described above and will not be repeated here.

[0190] 3. Electrostatic interaction constraint;

[0191] The electrostatic interaction constraint term enables the model to accurately predict the interactions between charged atoms. This can be achieved by adding a constraint term to the loss function that reflects the difference between the predicted charged atom pairs and the actual charged atom pairs.

[0192] Detailed operation steps:

[0193] Step 1: Identify real electrostatic interactions:

[0194] Obtain real information about charged atom pairs from experimental data or high-precision calculations.

[0195] Step 2: Electrostatic interactions predicted by the model.

[0196] The model outputs predicted information about charged atom pairs.

[0197] Step 3: Calculate electrostatic interaction losses:

[0198] Add an electrostatic interaction constraint term to the loss function, which can be defined as the difference between the predicted charged atom pairs and the actual charged atom pairs.

[0199] For example, suppose we have the following pairs of charged atoms:

[0200] Real charged atom pairs: [(positively charged atom 1, negatively charged atom 1), (positively charged atom 2, negatively charged atom 2)];

[0201] The model predicts the following charged atom pairs: [(positively charged atom 1', negatively charged atom 1'), (positively charged atom 2', negatively charged atom 2')].

[0202] The electrostatic interaction constraint term in the loss function can be expressed as:

[0203] Electrostatic interaction loss = Σ[(charged atom i - charged atom i')^2 + (charged atom j - charged atom j')^2].

[0204] The hydrogen bond loss mentioned above can be calculated using the nodal characteristics of charged atoms. The nodal characteristics of charged atoms have been described above and will not be repeated here.

[0205] Therefore, the overall loss function design for model training can integrate these constraint terms into the overall loss function, which can be expressed as:

[0206] Total loss = basic loss + λ1 * hydrogen bond loss + λ2 * hydrophobic interaction loss + λ3 * electrostatic interaction loss.

[0207] Here, λ1, λ2, and λ3 are weighting parameters used to adjust the contribution of each constraint term to the total loss.

[0208] Therefore, by incorporating hydrogen bond constraints, hydrophobic interaction constraints, and electrostatic interaction constraints into the loss function, prior physical knowledge can be further integrated to ensure that the model can more accurately capture and predict these interactions. Specific steps include identifying real physical interactions, interactions predicted by the model, and calculating the corresponding loss constraint terms. Through these operations, the model can learn more biologically meaningful features, improving the biological relevance of its predictions.

[0209] In this embodiment, the initial neural network model can be an Advanced Equivariant Model (AEMM), which can better capture the complex relationships in protein-ligand interactions. AEMM leverages the advantages of deep learning to automatically extract high-dimensional features and perform complex pattern recognition, thus enabling it to better capture the complex relationships in protein-ligand interactions. Compared to traditional rule-based and feature engineering methods, this model has stronger expressive and generalization capabilities. For example, an AEMM can be an equivariant graph neural network.

[0210] Advanced isovariant models can capture the complex relationships in protein-ligand interactions in several ways:

[0211] 1. Multi-scale feature extraction;

[0212] By extracting features at multiple scales, the model can capture the details of protein-ligand interactions at different scales (e.g., atomic, group, and molecular).

[0213] Specifically, this includes capturing the properties and interactions of individual atoms, such as atom type, charge, and bonding state, for atomic-level features; extracting the characteristics of amino acid residues or ligand functional groups and capturing the interactions between groups for group-level features; and integrating the geometric and topological features of the entire molecular structure, such as the overall shape and size of the molecule, for molecular-level features.

[0214] The model can process information at different scales through feature extraction modules at different scales, and then synthesize the information in the final stage.

[0215] 2. Attention mechanisms;

[0216] Through attention mechanisms, the model can dynamically focus on important interaction areas and ignore irrelevant parts, thereby capturing complex relationships more accurately.

[0217] Its specific implementation includes self-attention and multi-head attention mechanisms. Using self-attention, the model can dynamically adjust the nodes and edges it focuses on when calculating node and edge features. Self-attention calculates the correlation between each node and its neighbors and dynamically adjusts the weights based on this correlation.

[0218] Using a multi-head attention mechanism, the model can capture the features of interaction from multiple perspectives, with each attention head responsible for a different feature extraction perspective.

[0219] 3. Multi-perspective data fusion;

[0220] By fusing data from multiple perspectives, the model can integrate various types of data, such as structural data, sequence data, and physicochemical property data, to comprehensively understand protein-ligand interactions from different perspectives.

[0221] Its specific implementation includes, for structural data, processing the three-dimensional structural data of proteins and ligands to capture spatial conformation and geometric relationships; for sequence data, processing the sequence data of proteins and ligands to capture the linear sequence information of amino acids or chemical groups; and for physicochemical property data, including properties such as hydrogen bonding, hydrophobicity, and electrostatic interactions, extracting and integrating them into the overall features through specific physicochemical models.

[0222] The model processes different types of data through multiple channels and synthesizes them in a fusion layer to capture more comprehensive interaction features.

[0223] 4. Guided by the energy function;

[0224] By using energy function-based guidance, the model can more directly reflect the physical nature of protein-ligand interactions, optimize structural energy, and capture stable interaction modes.

[0225] Its specific implementation includes: an energy function design step, which designs energy functions based on physicochemical principles, including binding energy and potential energy, to guide the training and optimization of the model; an energy optimization step, which uses the energy function as part of the loss during model training to optimize the structure of the protein-ligand complex, making it tend towards a low-energy, stable conformation; and an energy minimization path step, which simulates the energy minimization path of protein-ligand binding, captures the dynamic process from the free state to the bound state, and extracts stable binding features.

[0226] For example, suppose we want to construct an advanced isovariant model to predict protein-ligand binding energies, capturing complex relationships through the mechanisms described above. This includes the following steps:

[0227] 1. Multi-scale feature extraction;

[0228] Atomic-level features: Extracting features such as charge and bonding state of each atom.

[0229] Group-level characteristics: extracting the characteristics of amino acid residues and ligand functional groups.

[0230] Molecular-level characteristics: the overall structural features of proteins and ligands.

[0231] 2. Attention mechanisms;

[0232] Self-attention mechanism: In graph neural networks, the self-attention mechanism is used to dynamically adjust the weights of nodes and edges, focusing on important interaction regions.

[0233] Multi-head attention mechanism: Extract interaction features from multiple perspectives through multi-head attention mechanism.

[0234] 3. Multi-perspective data fusion;

[0235] Structural data: Processing three-dimensional structural data to capture spatial configuration.

[0236] Sequence data: Processing sequence data and capturing information about linear sequences.

[0237] Physicochemical properties data: Integrating properties such as hydrogen bonding, hydrophobicity, and electrostatic interactions.

[0238] 4. Guided by the energy function;

[0239] Energy function design: Design a binding energy function to guide model optimization.

[0240] Energy optimization: During training, the structure of the protein-ligand complex is optimized using an energy function.

[0241] Energy minimization path: Simulate the dynamic process of binding and extract stable binding characteristics.

[0242] Through these mechanisms, models can capture the complex relationships in protein-ligand interactions more comprehensively and accurately, improving the accuracy and biological relevance of predictions.

[0243] For example, taking the equivariant graph neural network as an example, such as Figure 3 The model structure of the isovariant graph neural network shown is as follows: the model takes node features and edge features as input, extracts features from the input through graph convolutional layers, captures the interaction regions between proteins and ligands through graph attention layers, captures the details of protein-ligand interactions at different scales through multi-scale feature extraction layers, captures the various physical interactions mentioned above through message passing layers based on specific message functions and update rules, integrates various types of data such as structural data, sequence data, and physicochemical property data to comprehensively understand protein-ligand interactions from different perspectives, integrates data from multiple physical prior knowledge layers, pooling layers and fully connected layers to aggregate features and map features to the sample label space, and outputs the model's prediction results based on the fused features.

[0244] In some preferred embodiments, to significantly improve computational efficiency and complete the prediction task in a shorter time, advanced isovariant models can utilize parallel computing and efficient graph neural network (GNN) architectures for protein-ligand interaction prediction. The specific implementation steps and methods are as follows:

[0245] 1. Parallel computing;

[0246] Parallel computing can significantly accelerate the training and prediction processes of deep learning models. The following are specific implementation methods for parallel computing:

[0247] 1.1 Data parallelism;

[0248] Data parallelism is the most common parallel computing method, which divides the data into multiple subsets and processes each subset in parallel. Its steps include:

[0249] Data splitting: Dividing a large amount of data into multiple mini-batches, each of which is processed in parallel by different processing units (such as GPUs or TPUs).

[0250] Synchronous update: At the end of each iteration, the gradients calculated by each processing unit are summarized and the model parameters are updated synchronously.

[0251] 1.2 Model Parallelism;

[0252] Model parallelism is suitable for situations where there are too many model parameters and a single device cannot accommodate them. It involves dividing the model into multiple parts and computing each part in parallel. The steps include:

[0253] Model partitioning: Divide the model into different layers or parts and distribute them to multiple devices, with each device responsible for computing a part of the model.

[0254] Coordinated computation: Devices need to coordinate and communicate with each other via high-speed interconnects (such as NVLink and InfiniBand) to transmit intermediate computation results.

[0255] 1.3 Hybrid Parallelism;

[0256] Hybrid parallelism combines data parallelism and model parallelism, making it suitable for scenarios requiring further optimization of computational efficiency. Its steps include:

[0257] Combined use: Simultaneously process data and models in parallel. For example, use data parallel processing to process multiple small batches of data, while dividing the model into multiple parts for parallel computation on different devices.

[0258] 2. Highly efficient graph neural network architecture;

[0259] Efficient graph neural network architectures can fully utilize hardware resources and improve computational efficiency. Here are some key strategies:

[0260] 2.1 Graph Convolutional Networks (GCNs);

[0261] Graph convolutional networks aggregate features of nodes and their neighbors through graph convolution operations. This is achieved through the following strategies:

[0262] Sparse matrix operations: Using sparse matrix storage graph structures, efficient sparse matrix operations are performed, reducing computational load and memory usage.

[0263] Neighbor sampling: In large-scale graphs, neighbor sampling is used to randomly select some neighbors for calculation, reducing the complexity of each calculation.

[0264] 2.2 Graph Attention Network (GAT);

[0265] Graph attention networks assign different weights to each neighbor node through an attention mechanism, aggregating features. This is achieved through the following strategies:

[0266] Parallel Attention Heads: Using a multi-head attention mechanism, multiple attention heads are computed in parallel, enhancing the model's expressive power and computational efficiency.

[0267] Efficient implementation: The implementation of the attention mechanism is optimized by using matrix operations instead of loops to improve computational efficiency.

[0268] 3. Graph pooling and subgraph generation;

[0269] Graph pooling and subgraph generation techniques are used to reduce graph size and improve computational efficiency. They are achieved through the following strategies:

[0270] Graph pooling: Using graph pooling operations (such as Top-k pooling, SAGPool, etc.) to reduce large graphs into smaller graphs, thereby reducing computational load.

[0271] Subgraph generation: In a large-scale graph, several subgraphs are generated, and each subgraph is processed in parallel to reduce the scale of each computation.

[0272] The following are the specific steps to achieve efficient computation using parallel computing and an efficient GNN architecture:

[0273] Step 1: Prepare the parallel computing environment;

[0274] Hardware configuration: Configure a multi-GPU or TPU environment to ensure that the hardware supports parallel computing.

[0275] Software configuration: Use a deep learning framework that supports parallel computing, such as TensorFlow or PyTorch.

[0276] Step 2: Parallel data processing;

[0277] Data partitioning: The training dataset is divided into multiple mini-batch datasets for parallel processing.

[0278] Distributed training: Using distributed training frameworks (such as Horovod, PyTorch Distributed) to train models in parallel.

[0279] Step 3: Parallel processing of the model;

[0280] Model partitioning: Divide a large GNN model into multiple parts and distribute them to different devices.

[0281] Collaborative computing: Coordinating computations across different parts of the network through high-speed interconnected devices and transmitting intermediate results.

[0282] Step 4: Optimize the GNN architecture;

[0283] Using sparse matrices: Store graph structures for efficient sparse matrix operations.

[0284] Neighbor sampling: In large-scale graphs, randomly select some neighbors for computation to reduce the complexity of each computation.

[0285] Multi-head attention: Parallel computation of multiple attention heads enhances expressive power and computational efficiency.

[0286] Graph pooling and subgraph generation: reduce graph size and improve computational efficiency.

[0287] For example, suppose we want to build an advanced isovariant model to predict protein-ligand interactions, and achieve efficient computation through parallel computing and an efficient GNN architecture.

[0288] 1. Parallel computing;

[0289] Data parallelism: The training dataset is divided into multiple mini-batches, and each GPU processes a mini-batch in parallel.

[0290] Model parallelism: Different layers of the GNN model are distributed across multiple GPUs, with each GPU responsible for computing features of a portion of the layers.

[0291] 2. High-efficiency GNN architecture;

[0292] Graph Convolutional Networks (GCNs): Use sparse matrices to store graph structures and perform efficient sparse matrix convolution operations.

[0293] Graph Attention Network (GAT): Uses a multi-head attention mechanism to compute multiple attention heads in parallel, optimizing attention computation.

[0294] Graph pooling and subgraph generation: Reduce large graphs into smaller graphs and process multiple subgraphs in parallel to reduce computational scale.

[0295] Therefore, these measures can significantly improve the computational efficiency of the model, shorten the prediction task time, and enhance the model's application effect in protein-ligand interactions.

[0296] In other preferred embodiments, after model training is complete, the model can be further cross-validated and tuned. To achieve significantly higher accuracy than traditional methods in predicting protein-ligand binding sites and binding modes, the following steps can be used to train and validate large-scale datasets, perform cross-validation, and tune hyperparameters to ensure model stability and performance:

[0297] 1. Cross-validation;

[0298] Cross-validation is used to evaluate the stability and performance of a model, avoiding overfitting and underfitting. For example, K-fold cross-validation can be used, and its steps include:

[0299] Data partitioning involves dividing the dataset into K subsets. In each iteration, one subset is selected as the validation set, and the remaining subsets are used as the training set.

[0300] Training and validation are performed in K iterations. In each iteration, the model is trained using K-1 subsets and validated using the remaining subset.

[0301] The results are combined, and the average performance metrics (such as accuracy, AUC, etc.) are calculated.

[0302] 2. Hyperparameter tuning;

[0303] Model performance can be improved by optimizing the model's hyperparameters through hyperparameter tuning. Strategies include:

[0304] Grid search allows you to define the range of hyperparameters, such as the learning rate, the number of hidden layers, and the number of nodes.

[0305] Exhaustive search is used to train and validate the model for each hyperparameter combination, and the combination with the best performance is selected.

[0306] Random search allows you to define the range of hyperparameters, set the search range for hyperparameters, and perform random sampling. Randomly sampled hyperparameter combinations are used for model training and validation, and the combination with the best performance is selected.

[0307] Bayesian optimization allows you to define a hyperparameter space, set the search range for hyperparameters, and perform iterative optimization. Using the Bayesian optimization method, you can iteratively optimize the selection of hyperparameters based on the performance of the current combination of hyperparameters.

[0308] 3. Model evaluation and validation;

[0309] Appropriate performance metrics can be selected to evaluate the model's performance in predicting protein-ligand binding sites and binding modes. For example, these performance metrics may include the following:

[0310] Accuracy is the degree to which the predicted result matches the actual result.

[0311] AUC (Area Under the ROC Curve) is a metric used to evaluate the classification performance of a model.

[0312] Mean squared error (MSE) is used to evaluate prediction error in regression tasks.

[0313] When evaluating the results, the validation set can be used to assess the model's performance and adjust the model and hyperparameters; alternatively, an independent test set can be used to evaluate the model's final performance and ensure its generalization ability.

[0314] For example, to build an advanced isovariant model to predict protein-ligand binding sites and binding modes, cross-validation and optimization are required:

[0315] 1. Cross-validation;

[0316] Perform K-fold cross-validation (e.g., K=5), using 4 subsets to train the model and 1 subset to validate it in each iteration. Combine the results of 5 iterations to calculate the average accuracy and AUC.

[0317] 2. Hyperparameter tuning;

[0318] The hyperparameters of the model are optimized using grid search and random search methods.

[0319] Bayesian optimization is used to further fine-tune the hyperparameters and find the optimal combination for performance.

[0320] 3. Model evaluation and validation;

[0321] Use validation and test sets to evaluate the model's performance.

[0322] We selected metrics such as accuracy, AUC, and MSE to ensure high accuracy and stability of the model in predicting protein-ligand binding sites and binding modes.

[0323] Through these steps, an efficient and accurate advanced isovariant model can be constructed, which is significantly superior to traditional methods in predicting protein-ligand binding sites and binding modes.

[0324] In chemical molecular modeling, it is often desirable to predict certain properties of molecules (such as energy levels and reactivity). However, the position and orientation of molecules in three-dimensional space may undergo rotation, translation, and mirror transformations, which can affect the predictive stability of traditional models. To address this issue, Equivariant Graphical Neural Networks (E-GNNs) are designed with specific structures that make the model invariant and equivariant to these geometric transformations.

[0325] Therefore, in some preferred embodiments of this example, feature extraction and property prediction of the ligand molecule can also be performed on the ligand molecule. Thus, ligand molecule data can be input into the initial neural network model, causing the initial neural network model to perform the following steps based on the ligand molecule data: extracting node features of the ligand molecule, the node features representing the properties of each atom in the ligand molecule; extracting edge features of the ligand molecule, the edge features representing the properties of chemical bonds in the ligand molecule; and encoding and transforming the coordinates of each atom of the ligand molecule according to the geometric transformation of the ligand molecule to obtain the positional encoding features of each atom of the ligand molecule.

[0326] Each atom of the ligand molecule can be considered as a node. For each node, the data of its neighboring nodes are obtained, and the data of all neighboring nodes are aggregated to obtain aggregated information. The data of the node is then updated based on this aggregated information. The data of the neighboring nodes includes the node features, edge features, and position encoding features of the neighboring nodes. After each node completes its data update, the feature vector of each node is obtained. The feature vectors of all nodes of the ligand molecule are aggregated to obtain the global features of the ligand molecule. The global features are then converted into the index values ​​of the target index of the ligand molecule.

[0327] Positional feature encoding is a crucial step in equivariant graphical neural networks (E-GNNs), especially when dealing with molecular geometric transformations (such as rotation, translation, and mirroring), ensuring the model's invariance and equivariance to these transformations. Several specific methods for positional feature encoding are described in detail below.

[0328] When encoding and transforming the coordinates of each atom of the ligand molecule according to the geometric transformation of the ligand molecule to obtain the position encoding feature of each atom of the ligand molecule, a preferred embodiment may be to calculate the coordinates of the geometric center of the ligand molecule based on the coordinates of the atoms of the ligand molecule, perform a translation operation on all atoms of the ligand molecule so that the geometric center is located at the origin of the coordinate system; and, for each atom of the ligand molecule, calculate the coordinates of the atom after the translation operation based on the coordinates of the atom before the translation operation and the coordinates of the geometric center before the translation operation, and use the coordinates of the atom after the translation operation as the position encoding feature of the atom.

[0329] To achieve translation invariance, the geometric center of the ligand molecule is the average of the coordinates of all atoms in the molecule. Assuming there are N atoms in the molecule, the coordinates of the i-th atom are (x...). i y i , zi The coordinates of the geometric center are (x, y). center y center , z center The calculation is as follows:

[0330]

[0331] Translate the atomic coordinates, shifting the coordinates of all atoms so that the geometric center is located at the origin. Then the new coordinates (x, y) of the i-th atom are... i ′,y i ′,z i The calculation of ′) is as follows:

[0332] x′ i =x i -x center ;

[0333] g′ i =g i -g center ;

[0334] z′ i =z i -z center .

[0335] In obtaining the positional coding features of each atom of the ligand molecule by encoding and transforming the coordinates of each atom according to the geometric transformation of the ligand molecule, another preferred embodiment may be to calculate the spherical coordinates of the atom based on the coordinates of the atom of the ligand molecule, wherein the spherical coordinates include the sphere radius, polar angle and azimuth angle; encode the spherical coordinates of each atom of the ligand molecule according to the spherical harmonic function to obtain the spherical harmonic function value of each atom of the ligand molecule, and use the spherical harmonic function value of each atom as the positional coding feature of the atom.

[0336] To achieve rotational isotropy, the three-dimensional coordinates of atoms need to be specially encoded so that these codes change accordingly during rotation. A common method is to use spherical harmonics.

[0337] Spherical harmonics are a set of functions defined on a unit sphere that can naturally handle rotational problems in three-dimensional space. The specific steps are as follows:

[0338] For each atom, its Cartesian coordinates (x, y, z) can be converted to spherical coordinates (r, θ, φ), where:

[0339]

[0340] φ = arctan2(y, x) (azimuth angle).

[0341] Calculate the spherical harmonic function value:

[0342] Spherical harmonics (θ, φ) is determined by angles θ and φ, where l is the order and m is the degree. The definition of a spherical harmonic function is as follows:

[0343]

[0344] Where Plm is the associated Legendre polynomial.

[0345] Encoding position using spherical harmonic functions:

[0346] Encoding the spherical coordinates (θ, φ) of each atom using spherical harmonic functions yields a set of eigenvalues. Different orders and degrees produce different combinations of eigenvalues. By selecting appropriate values ​​for l and m, a set of rotationally equivalent eigenvalues ​​can be generated.

[0347] In another preferred embodiment, when encoding and transforming the coordinates of each atom of the ligand molecule according to the geometric transformation of the ligand molecule to obtain the position encoding feature of each atom of the ligand molecule, a preset plane is used as the reflection plane, and the coordinates of each atom of the ligand molecule are mirrored based on the reflection plane to obtain the mirrored transformation coordinates of each atom of the ligand molecule, and the mirrored transformation coordinates of each atom are used as the position encoding feature of that atom.

[0348] For example, mirror morphology requires that positional features be adjusted accordingly during a mirror transformation. The steps to achieve this are as follows:

[0349] Define a mirror operation, which is typically a reflection of a plane. Assuming the reflection plane is the xy plane, the mirror transformation of the coordinates of any atom in the ligand molecule can be expressed as:

[0350] (x, y, z) → (x, y, -z).

[0351] The feature adjustment following the mirror transformation involves corresponding adjustments to the features encoded by the spherical harmonic function. For example, in spherical coordinates after the mirror transformation, the polar angle θ becomes π-θ, ​​while the azimuth angle φ remains unchanged or undergoes specific changes. Accordingly, the spherical harmonic function values ​​are also adjusted to ensure that the encoded features correctly reflect the mirror transformation.

[0352] In summary, positional feature encoding ensures equivariance and invariance to molecular geometric transformations through the following steps:

[0353] Translation invariance: By moving the geometric center of the molecule to the origin, the translation does not affect the feature representation.

[0354] Rotational isomorphism: Atomic positions are encoded using spherical harmonic functions to ensure that features change according to rules during rotation.

[0355] Mirroring and Equivariation: Define mirroring operations and adjust the encoded features accordingly to ensure that the mirror transformation is correctly reflected.

[0356] By using the above positional feature encoding methods, the equivariant graph neural network can handle the geometric transformations of molecules more stably and accurately, thereby improving the model's predictive performance.

[0357] When extracting nodal features of each atom in a ligand molecule, these features can include the following aspects:

[0358] 1.1 Atom Types:

[0359] Each atom has a specific type, such as carbon (C), hydrogen (H), oxygen (O), etc. Atom types can be represented using one-hot encoding. For example, if there are 5 different atom types, then a carbon atom can be represented as [1,0,0,0,0], and a hydrogen atom can be represented as [0,1,0,0,0].

[0360] 1.2 Atomic number:

[0361] Atomic number is the position of an element in the periodic table; for example, carbon has an atomic number of 6, and hydrogen has an atomic number of 1. This can be used directly as a numerical characteristic.

[0362] 1.3 Electronegativity of atoms:

[0363] Electronegativity refers to an atom's ability to attract electrons, which has a significant impact on chemical reactions and molecular structure. For example, fluorine has an electronegativity of 3.98, and carbon has an electronegativity of 2.55. This is also a numerical characteristic.

[0364] 1.4 Atomic mass:

[0365] The mass of an atom can be used as another numerical characteristic. For example, the atomic mass of carbon is approximately 12.01, and the atomic mass of hydrogen is approximately 1.008.

[0366] 1.5 Atom Hybrid Orbital Types:

[0367] Different atoms may have different hybrid orbital types, such as sp, sp2, sp3, etc. These types can be represented using one-hot encoding.

[0368] For example, assuming an ethane molecule has two carbon atoms and six hydrogen atoms, each atom can be initialized with the following characteristics:

[0369] Atom type: represented by unique thermal encoding, a carbon atom (C) can be represented as [1, 0]; a hydrogen atom (H) can be represented as [0, 1].

[0370] Atomic number: expressed numerically, the carbon atom (C) can be represented as 6; the hydrogen atom (H) can be represented as 1.

[0371] Electronegativity: Expressed numerically, carbon atom (C) can be represented as 2.55; hydrogen atom (H) can be represented as 2.20.

[0372] Atomic mass: expressed numerically, the carbon atom (C) can be represented as 12.01; the hydrogen atom (H) can be represented as 1.008.

[0373] Hybrid orbital type: represented by uniquely thermal encoding (assuming all are sp3), then a carbon atom (C) can be represented as [1, 0, 0]; a hydrogen atom (H) can be represented as [1, 0, 0].

[0374] Thus, the node features of a carbon atom can be represented as a vector [1, 0, 6, 2.55, 12.01, 1, 0, 0], and the node features of a hydrogen atom can be represented as [0, 1, 1, 2.20, 1.008, 1, 0, 0].

[0375] When extracting edge features of ligand molecules, these features can include the following aspects:

[0376] 2.1 Key Type:

[0377] Chemical bonds come in different types, such as single bonds, double bonds, and triple bonds. They can be represented using one-hot coding. For example, a single bond is represented as [1, 0, 0], a double bond as [0, 1, 0], and a triple bond as [0, 0, 1].

[0378] 2.2 Key length:

[0379] The length of a chemical bond can affect the properties of a molecule. The actual length of a bond can be represented using numerical characteristics.

[0380] 2.3 Key Angle:

[0381] In some cases, bond angles have a significant impact on the geometry and properties of molecules. Bond angles can be represented using numerical characteristics.

[0382] Electron cloud distribution of 2.4 bonds:

[0383] The electron cloud distribution describes the electron density on the bond, which can be obtained using quantum chemical calculations and serves as a numerical characteristic.

[0384] For example, assuming all chemical bonds in an ethane molecule are single bonds, each bond can be initialized with the following characteristics:

[0385] Key type: If represented by one-hot encoding, a single key can be represented as [1, 0, 0].

[0386] Bond length: expressed numerically (assuming CH bond length is 1). The CC bond length is If the CH bond is represented as 1.09, then the CC bond can be represented as 1.54.

[0387] Bond angle: Represented by numerical characteristics (assuming the CCH bond angle is 109.5 degrees), the CCH bond angle can be expressed as 109.5.

[0388] Electron cloud distribution: represented by numerical characteristics (assuming a certain calculated electron density), then the electron density is assumed to be a certain value.

[0389] Thus, the edge features of each CH bond can be represented as a vector [1, 0, 0, 1.09, 109.5, some value], and the edge features of each CC bond can be represented as [1, 0, 0, 1.54, 109.5, some value].

[0390] Furthermore, node information can be updated based on a message-passing mechanism. The message-passing mechanism is a core step in Graph Neural Networks (GNNs), through which nodes can exchange information with their neighbors, thereby updating their features. In Equivariant Graph Neural Networks (E-GNNs), the message-passing mechanism needs to be designed to maintain equivariance, ensuring that the model is invariant and equivariant to geometric transformations of the input molecules (such as rotation, translation, and mirroring).

[0391] Message computation refers to each node receiving information from its neighboring nodes and calculating the message to be passed to itself. The specific steps are as follows:

[0392] Collecting neighbor information: Each node collects information from all its directly connected neighbor nodes. This information includes the characteristics of the neighbor nodes, the characteristics of the edges between the two nodes, and the location information of the neighbor nodes.

[0393] Combining feature and location information: Messages are computed by combining the features and location information of neighboring nodes. For example, a node can determine how it should update itself based on the features and relative positions of its neighbors. This process needs to consider the effects of geometric transformations, such as how the relative positions of nodes change under rotation, translation, and mirror transformations.

[0394] Isovariability Design: The design of message computation needs to ensure equivariance of geometric transformations. For example, when a molecule is rotated, the relative positions of neighboring nodes will change. Therefore, the message computation function must be designed to correctly handle this change, so that the feature update after rotation is consistent with that before rotation.

[0395] Message aggregation refers to the process by which each node integrates the messages received from all its neighboring nodes. The specific steps are as follows:

[0396] Collect all messages: Each node will collect the messages received from all its neighboring nodes, which may contain information from multiple different sources.

[0397] Aggregation methods: These methods (such as summation, averaging, or maximization) are used to integrate all received messages into a single, unified message. Choosing the appropriate aggregation method is crucial for ensuring equivariance, as the aggregation method must be insensitive to the order of neighboring nodes. For example, summation and averaging methods inherently possess this characteristic.

[0398] Global feature consideration: In some designs, global features can be added so that when a node is updated, it not only considers local neighbor information, but also refers to the global information of the entire molecule.

[0399] Furthermore, feature updating refers to each node using the aggregated messages to update its own features. The specific steps are as follows:

[0400] Combining aggregated messages with their own characteristics: Each node combines the aggregated message with its own characteristics. This process can be accomplished through simple addition, weighted summation, or other non-linear combinations.

[0401] Apply an update function: Use an update function to process the combined features and messages. This update function needs to be designed to maintain isotropy under geometric transformations; for example, ensure that the update result after rotation is consistent with the result before rotation.

[0402] Ensuring stability and accuracy: By designing a reasonable update mechanism, ensure that the feature update process of each node is stable and accurate after receiving and processing information, unaffected by the geometric transformation of the input molecules.

[0403] Through the detailed message passing mechanism design described above, the Equivariant Graph Neural Network (E-GNN) ensures equivariance and invariance to geometric transformations (such as rotation, translation, and mirroring). Specifically, in the message computation phase, by combining the features and positional information of neighboring nodes, it ensures that each node can correctly handle the effects of geometric transformations. In the message aggregation phase, by selecting an appropriate aggregation method, it ensures that the process of integrating neighboring node information is insensitive to the node's order, maintaining equivariance. In the feature update phase, by rationally designing the update function, it ensures that the feature update process of nodes under geometric transformations remains stable and accurate.

[0404] Taking ethane molecule (C2H6) as an example, the message calculation includes the following steps:

[0405] 1. Collect neighbor information:

[0406] Suppose we are dealing with carbon atom C1. C1's neighboring nodes include another carbon atom C2 and three hydrogen atoms H1, H2, and H3. C1 needs to collect information from these neighboring nodes, including the characteristics of each neighboring node, the characteristics of the edges between C1 and C1, and the location information of the neighboring nodes.

[0407] Characteristics of a carbon atom (C2): type (carbon), electronegativity, atomic mass, etc.

[0408] Characteristics of hydrogen atoms H1, H2, and H3: type (hydrogen), electronegativity, atomic mass, etc.

[0409] Edge characteristics: There is a single bond between C1 and C2, and there is also a single bond between C1 and H1, H2, and H3.

[0410] Location information: The positions of C2, H1, H2 and H3 relative to C1.

[0411] 2. Combining features and location information:

[0412] C1 combines the features of these neighboring nodes with their relative position information. Assuming that in the original coordinate system, C2's coordinates are (1.54,0,0), H1's coordinates are (0.77,0.77,0), and H2 and H3's coordinates are similar, these positional features are transformed into rotationally equivalent features through spherical harmonic function encoding.

[0413] 3. Isovariant design:

[0414] The message computation function ensures that messages received by C1 from C2 and H1, H2, and H3 remain consistent under geometric transformations (such as rotation, translation, and mirroring). For example, if the entire molecule is rotated 90 degrees, the message function will process the relative positions after the rotation so that the messages received by C1 still correctly reflect the molecular structure.

[0415] Message aggregation involves the following steps:

[0416] 1. Collect all messages:

[0417] After receiving messages from C2, H1, H2, and H3, C1 needs to integrate these messages. Assume the message received from C2 is M_C2, the message received from H1 is M_H1, and so on.

[0418] 2. Aggregation methods:

[0419] To maintain equivariance, addition is chosen as the aggregation method. C1 adds all received messages together to form a comprehensive message M_C1. M_C1 = M_C2 + M_H1 + M_H2 + M_H3.

[0420] This aggregation method ensures the stability of messages regardless of changes in the node arrangement order.

[0421] Feature updates involve the following steps:

[0422] 1. Combining aggregated messages with its own characteristics:

[0423] C1 combines the aggregated message M_C1 with its own features. Assume that the initial feature of C1 is H_C1.

[0424] Update feature = function (H_C1+M_C1).

[0425] 2. Apply the update function:

[0426] Use a nonlinear update function to process the combined features and messages. For example, use an activation function to add nonlinear features, thereby better capturing the complexity of molecular structures.

[0427] 3. Ensure stability and accuracy:

[0428] The updated features will reflect the effects of molecular structural changes on C1 after receiving messages from C2 and H1, H2, and H3. If there are molecular rotations or mirror transformations, the update function ensures that these geometric transformations do not alter the equivariance of C1's updated features.

[0429] For example, suppose that in the initial state, C1 has the characteristics [carbon, 2.55, 12.01], C2 has the characteristics [carbon, 2.55, 12.01], and H1 has the characteristics [hydrogen, 2.20, 1.008]. There is a single bond between C1 and C2, and there are also single bonds between C1 and H1, H2, and H3. The position information of C1 is encoded as P_C1 using a spherical harmonic function.

[0430] The message M_C2 received by C1 from C2 may be the encoded result of combining the features of C2 with the positional features.

[0431] The message M_H1 received by C1 from H1 is similar.

[0432] The aggregated message M_C1 is the sum of M_C2, M_H1, M_H2, and M_H3.

[0433] After rotating 90 degrees, the relative positions of C1 with C2, H1, H2, and H3 change. The spherical harmonic function encoding ensures that the new positional features can correctly reflect the situation after rotation, and the messages M_C2, M_H1, etc., after the message function adjustment can still maintain consistency.

[0434] Furthermore, feature updating and aggregation are key steps in Equivariant Graph Neural Networks (E-GNNs). Through multi-layer message passing, the features of each atom are progressively updated, ultimately reflecting the structural information of the entire molecule. The following is a detailed description of this process, including multi-layer message passing, feature updating, and global aggregation operations.

[0435] I. Multi-level message passing:

[0436] In E-GNN, the message passing mechanism is implemented through a multi-layer network. Each layer performs a process of message computation, message aggregation, and feature update. The main purpose of multi-layer message passing is to propagate information layer by layer, so that the features of each node (atom) can gradually contain the global information of the entire molecule.

[0437] The steps include:

[0438] Initial characteristics: Each atom (node) has its initial characteristics, such as atom type, electronegativity, atomic mass, etc.

[0439] The first layer of message passing: Each node receives messages from its neighboring nodes, computes and aggregates these messages, and then updates its own characteristics. The updated characteristics include not only the atom's own information, but also information about its direct neighbors.

[0440] Subsequent message passing layers: In each layer of message passing, each node's features continue to receive messages from its neighboring nodes (including direct and indirect neighbors) and are updated accordingly. Through multiple layers of passing, nodes gradually aggregate information from more distant neighbors. For example, in the second layer of message passing, each node's features will include information about its direct neighbors and the neighbors of those neighbors.

[0441] Multi-level iteration: After multiple layers of message passing, the features of each node gradually contain information about the entire molecular structure, reflecting a broader graph structure.

[0442] II. Feature Update:

[0443] Feature updates in each layer of message passing are achieved through a designed update function, ensuring that the feature update process can capture the complexity of the molecular structure and maintain equivariance.

[0444] Update process:

[0445] Combining aggregated messages and its own characteristics: In each layer, each node combines the messages aggregated from its neighboring nodes with its own characteristics. The combination can be a simple addition or a more complex combination.

[0446] Applying nonlinear transformations: The combined features are updated through nonlinear update functions (e.g., linear transformation plus activation function), which increases the complexity and nonlinearity of feature representation.

[0447] III. Global Aggregation Operations:

[0448] After completing multi-level message passing and feature updates, the features of each node need to be aggregated into a global feature vector, representing the structural information of the entire molecule. The global aggregation operation integrates the features of all nodes into a single global feature vector, used to predict the overall properties of the molecule.

[0449] Global aggregation methods:

[0450] Summation aggregation: Summing the features of all nodes yields a global feature. This method is simple and effective, and it preserves equivariance.

[0451] Average aggregation: Calculate the average of all node features as the global feature. This method is applicable to molecules of different sizes, ensuring consistent scale of the global feature.

[0452] Maximum value aggregation: This method extracts the maximum value of each dimension of all node features to form a global feature. It can capture salient information from the features.

[0453] Attention-based aggregation: This method uses an attention mechanism to sum the features of each node in a weighted manner based on their importance, forming a global feature. This approach dynamically adjusts the contribution of each node's feature to the global feature set.

[0454] Taking ethane molecule (C2H6) as an example, its multi-layered message passing is as follows: assuming the initial characteristics of ethane molecule are: carbon atom (C1, C2): type (carbon), electronegativity, atomic mass; hydrogen atom (H1, H2, H3, H4, H5, H6): type (hydrogen), electronegativity, atomic mass.

[0455] After the first layer of message passing, the characteristic of each carbon atom is updated by adding the messages received from three hydrogen atoms and one other carbon atom to its own characteristic. The characteristic of a hydrogen atom is updated by adding the messages from the carbon atoms connected to it to its own characteristic.

[0456] After the second layer of message passing, the characteristics of each carbon atom are further updated, including characteristics from neighboring hydrogen atoms and characteristic information from indirectly connected hydrogen atoms.

[0457] Its global aggregation operation is as follows: after completing multi-level message passing and feature updates, assume that the final features of each atom are: carbon atoms C1 and C2, with feature vectors A and B; hydrogen atoms H1 to H6, with feature vectors C, D, E, F, G, H.

[0458] Then, using the summation aggregation method: Global features = A + B + C + D + E + F + G + H.

[0459] Using the average aggregation method: Global features = (A+B+C+D+E+F+G+H) / 8.

[0460] The resulting global feature vector is used to predict a specific chemical property of the ethane molecule. Through these detailed steps, E-GNN can reflect the global information of the molecule in the final feature representation, improving the stability and accuracy of the prediction.

[0461] In Equal Variation Graph Neural Networks (E-GNNs), the output layer is responsible for transforming the aggregated global features into the final prediction result. This step is crucial because it directly determines the model's predictive performance. The design of the output layer needs to take into account the specific requirements of the target task, such as classification or regression. The following is a detailed description of the output layer and its application in examples.

[0462] The main function of the output layer is to receive the global features aggregated from the previous layers and map them to the target prediction value. The design of the output layer typically involves the following steps:

[0463] The global feature input, obtained from the global aggregation operation, will be used as the input to the output layer.

[0464] Linear transformation maps a high-dimensional global feature vector to the desired output dimension. It is typically implemented using a fully connected layer, with the formula: Output = Weight Matrix * Input Features + Bias Vector.

[0465] The activation function should be chosen appropriately based on the specific task. For regression tasks, linear activation functions are typically used; for classification tasks, non-linear activation functions (such as ReLU, Sigmoid, or Softmax) are typically used.

[0466] Output dimension adjustment: Adjust the output dimension according to task requirements. For example, for binary classification tasks, the output can be a scalar (activated by Sigmoid); for multi-class classification tasks, the output can be a vector (activated by Softmax).

[0467] Taking ethane molecules as an example, the operation of outputting prediction results in the output layer includes the following steps:

[0468] 1. Global feature input;

[0469] Through multi-layer message passing and global aggregation operations, the global feature vector of the ethane molecule is obtained. Assume the global feature vector is G, with dimension d. This means that G contains the feature information of all atoms in the molecule, comprehensively reflecting the structure and properties of the entire molecule.

[0470] 2. Linear transformation;

[0471] The global feature vector G is linearly transformed through a fully connected layer. The specific steps are as follows:

[0472] Define the weight matrix and bias vector:

[0473] The weight matrix W has dimensions m x d, where m is the output dimension and d is the input feature dimension. The bias vector b has dimensions m.

[0474] Calculate the linear transformation:

[0475] The global feature vector G is linearly transformed using a weight matrix and a bias vector, calculated as follows:

[0476] Output = W*G+b

[0477] This step maps the high-dimensional global feature vector G to the desired output dimension m.

[0478] Assuming we are predicting energy levels, here m = 1, because only a single scalar output is needed. Assuming the dimension of G is 128, then the dimension of W is 1 x 128, and the dimension of b is 1.

[0479] 3. Activation function;

[0480] Choose an appropriate activation function based on the specific task. Since this is a regression task (predicting energy levels), a linear activation function is used: final output = W*G + b.

[0481] No additional nonlinear activation function is needed here; the result of the linear transformation is used directly as the final output.

[0482] 4. Adjust output dimensions;

[0483] Since the task is to predict a scalar (energy level), the output dimension already meets the requirements. Therefore, no further adjustment of the output dimension is needed.

[0484] The following is the complete process for a specific example.

[0485] Suppose that through multi-layer message passing and global aggregation, the global feature vector G of the ethane molecule is obtained as follows: G = [0.5, -0.3, 0.8, ..., 0.2] (a vector of length 128).

[0486] Next, define the weight matrix W and the bias vector b:

[0487] W = [0.2, -0.1, 0.4, ..., 0.5] (a vector of length 128, since W is 1 x 128); b = 0.1.

[0488] Calculate the linear transformation: Output = W*G + b.

[0489] Detailed calculation steps:

[0490] Output = (0.2 * 0.5) + (-0.1 * -0.3) + (0.4 * 0.8) + ... + (0.5 * 0.2) + 0.1

[0491] Multiply all elements and sum them, then add the bias b to obtain the final output:

[0492] Output = 1.2 (assuming the calculation result).

[0493] Therefore, through the above steps, the global feature vector of the ethane molecule was successfully converted into a scalar output representing the predicted energy level value. This process includes global feature input, linear transformation, and an appropriate activation function, while ensuring that the output layer design meets the task requirements. In practical applications, this prediction result can be used for further chemical analysis or experimental verification, thus demonstrating the powerful capabilities of E-GNN in chemical molecule modeling.

[0494] The computer device in the embodiments of this application is described below. Please refer to [link / reference]. Figure 4 One embodiment of the computer device in this application includes:

[0495] The computer device 400 may include one or more central processing units (CPUs) 401 and a memory 405, in which one or more applications or data are stored.

[0496] The memory 405 can be volatile or persistent storage. The program stored in the memory 405 can include one or more modules, each module including a series of instruction operations on the computer device. Furthermore, the central processing unit 401 can be configured to communicate with the memory 405 and execute the series of instruction operations stored in the memory 405 on the computer device 400.

[0497] The computer device 400 may also include one or more power supplies 402, one or more wired or wireless network interfaces 403, one or more input / output interfaces 404, and / or one or more operating systems, such as Windows Server™, Mac OS X™, Unix™, Linux™, FreeBSD™, etc.

[0498] The central processing unit 401 can perform the aforementioned... Figures 1 to 2 The specific operations performed by the computer device in the illustrated embodiment will not be described in detail here.

[0499] This application also provides a computer storage medium, one embodiment of which includes: the computer storage medium storing instructions, which, when executed on a computer, cause the computer to perform the aforementioned... Figures 1 to 2 The operations performed by the computer device in the illustrated embodiment.

[0500] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working processes of the systems, devices, and units described above can be referred to the corresponding processes in the foregoing method embodiments, and will not be repeated here.

[0501] In the several embodiments provided in this application, it should be understood that the disclosed systems, apparatuses, and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be an indirect coupling or communication connection between apparatuses or units through some interfaces, and may be electrical, mechanical, or other forms.

[0502] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0503] Furthermore, the functional units in the various embodiments of this application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0504] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

Claims

1. A method for predicting protein-ligand interactions, characterized in that, The method includes: An initial neural network model is obtained by inputting protein data and ligand molecule data into the initial neural network model, so that the initial neural network model performs the following steps based on the protein data and the ligand molecule data: Based on the data of the protein and the data of the ligand molecule, a predicted interaction pair consisting of atoms of the protein and atoms of the ligand molecule is determined. The predicted interaction pair is used to indicate that the model predicts that there is an interaction between atoms of the protein and atoms of the ligand molecule. Extract the node features and edge features of the predicted interaction pair. The node features are used to represent the features of each atom in the predicted interaction pair, and the edge features are used to represent the features of the interactions present in the predicted interaction pair. Obtain the true interaction pairs between the protein and the ligand molecule, establish a loss function based on the node features and edge features of the true interaction pairs and the node features and edge features of the predicted interaction pairs, adjust the model parameters of the initial neural network model according to the loss function, and stop model training when the convergence condition is met to obtain the target neural network model; The target neural network model is used to predict the interaction between proteins and ligand molecules.

2. The method according to claim 1, characterized in that, The determination of the predicted interaction pairs consisting of atoms of the protein and atoms of the ligand molecule includes: Obtain the three-dimensional structure of the protein and the three-dimensional structure of the ligand molecule; determine the hydrogen bond donor and hydrogen bond acceptor of the protein based on the three-dimensional structure of the protein; determine the hydrogen bond donor and hydrogen bond acceptor of the ligand molecule based on the three-dimensional structure of the ligand molecule. In the hydrogen bond acceptor and hydrogen bond donor of the protein, and in the hydrogen bond acceptor and hydrogen bond donor of the ligand molecule, the hydrogen bond acceptor and hydrogen bond donor whose geometric parameters satisfy the preset geometric parameters are identified as predicted hydrogen bond pairs. The predicted hydrogen bond pairs are used to indicate that the model predicts that there is a hydrogen bond interaction between the atoms of the protein and the atoms of the ligand molecule.

3. The method according to claim 1, characterized in that, The determination of the predicted interaction pairs consisting of atoms of the protein and atoms of the ligand molecule includes: Hydrophobic atoms in the protein are determined based on the protein data, and hydrophobic atoms in the ligand molecules are determined based on the ligand molecule data; Identify adjacent hydrophobic atoms in the hydrophobic atoms of the protein and the hydrophobic atoms of the ligand molecule; The extraction of node features and edge features of the predicted interaction pairs includes: Node feature labels are assigned to the hydrophobic atoms of the protein and the hydrophobic atoms of the ligand molecule, respectively, and the node feature labels are used to indicate that the labeled atoms are hydrophobic atoms; The adjacent hydrophobic atoms are assigned edge feature labels, which are used to indicate that there is a hydrophobic interaction between the adjacent hydrophobic atoms.

4. The method according to claim 1, characterized in that, The determination of the predicted interaction pairs consisting of atoms of the protein and atoms of the ligand molecule includes: The partial charge of each atom in the protein is determined based on the protein data, and the partial charge of each atom in the ligand molecule is determined based on the ligand molecule data; Identify adjacent charged atom pairs among the partially charged atoms of the protein and the partially charged atoms of the ligand molecule. The extraction of node features and edge features of the predicted interaction pairs includes: The partial charge of each atom in the protein is used as the node feature of that atom, and the partial charge of each atom in the ligand molecule is used as the node feature of that atom. The adjacent charged atom pairs are assigned edge features, which are used to represent the electrostatic interaction strength between the two charged atoms in the adjacent charged atom pairs.

5. The method according to claim 1, characterized in that, The method further includes: Input the ligand molecule data into the initial neural network model so that the initial neural network model performs the following steps based on the ligand molecule data: Extract the node features of the ligand molecule, which are used to represent the properties of each atom of the ligand molecule in the ligand molecule; The edge features of the ligand molecule are extracted, and the edge features are used to represent the properties of the chemical bonds in the ligand molecule; The coordinates of each atom in the ligand molecule are encoded and transformed according to the geometric transformation of the ligand molecule to obtain the position encoding features of each atom in the ligand molecule; Each atom of the ligand molecule is considered as a node. For each node, the data of its neighboring nodes are obtained, and the data of all neighboring nodes are aggregated to obtain aggregated information. The data of the node is updated according to the aggregated information. The data of the neighboring nodes includes the node features, edge features, and position encoding features of the neighboring nodes. After each node completes the data update, the feature vector of each node is obtained. The feature vectors of all nodes of the ligand molecule are aggregated to obtain the global features of the ligand molecule. The global features are converted into index values ​​of the target index of the ligand molecule.

6. The method according to claim 5, characterized in that, The step of encoding and transforming the coordinates of each atom of the ligand molecule according to the geometric transformation of the ligand molecule to obtain the positional encoding features of each atom of the ligand molecule includes: The coordinates of the geometric center of the ligand molecule are calculated based on the coordinates of the atoms of the ligand molecule; All atoms of the ligand molecule are translated such that the geometric center is located at the origin of the coordinate system; and, For each atom of the ligand molecule, the coordinates of the atom after the translation operation are calculated based on the coordinates of the atom before the translation operation and the coordinates of the geometric center before the translation operation, and the coordinates of the atom after the translation operation are used as the position encoding feature of the atom.

7. The method according to claim 5, characterized in that, The step of encoding and transforming the coordinates of each atom of the ligand molecule according to the geometric transformation of the ligand molecule to obtain the positional encoding features of each atom of the ligand molecule includes: The spherical coordinates of the atom are calculated based on the coordinates of the atom in the ligand molecule, and the spherical coordinates include the sphere radius, polar angle, and azimuth angle. The spherical coordinates of each atom in the ligand molecule are encoded according to the spherical harmonic function to obtain the spherical harmonic function value of each atom in the ligand molecule, and the spherical harmonic function value of each atom is used as the position encoding feature of that atom.

8. The method according to claim 5, characterized in that, The step of encoding and transforming the coordinates of each atom of the ligand molecule according to the geometric transformation of the ligand molecule to obtain the positional encoding features of each atom of the ligand molecule includes: Using a preset plane as the reflection plane, the coordinates of each atom of the ligand molecule are mirrored based on the reflection plane to obtain the mirrored transformation coordinates of each atom of the ligand molecule. The mirrored transformation coordinates of each atom are used as the position encoding feature of that atom.

9. The method according to claim 1, characterized in that, The method further includes: Data on the protein-ligand complex is acquired, and geometric transformation is performed on the data to obtain geometric transformation data of the protein-ligand complex. And / or, Data of the protein-ligand complex is obtained, and molecular dynamics simulation of the protein-ligand complex is performed based on a preset force field model and simulation parameters to obtain dynamic simulation data of the protein-ligand complex. And / or, Data of the protein-ligand complex is acquired, and each atom, group, or molecule of the protein-ligand complex is moved based on the initial spatial conformation of the protein-ligand complex and a preset energy function. The energy of the protein-ligand complex after the movement is calculated, and the new spatial conformation of the protein-ligand complex is determined based on the energy of the protein-ligand complex after the movement. The geometric transformation data of the protein-ligand complex, the dynamic simulation data of the protein-ligand complex, and the new spatial conformation of the protein-ligand complex are used as training data for the initial neural network model.

10. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the method as described in any one of claims 1 to 9.

11. A computer storage medium, characterized in that, The computer storage medium stores instructions that, when executed on the computer, cause the computer to perform the method as described in any one of claims 1 to 9.

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