An efficient protein stability prediction method with selective state space modeling

Abstract

The present application relates to the technical field of protein prediction, and discloses a high-efficiency protein stability prediction method based on selective state space modeling. The present application adopts two core modules, BiMamba and CoGNN, and breaks through the limitations of existing methods in computational efficiency and multi-scale information processing by combining selective state space modeling and collaborative graph neural networks. The present application proposes a local sampling strategy based on k-hop subgraphs to achieve efficient computation by focusing on the key environment around the mutation site. A bidirectional selective state space model is used to model long-range dependencies with linear complexity, effectively overcoming the computational bottleneck of traditional Transformer architecture. The developed gating fusion module can adaptively integrate long and short-range features, allowing the model to flexibly adjust the feature combination strategy for different types of mutations, improving the accuracy and efficiency of protein ΔΔG prediction.

Description

Technical Field

[0001] The present invention relates to the technical field of protein prediction, and in particular to an efficient protein stability prediction method based on selective state space modeling. Background Art

[0002] Proteins are among the most important biomolecules in cells, and their thermodynamic stability is crucial for maintaining normal biological functions. Changes in stability (ΔΔG) caused by single-point mutations can lead to protein misfolding, which in turn can cause a variety of genetic diseases, cancers, and neurodegenerative diseases. In the fields of protein engineering and drug development, accurate prediction of ΔΔG can not only reveal the pathogenic mechanism of mutations, but also guide the optimization of protein stability. However, experimental measurement of ΔΔG requires a lot of time and resources, making it difficult to apply to large-scale screening, which makes the development of efficient and accurate computational prediction methods an important research direction in this field.

[0003] With the development of machine learning technology, protein stability prediction methods have evolved from physical force field methods to machine learning methods. Early research mainly focused on two types of methods: physics-based methods and statistical machine learning methods. Physics-based methods such as FoldX and Rosetta predict the effects of mutations on folding free energy through molecular dynamics simulations and statistical physics principles. These methods have good physical interpretability, but are computationally expensive and have limited accuracy. Subsequently developed statistical machine learning methods such as PoPMuSiC, SDM, and mCSM predict ΔΔG by integrating physicochemical features, evolutionary information, and statistical potential functions. Although these methods have significantly improved computational efficiency, they heavily rely on expert-designed feature engineering and use relatively shallow machine learning models such as random forests and support vector machines.

[0004] The recent boom in deep learning technology, particularly the breakthrough of AlphaFold2 in protein structure prediction, has brought new opportunities for ΔΔG prediction. Current deep learning methods can be broadly divided into two categories: sequence-based and structure-based. Sequence-based methods have evolved from simple sequence features to pre-trained representations. Early methods such as SAAFEC-SEQ, DDGun, BayeStab, PremPS, and INPS primarily relied on features extracted directly from sequences for prediction. With the development of protein language models, a new generation of sequence-based methods has begun leveraging pre-trained models to obtain richer sequence representations. For example, PROSTATA predicts ΔΔG by fine-tuning evolutionary features learned by the ESM2 model, better capturing the evolutionary information and structural biases embedded in the sequence. Structure-based deep learning methods focus on modeling protein structural information. For example, ProSTAGE uses graph neural networks to process atomic-level interactions, while ThermoAGT-GA utilizes a graph attention mechanism to capture spatial relationships between residues. The latest Stability Oracle integrates local and global structural information through a hybrid graph-Transformer architecture.

[0005] However, existing deep learning methods face serious computational efficiency challenges in practical applications. First, mainstream Transformer-based methods incur huge computational costs when processing large proteins, which is caused by the quadratic computational complexity of the self-attention mechanism. Second, structure-based methods usually adopt a full-graph computation strategy and need to process the complete molecular graph, resulting in a large amount of memory consumption when processing large proteins containing thousands of atoms. Third, in order to improve prediction accuracy, existing methods usually adopt deeper network structures or a larger number of parameters, further exacerbating the computational burden. These challenges severely limit the application of existing methods on large-scale datasets, highlighting the urgent need to develop lightweight and efficient prediction frameworks.

[0006] The Selective State Space Model (Mamba), a novel deep learning architecture, effectively captures long-range dependencies in sequences with linear computational complexity through its unique selective gating mechanism. Unlike the global self-attention of the Transformer, Mamba processes sequence data using a recursive scanning approach, employing hidden states to dynamically encode and compress contextual information. Its selective mechanism allows the model to adaptively decide which historical information to retain or discard based on the current input, a feature that is particularly important for protein stability prediction. The complex spatial relationships in protein structure (from local secondary structure to global folding domains) require simultaneous attention to the local chemical environment and global conformational changes, which is highly consistent with Mamba's context-aware selection mechanism. Although recent studies have attempted to extend Mamba to graph-structured data, how to effectively combine Mamba's long-range modeling capabilities with the local structure-aware capabilities of graph neural networks, as well as how to design specific architectures suitable for protein stability prediction, remain unresolved challenges. Summary of the Invention

[0007] In view of the shortcomings of existing protein stability prediction models based on deep learning, the present invention solves the following technical problems:

[0008] (1) The existing Transformer-based model is computationally expensive when processing large protein structures. This is due to the quadratic computational complexity of the self-attention mechanism, which severely limits its application on large-scale protein datasets. Specifically, for a protein containing N residues, the computational complexity of the Transformer is O(N²). When N increases, the computational resource requirements increase quadratically, resulting in an efficiency bottleneck in model training and inference.

[0009] (2) Existing structure-based methods generally adopt a full-graph calculation strategy, which requires processing the entire molecular graph, resulting in significant memory consumption when processing large proteins containing thousands of atoms. This strategy may lead to memory overflow problems when processing large proteins, limiting the promotion of the model in practical applications.

[0010] (3) Existing methods often struggle to balance long-range dependencies and local structural features in modeling proteins, which limits their ability to capture multi-scale information in protein structures. In particular, current methods either focus too much on local structural features and ignore long-range interactions, or overemphasize global dependencies and lose local structural details.

[0011] In order to overcome the deficiencies of the prior art, the present invention provides an efficient protein stability prediction method based on selective state space modeling, comprising the following steps:

[0012] 1. Subgraph construction based on k-hop local subgraph sampling strategy:

[0013] A subgraph is constructed using a k-hop local subgraph sampling strategy centered on the mutation site. This strategy focuses on the critical environment surrounding the mutation site, reducing memory consumption while retaining the key structural information required for protein stability prediction. It can efficiently cover the key residue structures around the mutation site and comprehensively include the amino acid network that has direct physical contact and indirect interactions with the mutation site, thereby providing sufficient structural environment information to accurately capture the impact of amino acid mutations on local conformational stability. Specifically, the strategy determines the mutation site by calculating the difference in sequence before and after the amino acid mutation. Then, a local subgraph within the k-hop range is constructed with this site as the center, thereby narrowing the calculation scope from the entire protein structure to the local region most relevant to the prediction task.

[0014] 2. Capturing Long-Range Dependencies Based on Bidirectional Selective State Space Modeling

[0015] A bidirectional selective state-space model, BiMamba, is designed. It models long-range dependencies with linear computational complexity and efficiently captures global context through its selective gating mechanism. Compared to the quadratic computational complexity of the Transformer self-attention mechanism, BiMamba efficiently captures global context through its selective gating mechanism, making it particularly suitable for processing large protein structures. The model includes two key components: 1) a degree-based node sorting strategy that arranges residues of different connectivity degrees to adapt to the sequential processing characteristics of state-space models; and 2) bidirectional selective state-space scanning, which models long-range dependencies between residues in two directions, from low to high and from high to low degrees. Bidirectional features are integrated through an adaptive gating mechanism to comprehensively capture multi-scale information in protein structures.

[0016] 3. Local Structural Feature Extraction Based on Collaborative Graph Neural Network

[0017] The collaborative graph neural network CoGNN is used to enhance the extraction of local structural features of proteins. CoGNN effectively models local residue interactions through a dynamic message passing mechanism. In the constructed protein graph structure, interconnected residue nodes achieve selective information exchange through a dynamic message passing mechanism, effectively breaking through the inherent one-dimensional spatial limitation of sequence modeling methods. This flexible information flow mechanism provides BiMamba with fine-grained spatial structural supplementary information for its long-range dependency modeling capabilities, enabling the model to simultaneously take into account the characterization of local protein interaction networks and global conformational changes while maintaining lightweight parameters. CoGNN treats each residue as an intelligent agent and can adaptively select four interaction strategies based on the structural environment: sending and receiving messages simultaneously (STANDARD), only receiving messages (LISTEN), only sending messages (BROADCAST), or neither sending nor receiving messages (ISOLATE), thereby more accurately simulating the interaction patterns of different regions in the protein.

[0018] 4. Multi-scale feature fusion

[0019] A gated fusion module is introduced to adaptively integrate long-range dependency information from BiMamba and local structural features from CoGNN to achieve comprehensive modeling of protein stability changes at different scales;

[0020] The gated fusion module first reweights the output features of BiMamba and CoGNN respectively through a channel attention mechanism, then adaptively fuses the two features through a learnable gating mechanism. Finally, the final output is obtained through a feature enhancement network and residual connections. The feature enhancement network adopts a multi-layer perceptron (MLP) architecture and further optimizes the fused representation of the two through nonlinear transformations. The introduced residual connection mechanism allows the original features to be directly connected to the representation processed by the feature enhancement network through additional skip connections. This design not only promotes the stable propagation of gradients in deep networks, but also enables the model to build deeper network structures while effectively maintaining the convergence stability of the training process. This design enables the model to flexibly adjust the feature combination strategy according to different types of mutations. For example, for mutations involving long-range interactions, it may rely more on the long-range dependency features captured by BiMamba; while for mutations that mainly affect local structure, it may focus more on the local structural information provided by CoGNN.

[0021] 5. Stability Prediction

[0022] To accurately capture the structural changes caused by mutations, the present invention uses a dual-stream network architecture to process wild-type and mutant proteins separately. Specifically, a parameter-sharing hybrid message passing network processes two conformations in parallel:

[0023] ;

[0024] ；

[0025] in and Denote the characteristic representation of wild-type and mutant proteins, and Represent the wild-type and mutant residue contact maps constructed from PDB (protein data bank) structure files, This represents a hybrid message passing module, comprising bidirectional Mamba-based sequence feature extraction and CoGNN-based structural feature extraction. The two extractors share the same network architecture and parameters, ensuring that the model captures the differences caused by the mutation itself, rather than changes caused by differences in model parameters.

[0026] The present invention then performs a differential calculation:

[0027] ;

[0028] in Differential representation of features representing wild-type and mutant forms, and prediction of stability changes from differential representation using MLP.

[0029] Finally, the stability change is predicted by the multi-layer perceptron:

[0030] ;

[0031] in is the change in protein stability, expressed in kcal / mol. A positive value indicates that the mutation reduces stability, while a negative value indicates that the mutation enhances stability.

[0032] The entire model (including the BiMamba module, CoGNN module, multi-scale feature fusion module, and two-stream network framework) is trained in an end-to-end manner by minimizing the mean absolute error loss:

[0033] ;

[0034] in represents the number of training samples, Indicates the The predicted value of the sample, Indicates the The true labels of samples, The proposed method is a classifier consisting of three fully connected linear layers. This differential modeling approach, based on a two-stream architecture and combined with a hybrid long- and short-range message passing module, comprehensively characterizes the impact of protein mutations on structural stability. In particular, the shared parameter design of the two-stream network enables the model to learn the differences caused by the mutations themselves between wild-type and mutant proteins, helping to capture key structural changes. This design ensures both accurate predictions and good interpretability of the results.

[0035] In summary, the overall architecture of this invention comprises four key modules: 1) a local subgraph construction strategy for mutation sites based on k-hop sampling; 2) an efficient long-range dependency modeling method based on the bidirectional selective state space model (BiMamba); 3) a local structural information extraction method based on the collaborative graph neural network (CoGNN); and 4) a gated fusion module that adaptively integrates long-range dependency information (BiMamba layer) with local structural features (CoGNN layer). Through the organic combination of these modules, this framework significantly reduces computational overhead while maintaining high accuracy.

[0036] Preferably, in step 1, the construction of the protein structure subgraph is achieved by the following steps:

[0037] First, the protein structure is modeled as Contact diagram of atomic distances (referring to the central carbon atom in the amino acid backbone) ,in Represents a set of nodes in the graph, each node corresponds to an amino acid residue; Represents the set of edges between nodes. When the two residues The distance between atoms is less than the preset threshold of 8 Å (angstrom, 1 Å = 10 -10 Meters are the common units of distance between atoms) to represent the spatial interactions between residues; is the node feature matrix, where is the number of nodes, each node has dimensional features; is the edge feature matrix, where is the number of nodes, and each edge has dimensional features;

[0038] Given mutation site , obtain the local subgraph through k-hop sampling:

[0039] ;

[0040] Among them, the subgraph Maintain the structural characteristics of the original image, and Represent the node set and edge set in the local subgraph respectively, is the node feature matrix of the subgraph, is the subgraph edge feature matrix; specifically, starting from the mutation site, the neighbor residues within k hops in the contact graph are collected to form a node subset;

[0041] ;

[0042] in, Indicates the mutation site, which refers to the residue position where the amino acid substitution occurs. Representation node and The shortest path length in the graph is less than , collect all nodes that meet the requirements Constituting a subgraph node set ;

[0043] Then retain the edges between subgraph nodes and construct edge subsets:

[0044] ;

[0045] in, Represents a connected node and , collect all and All in the subgraph node set The edges in the subgraph form the edge set ;

[0046] Accordingly, construct the feature matrix of the subgraph and the adjacency matrix ,Experiments show that when k=3, the model can achieve the best computational efficiency while ,maintaining prediction accuracy.

[0047] Preferably, in step 2, the bidirectional selective state space model is implemented by the following method:

[0048] In protein structures, the degree value of a node usually reflects the interaction strength between the residue and its surrounding environment; residues with high degree values ​​are often located in the core of the structure and have richer local environmental information, while residues with low degree values ​​may be located on the surface or in flexible areas; considering this unbalanced information distribution, the present invention proposes a bidirectional selective state space model (BiMamba) to enhance feature extraction; the forward scan processes nodes in order from low to high values, allowing the model to gradually integrate structural information from simple to complex; while the backward scan starts from high-degree nodes, first establishing an understanding of key structural areas, and then gradually focusing on local details; this bidirectional complementary information processing mechanism can more comprehensively capture structural features of different degrees, thereby providing a richer representation.

[0049] At the same time, in order to convert graph structure data into a sequence form suitable for the state space model, the present invention proposes a degree-based serialization strategy.

[0050] First, for each node Calculate its degree:

[0051] ;

[0052] in, and Represents a node, Represents a collection of nodes, Representation and Node The number of connected edges.

[0053] In order to make the serialization process more flexible, the Gumbel-Softmax mechanism is introduced. For each node:

[0054] ;

[0055] in Is an activation function that normalizes the numerical vector into a probability distribution vector. is the degree vector of all nodes, where each element Representation node The value of g is the noise sampled from a Gumbel distribution for random sampling, is the temperature parameter, which controls the smoothness of the softmax operation. It is the degree vector after softening based on Gumbel-Softmax. represents the field of real numbers, Represents an n-dimensional real vector space; based on the Gumbel-Softmax softened degree value, construct the sorting map π, and then obtain the rearranged feature sequence:

[0056] ;

[0057] in, is the input feature after layer normalization and linear projection, is the characteristic matrix sorted by degree value, represents the field of real numbers, Indicates the number of nodes, Represents the feature dimension.

[0058] The serialized features are processed through a selective state-space layer to model long-range dependencies:

[0059] ;

[0060] in is the SiLU activation function, defined as , is a one-dimensional convolution operation used to capture local context, Represents a fully connected layer for feature transformation, is the activation function, defined as ,make sure is a positive value, Controls the time step of the state-space model, affecting the rate of information transfer, 、 denote the input and output projection matrices in the state-space model, respectively, Used to map input features to state space, Used to map state space features back to output space, represents the feature sequence in the state space model, It is a gate that controls the ratio of information passing through.

[0061] Then, forward and backward selective state-space transformations are performed; the forward scan processes the sequence of nodes from low to high degree values, while the backward scan processes the sequence of nodes from high to low degree values; finally, the forward and backward features are fused through an adaptive gating mechanism:

[0062] ;

[0063] in represents the gate value, yes The activation function is defined as , used to map variables to between [0,1], is a multi-layer perceptron used to generate gating weights for fusion, and represent the sequence features after forward and backward selective state space transformation, Indicates flipping along the sequence dimension to align it with the forward direction for easy subsequent fusion processing. represents the Hadamard product (element-wise multiplication), This bidirectional and complementary information processing mechanism more comprehensively captures the characteristics of residues with different connectivity within a protein structure, thereby providing a richer representation. Furthermore, the linear complexity computation based on the selective state-space model enables this method to efficiently process large protein structures.

[0064] Preferably, in step 3, the collaborative graph neural network is implemented as follows:

[0065] To model local structural relationships between residues, the present invention employs a collaborative graph neural network (CoGNN). Unlike traditional message-passing mechanisms, CoGNN treats each node as an intelligent agent capable of adaptively selecting information exchange strategies. This design is particularly well-suited for handling complex local interactions in protein structures.

[0066] Given an input graph , where each node With initial feature representation For each node, the available action space is ,in:

[0067] S (standard): send and receive messages simultaneously;

[0068] L (listen): only receive messages;

[0069] B (broadcast): only send messages;

[0070] I (Isolate): neither sends nor receives messages;

[0071] Specifically, the present invention uses a two-layer graph convolutional network to construct a strategy network and , respectively predict the receiving and sending actions of the node; let the node In the layer The features in are represented as ,in ; The first layer feature transformation is:

[0072] ;

[0073] in is a node The neighbor set of Represents a set union operation, that is, the node Add itself to its neighbor set In , a neighbor set containing self-loops is formed, Indicates adding a self-loop node The degree, Indicates adding a self-loop node The degree, is the first layer of learnable weight matrix in CoGNN, Dimensions representing node features.

[0074] The second layer calculates the logits of receiving and sending actions separately:

[0075] ;

[0076] in Map the features to a two-dimensional action space. Generate action probabilities through the Gumbel-Softmax mechanism:

[0077] ;

[0078] in is the noise sampled from a Gumbel distribution, , is the temperature parameter that controls the sampling discreteness.

[0079] Based on the combination of two action probability vectors, four action states of the node can be defined (standard, listening, broadcasting, isolation); , whose weight is determined by the actions of the source node and the target node:

[0080] ;

[0081] in Indicates that the edge is reserved for message passing, Indicates that the edge is temporarily masked.

[0082] Based on edge weights and edge features , the update of node features can be expressed as:

[0083] ;

[0084] here It is The environment network of the layer updates the representation of the central node by aggregating features from active neighbor nodes and corresponding side information. Indicates that the neighbor nodes Feature representation and the edge Features The ordered pairs, represents the set of all feature-side information pairs that meet the conditions: yes The neighbor of the node has an edge weight of 1 (i.e., an active edge). ), it is updated only based on its own features, and the final local structural features are obtained through residual connections:

[0085] ;

[0086] This action-selection-based message passing mechanism allows the model to adaptively process different regions within a protein structure. For example, for conserved domains, nodes may tend to choose the standard mode (S) to maintain stable information exchange; whereas for variable regions, nodes may more often choose the listening mode (L) or the isolation mode (I) to filter out potential noise. Through this dynamically adjusted information exchange strategy, CoGNN is able to extract more accurate local structural features, providing a reliable local environment representation for subsequent stability change predictions.

[0087] Preferably, in step 4, multi-scale feature fusion is achieved by the following method: in order to make full use of the long-range dependency information captured by BiMamba and the local structural features extracted by CoGNN, the present invention designs an adaptive feature fusion mechanism based on channel attention. First, the present invention performs the feature fusion of the two modules output. and Apply channel attention separately:

[0088] (1) First, the features output by the two modules and , apply channel attention respectively:

[0089] ;

[0090] in and The channel attention weights corresponding to the output features of BiMamba and CoGNN, represents the Sigmoid activation function, It is a multi-layer perceptron.

[0091] After obtaining the attention weights, the features are reweighted by the Hadamard product:

[0092] ;

[0093] in stands for Hadamard product, which is element-wise multiplication and is used to weight features.

[0094] (2) Then, a learnable gating mechanism is used to dynamically fuse the two types of features:

[0095] ;

[0096] Thus, dynamic fusion features are obtained ;in is the normalized exponential function, is a multi-layer perceptron, is the feature concatenation operation, are the weights of BiMamba and CoGNN, and .

[0097] (3) Finally, the final output is obtained through the feature enhancement network and residual connection:

[0098] ;

[0099] in Normalization of the representative layer, It is a multi-layer perceptron used to enhance features. Represents the final output of the previous layer, Represents the final output of this layer.

[0100] This multi-scale feature fusion mechanism can adaptively balance the importance of long-range dependencies and local structural information. For example, for mutations involving long-range interactions, the model may assign higher weights to BiMamba's output; while for mutations that mainly affect local structure, it may rely more on CoGNN features.

[0101] This dynamic weighting method allows the model to flexibly adjust feature combination strategies based on different types of mutations. The updated representations derived from multi-scale feature fusion are used as input to BiMamba and CoGNN for multiple feature extractions. By stacking multiple layers, the final wild-type and mutant protein representations for stability prediction are extracted.

[0102] Preferably, node features By sequence characteristics and structural characteristics composition:

[0103] ;

[0104] in Represents a feature concatenation operation.

[0105] Sequence characteristics Combine three important types of information:

[0106] 1) One-hot encoding of amino acid types (20 dimensions): represents the identity information of 20 standard amino acids;

[0107] 2) Evolutionary information including PSSM matrix and conservation score (21 dimensions): including Position-Specific Scoring Matrix (PSSM, 20 dimensions) and conservation score (1 dimension);

[0108] 3) Physicochemical properties (12 dimensions): including hydrophilicity, volume, charge, and other properties that have an important impact on protein folding and stability.

[0109] Structural characteristics Integrates structural properties of residues, including:

[0110] 1) Secondary structure elements (3D): Indicates the type of secondary structure to which the residue belongs, such as α-helix, β-sheet, or random coil;

[0111] 2) Solvent accessibility (2D): indicates the extent to which residues are exposed to the solvent, which is closely related to protein stability;

[0112] 3) Local environment descriptor (8 dimensions): describes the chemical environment around the residue, such as polarity, hydrophobicity, and hydrogen bond formation ability.

[0113] This comprehensive feature design can comprehensively capture the sequence and structural information that affects protein stability, providing rich input data for accurately predicting the effects of mutations.

[0114] Preferably, when calculating edge features, in order to model the interactions between residues, the present invention uses distance-based position encoding to construct edge features. Consider a pair of residues Euclidean distance between , edge eigenvector The build is as follows:

[0115] ;

[0116] ;

[0117] in is the total dimension of edge features, is the frequency parameter associated with position k, Residue pairs The Euclidean distance between Represents the position encoding function, when k is an even number , otherwise ,This design based on sinusoidal position encoding can capture the multi-scale spatial relationships between ,residue pairs through a combination of trigonometric functions of different frequencies, ,while maintaining the monotonicity and continuity of the distance.

[0118] The present invention adopts the above-mentioned multiple innovative modules, which can significantly reduce computational overhead and memory consumption while maintaining or improving prediction performance, significantly improve efficiency when processing large protein data sets, and is suitable for practical application scenarios.

[0119] Compared with the prior art, the present invention has the following advantages:

[0120] (1) The proposed k-hop subgraph local sampling strategy significantly reduces computational complexity and memory consumption, enabling the model to effectively process large protein structures while retaining the key local environment information required for prediction. Compared with the full-graph processing method, this strategy reduces memory consumption by 82%, making large-scale protein analysis feasible;

[0121] (2) The bidirectional selective state-space model (BiMamba) designed in this paper innovatively introduces Mamba into the task of protein stability prediction, efficiently capturing long-range dependencies in proteins with linear computational complexity, breaking through the computational bottleneck of the traditional Transformer architecture. Through a bidirectional processing strategy of degree sorting, the model can adaptively capture the structural features of different regions of the protein;

[0122] (3) The collaborative graph neural network (CoGNN) employed in the present invention achieves detailed modeling of the local structure of proteins through a dynamic action selection mechanism, enabling the model to better understand environmental changes around mutation sites. Compared with traditional graph neural networks, CoGNN can adaptively select message passing strategies, improving the quality of local feature extraction. The gated fusion module of the present invention achieves adaptive integration of long-range dependency information and local structural features, enabling the model to flexibly adjust feature combination strategies for different types of mutations, thereby improving prediction accuracy and generalization ability. BRIEF DESCRIPTION OF THE DRAWINGS

[0123] The present invention will be further described below with reference to the accompanying drawings.

[0124] Figure 1 This is the technical roadmap of the present invention; Figure 1 A in the figure is the overall technical roadmap of the present invention. Figure 1 B is a schematic diagram of the k-hop subgraph sampling strategy of the present invention, Figure 1 Figure C is a schematic diagram of the working principle of the CoGNN module of the present invention; Figure 1 D in the figure is a schematic diagram of the working principle of the BiMamba module of the present invention. Figure 1 E in the middle is a schematic diagram of the feature fusion module of the present invention; Figure 1 Figure F is a schematic diagram of the gated fusion module of the present invention;

[0125] Figure 2 is the five-fold cross validation result; among them, Figure 2 A in the middle is the five-fold cross-validation Pearson correlation coefficient PCC result, Figure 2 Middle B is the root mean square error RMSE result of five-fold cross validation;

[0126] Figure 3 This is a scatter plot of the correlation predicted by the present invention; wherein, Figure 3 A in the middle is a scatter plot of the predicted correlation of the test set S605. Figure 3 Middle B is the scatter plot of the prediction correlation of the test set S1925, Figure 3 C in the middle is the SSYM prediction correlation scatter plot of the test set. Figure 3 Middle D is the scatter plot of the prediction correlation of the test set S250;

[0127] Figure 4 This is the antisymmetric scatter plot of the test set S250 of the present invention; wherein, Figure 4 A in the middle is the antisymmetric graph of the test set S250; Figure 4 Middle B is the reverse graph of the test set S250; Figure 4 C in the middle is the positive graph of the test set S250;

[0128] Figure 5 This is the SSYM antisymmetric scatter plot of the test set of the present invention; wherein, Figure 5 A in the middle is the SSYM antisymmetric graph of the test set; Figure 5 B in the middle is the SSYM reverse graph of the test set; Figure 5 C in the middle is the SSYM forward graph of the test set;

[0129] Figure 6 The calculation efficiency comparison of different k jumps of the present invention is shown in FIG. 1 ; wherein, Figure 6 A in the middle is the S2648 dataset algorithm complexity benchmark test, Figure 6 Middle B is the S2648 data set memory usage benchmark test;

[0130] Figure 7 is the mutation prediction result on the p53 tumor suppressor protein-DNA complex of the present invention;

[0131] Figure 8 This is the attention heat map for predicting the myoglobin F123K mutation of the present invention; wherein, Figure 8 A in the middle is the forward Mamba attention map, Figure 8 B in the middle is the backward Mamba attention map, Figure 8 C in the middle is the F123K bidirectional fusion attention map;

[0132] Figure 9 This is the attention heat map for predicting the myoglobin G129A mutation of the present invention; wherein, Figure 9 A in the middle is the forward Mamba attention map, Figure 9 B in the middle is the backward Mamba attention map, Figure 9 Middle C is the G129A bidirectional fusion attention map;

[0133] Figure 10 This is the attention heat map for predicting myoglobin mutations of the present invention; wherein, Figure 10 A in the middle is the attention visualization of myoglobin G129A, Figure 10 Middle B is the attention visualization of myoglobin F123K. DETAILED DESCRIPTION

[0134] The present invention will be further described below with reference to the accompanying drawings.

[0135] Example 1

[0136] The overall architecture of this invention comprises four key modules: 1) a strategy for constructing local subgraphs of mutation sites based on k-hop sampling; 2) an efficient long-range dependency modeling method based on the bidirectional selective state space model (BiMamba); 3) a method for extracting local structural information based on the collaborative graph neural network (CoGNN); and 4) a gated fusion module that adaptively integrates long-range dependency information (BiMamba layer) with local structural features (CoGNN layer). Through the organic combination of these modules, the framework significantly reduces computational overhead while maintaining high accuracy.

[0137] The information flow and connection relationship between the modules in the detailed drawings of the present invention are shown in FIG. Figure 1 .

[0138] Example 2

[0139] The efficient protein stability prediction method proposed in the present invention adopts a combination of selective state space modeling and graph neural network, and is implemented through the following five key modules: (1) a local subgraph construction strategy for mutation sites based on k-hop sampling; (2) an efficient long-range dependency modeling method based on a bidirectional selective state space model (BiMamba); (3) a local structural information extraction method based on a collaborative graph neural network (CoGNN); (4) a gated fusion module that adaptively integrates long-range dependency information and local structural features; and (5) a stability prediction module based on a dual-stream network.

[0140] 1. Subgraph construction based on k-hop local subgraph sampling strategy:

[0141] Considering that amino acid mutations mainly affect local structure, the present invention proposes a protein local subgraph construction strategy based on k-hop sampling. First, the present invention represents the protein structure as a contact graph ,in represents a set of nodes, each node corresponds to an amino acid residue; E represents a set of edges, which are connected when the distance between the Cα atoms of two residues is less than a preset threshold (usually 8Å); is the node feature matrix; is the edge feature matrix.

[0142] 1. First, the present invention locates the mutation site vmut by comparing the amino acid type one-hot encoding of the wild-type and mutant proteins:

[0143] ;

[0144] in Calculate the similarity of two amino acid one-hot encoded vectors, Indicates the wild-type protein The feature vector of the residues, Indicates the mutant protein The feature vector of the residues.

[0145] 2. Positioning of mutation sites As the center, the present invention constructs a local subgraph:

[0146] ;

[0147] Specifically, starting from the mutation site, the present invention collects neighbor residues within k hops in the contact graph to form a node subset:

[0148] ;

[0149] in Representation node To the mutation site The shortest path length.

[0150] 3. Keep the edges between subgraph nodes and construct edge subsets.

[0151] ;

[0152] 4. Accordingly, construct the feature matrix of the subgraph and the adjacency matrix .

[0153] Experiments show that when k = 3, the model achieves optimal computational efficiency while maintaining predictive accuracy, effectively balancing information capture and computational resource consumption. This strategy reduces memory consumption by up to 82%, making large-scale protein analysis feasible.

[0154] 2. Capturing Long-Range Dependencies Based on Bidirectional Selective State Space Modeling

[0155] To effectively capture long-range dependencies in protein structures, the present invention designs a bidirectional selective state-space model (BiMamba). In protein structures, the degree of a node typically reflects the strength of the interaction between the residue and its surrounding environment. Therefore, the present invention proposes a degree-based sequencing strategy and a bidirectional scanning mechanism.

[0156] 1. First, the present invention performs Calculate its degree:

[0157] ;

[0158] in Representation and Node Number of connected edges

[0159] 2. To make the serialization process more flexible, this paper introduces the Gumbel-Softmax mechanism:

[0160] ;

[0161] in From the Gumbel distribution The noise of the sampling, is the temperature parameter, which is used to control the smoothness of softmax.

[0162] 3. Based on the softened degree value, the present invention constructs a sorting map , and then obtain the rearranged feature sequence:

[0163] ;

[0164] in represents the initial feature matrix after layer normalization and linear transformation, The nodes are arranged according to A mapping sorted from small to large, satisfying .

[0165] 4. The sequenced features are processed by a selective state-space layer to model long-range dependencies. First, the key parameters of the state-space model are calculated:

[0166] ;

[0167] in represents the SiLU activation function, represents a one-dimensional convolution operation, represents the fully connected layer, is the activation function.

[0168] 5. Then perform the forward and backward selective state space transformation. The forward scan processes the sequence of nodes from low to high degree values, while the backward scan processes the sequence of nodes from high to low degree values. The core calculation of the state space transformation is as follows:

[0169] ;

[0170] in is the state transition matrix of the state space model, is the identity matrix, is the time step The hidden state of is the output state, Represents Hadamard product (element-wise multiplication)

[0171] 6. Finally, the forward and backward features are fused through an adaptive gating mechanism:

[0172] ;

[0173] in represents the reverse feature along the sequence dimension, represents the feature concatenation operation, This selective state-space modeling approach can efficiently capture long-range dependencies in protein structure with linear computational complexity, which is significantly better than the quadratic computational complexity of the Transformer.

[0174] 3. Local Structural Feature Extraction Based on Collaborative Graph Neural Network

[0175] To accurately model the local structural relationships between residues, we employ a collaborative graph neural network (CoGNN). CoGNN treats each node as an intelligent agent that can adaptively select from four information exchange strategies: STANDARD (sends and receives messages simultaneously), LISTEN (receives messages only), BROADCAST (sends messages only), and ISOLATE (neither sends nor receives messages).

[0176] 1. This invention uses a two-layer graph convolutional network to build a policy network and , respectively predicting the node’s receiving and sending actions:

[0177] ;

[0178] in is a node The neighbor set of Indicates adding a self-loop node The degree, is a learnable weight matrix, Representation node initial features.

[0179] 2. The second layer calculates the logits of receiving and sending actions respectively:

[0180] ;

[0181] in The features are mapped to a two-dimensional action space, corresponding to the logits of sending and receiving actions respectively.

[0182] 3. Generate action probabilities through the Gumbel-Softmax mechanism:

[0183] ;

[0184] in is the noise sampled from a Gumbel distribution, , is the temperature parameter that controls the sampling discreteness.

[0185] 4. Based on the combination of the two action probability vectors, determine the edge Weight:

[0186] ;

[0187] in Indicates that the edge is reserved for message passing, Indicates temporarily masking the edge. Representation node The probability of choosing to send a message, Representation node Choose the probability of receiving a message.

[0188] 5. Update node features based on edge weights:

[0189] ;

[0190] in is the environment network that updates the representation of the central node by aggregating features from active neighbor nodes and corresponding side information, It's the edge characteristics.

[0191] 6. Finally, local structural features are obtained through residual connections:

[0192] ;

[0193] in Representation layer normalization, Represents a multilayer perceptron.

[0194] This action-selection-based message-passing mechanism allows the model to adaptively process different regions in the protein structure, providing refined local structural representation.

[0195] 4. Multi-scale feature fusion

[0196] In order to make full use of the long-range dependency information captured by BiMamba and the local structural features extracted by CoGNN, the present invention designs an adaptive feature fusion mechanism based on channel attention.

[0197] 1. First, calculate the adaptive feature fusion mechanism based on channel attention

[0198] ;

[0199] in It is a multi-layer perceptron used for channel attention calculation, outputting the attention weights on the channel dimension. is the sigmoid activation function.

[0200] 2. After obtaining the attention weights, re-weight the features through the Hadamard product:

[0201] ;

[0202] 3. Then, a learnable gating mechanism is used to dynamically fuse the two types of features:

[0203] ;

[0204] in Output two fusion weights and , corresponding to the importance of BiMamba features and CoGNN features respectively.

[0205] 4. Finally, the final output is obtained through the feature enhancement network and residual connection:

[0206] ;

[0207] in It is a feature enhancement network used to further extract the representation ability of fused features.

[0208] This multi-scale feature fusion mechanism can adaptively balance the importance of long-range dependencies and local structural information, and flexibly adjust feature combination strategies for different types of mutations.

[0209] 5. Prediction of protein stability changes

[0210] The present invention uses a dual-stream network architecture to process wild-type and mutant proteins separately:

[0211] 1. First, the two protein structures are input into the hybrid message passing module separately:

[0212] ;

[0213] ；

[0214] in This represents the hybrid message passing module described above, which includes long-range feature extraction based on BiMamba and local feature extraction based on CoGNN. The two processing streams share the same network architecture and parameters, ensuring that the model captures the differences caused by the mutation itself, rather than differences caused by different parameters.

[0215] 2. Then perform the difference calculation:

[0216] ;

[0217] in is the final representation used for protein stability prediction.

[0218] 3. Finally, predict stability changes through multi-layer perceptron:

[0219] ;

[0220] in Contains three fully connected layers to map the difference features to stability change values.

[0221] 4. The entire model (including the BiMamba module, CoGNN module, multi-scale feature fusion module, and two-stream network framework) is trained in an end-to-end manner by minimizing the mean squared error loss:

[0222] ;

[0223] in is the number of training samples, It is a sample This combined strategy enables efficient and accurate prediction of protein stability changes, significantly reducing computing resource consumption while maintaining prediction performance.

[0224] Example 3 Verification and Evaluation

[0225] To validate the effectiveness and practicality of our method, we systematically evaluated it on six widely used benchmark datasets. These datasets were primarily derived from the ProTherm database, including the S2648 dataset (containing 2,648 single-point mutations in 131 globular proteins) as the basis for the training set. Taking into account the antisymmetric nature of ΔΔG as a state function (i.e., the ΔΔG value for a mutation from A to B should be equal to the negative of the ΔΔG value for a mutation from B to A), we constructed corresponding reverse mutation data for each mutation, ultimately generating the S5296 training set.

[0226] To comprehensively evaluate model performance, we used five primary test sets: S350, S605, S1925, S250, and Ssym. S350 consists of 350 randomly selected mutations from S2648; S605 contains 605 mutations from 58 proteins; S1925 contains 1,925 mutations from 55 proteins; S250 and SSYM contain 250 and 684 mutations, respectively, specifically designed to evaluate the model's antisymmetric performance. The S5296 dataset has a relatively balanced ratio of stability-enhancing (ΔΔG < 0) and stability-degrading (ΔΔG ≥ 0) mutations, enabling the model to better learn the characteristics of different mutation types. The following table summarizes the key statistics of the test datasets:

[0227] Table 1 Dataset statistics

[0228]

[0229] The present invention uses four main evaluation indicators, namely Pearson correlation coefficient (PCC), root mean square error (RMSE), mean absolute error (MAE) and antisymmetric deviation (δ), to quantitatively evaluate the prediction performance of the model.

[0230] 1. Pearson Correlation Coefficient (PCC):

[0231] ;

[0232] 2. Root Mean Square Error (RMSE):

[0233] ;

[0234] 3. Mean Absolute Error (MAE):

[0235] ;

[0236] 4. Antisymmetric deviation (δ):

[0237] ;

[0238] in and Respectively represent The predicted and true values ​​of samples, is the total number of samples. Ideally, δ should be close to 0, indicating that the model has good consistency in predicting forward and reverse mutations.

[0239] We implemented the CoMamba model in PyTorch and trained it using the AdamW optimizer with an initial learning rate of 0.0012, a weight decay of 1e-5, a batch size of 128, and 200 epochs. We conducted a systematic experimental investigation, focusing on two hyperparameters that most significantly impact model performance: the number of model layers and the k-hop neighborhood range. To ensure the reliability of our results, we performed a 5-fold cross-validation experiment on the training set. Figure 2 Experimental results show that when the number of model layers is 4 and the k-hop range is 3, the model achieves the best performance on the validation set, with a PCC of 0.962 and an RMSE of 0.487.

[0240] The CoMamba model achieved the best performance on all five test sets. On the S350 dataset, CoMamba achieved a PCC of 0.983 and an RMSE of 0.288, which is a significant improvement over the second-best method, ThermoAGT-GA (PCC=0.882, RMSE=0.899). On the more challenging S605 ( Figure 3 On the dataset (A), CoMamba also performs well, with PCC improved to 0.805, surpassing all existing methods.

[0241] It is worth noting that CoMamba achieved PCCs of 0.921 and 0.851 on the and SSYM datasets, respectively, which test the antisymmetric performance, indicating that the proposed method has good consistency in handling forward and reverse mutations. Figure 3 On the dataset (B), CoMamba also maintains excellent performance (PCC=0.791, RMSE=1.123). These results show that despite its lightweight design, CoMamba can still maintain competitive prediction performance. In terms of antisymmetric deviation, CoMamba is superior to SSYM ( Figure 4 ) and S250 ( Figure 5 ) datasets. On SSYM, the forward and reverse prediction correlation coefficient (Rfr) reached -0.99, with an antisymmetric deviation (δ) of only -0.02 kcal / mol. On S250, the performance was equally impressive, with Rfr = -0.99 and δ = -0.01 kcal / mol. This significantly outperforms other methods, such as FoldX and PoPMuSiC, which have Rfr values ​​ranging from -0.65 to -0.80 and δ values ​​exceeding -0.30 kcal / mol. This performance improvement is primarily due to the combination of our bidirectional selective state-space model (BiMamba) and collaborative graph neural network (CoGNN), as well as the dual-stream network architecture design.

[0242] To validate CoMamba's computational efficiency, we systematically analyzed the model's floating-point operations (FLOPs) and GPU memory consumption. Experimental results show that CoMamba exhibits significant efficiency advantages when processing large-scale graph structures. When k=7, CoMamba's FLOPs are 37.1% lower than GPS-Transformer, and its memory consumption is reduced by 82.8%, fully demonstrating CoMamba's potential for training large-scale datasets.

[0243] In particular, the present invention observed Figure 6 As the range of k hops increases, CoMamba's memory consumption shows a near-linear growth, requiring only 4GB of memory when k=7, and is able to maintain stable training with a batch size of 256. In contrast, GPS-Transformer's memory consumption shows a clear superlinear growth, requiring 19GB of memory under the same conditions. This result highlights the superiority of the method of the present invention when processing large-scale protein structure graphs. Notably, even under such efficient computing conditions, CoMamba still achieves excellent prediction performance, indicating that the method of the present invention successfully strikes a balance between efficiency and performance.

[0244] Example 4 Application Case Analysis

[0245] To demonstrate the predictive power of CoMamba on different protein systems, we simultaneously investigated p53 tumor suppressor protein and myoglobin as case studies.

[0246] 1) p53 tumor suppressor gene-DNA complex: The p53 tumor suppressor gene-DNA complex (PDB ID: 1TUP) represents a crucial protein in cancer biology. Mutations in its DNA binding domain are frequently associated with various cancers. Five known common mutation sites were analyzed in this study, and the predicted values ​​of CoMamba showed a high correlation with the experimental values ​​(PCC = 0.89). For the R248Q mutation ( Figure 7 The model predicted a ΔΔG value of 1.95 kcal / mol, which is almost identical to the experimentally determined value of 1.94 kcal / mol. This mutation site is particularly critical because R248 forms a key contact with the DNA minor groove in the wild-type structure.

[0247] 2) Myoglobin protein: The present invention further uses myoglobin to evaluate CoMamba ( Figure 8-10), analyzed two representative mutations with opposite effects: G129A (stabilizing mutation, ΔΔG = -1.05 kcal / mol) and F123K (destabilizing mutation, ΔΔG = 2.10 kcal / mol). CoMamba accurately predicted the stability changes to be -1.03 kcal / mol and 2.15 kcal / mol, respectively.

[0248] In the case of G129A, the model identified interactions from the nearest residue GLN 128 (3.787 Å) to the highest scoring distant residue LEU 2 (10.524 Å). Similar selective attention was observed for F123K, with the nearest PRO 120 (4.766 Å) and the highest assigned attention to GLY 5 (14.292 Å). Forward and backward Mamba attention patterns ( Figure 10 The blue and red heatmaps (in the middle) show the varying strength of attention between residue pairs, demonstrating the selective scanning advantage of our method. This example demonstrates a core advantage of our selective state-space modeling: the ability to selectively focus on residues at varying distances from the mutation site, rather than treating all residues equally.

[0249] Overall, the case study results demonstrate that CoMamba can accurately predict stability changes in different types of proteins and provide in-depth insights into the mechanisms of mutational impact. Through visualization analysis, the present invention further validates the advantages of combining selective state space modeling with collaborative graph neural networks in capturing multi-scale interactions in protein structure.

Claims

1. An efficient protein stability prediction method based on selective state space modeling, characterized in that: The following steps are involved:

1. Subgraph Construction Based on k-Hop Local Subgraph Sampling Strategy The subgraph is constructed by a k-hop local subgraph sampling strategy centered on the mutation site; 2. Capturing Long-Range Dependencies Based on Bidirectional Selective State Space Modeling We design a bidirectional selective state-space model, BiMamba, to model long-range dependencies with linear computational complexity. BiMamba efficiently captures global context through its selective gating mechanism.

3. Local Structural Feature Extraction Based on Collaborative Graph Neural Network A collaborative graph neural network (CoGNN) is used to enhance the extraction of local protein structural features. CoGNN effectively models local residue interactions through a dynamic message passing mechanism, providing fine-grained local complementarity to BiMamba's long-range modeling capabilities while maintaining lightweight parameters.

4. Multi-scale feature fusion A gated fusion module is introduced to adaptively integrate long-range dependency information from BiMamba and local structural features from CoGNN to achieve comprehensive modeling of protein stability changes at different scales; The gated fusion module first reweights the output features of BiMamba and CoGNN using a channel-wise attention mechanism, then adaptively fuses the two features using a learnable gating mechanism. Finally, the final output is obtained through a feature enhancement network and residual connections. The updated representations from multi-scale feature fusion are used as inputs to BiMamba and CoGNN for multiple feature extractions. By stacking multiple layers, the final wild-type and mutant protein representations for stability prediction are extracted.

5. Stability Prediction The final protein representation obtained from the multi-scale feature fusion module processes the wild-type and mutant proteins separately through a two-stream network architecture and performs differential calculations: ； ； ； in and Denote the characteristic representation of wild-type and mutant proteins, and Represent the wild-type and mutant residue contact maps constructed from the PDB protein database structure files, represents the hybrid message passing module, including sequence feature extraction based on bidirectional Mamba and structural feature extraction based on CoGNN, The final differential representation represents the characteristics of wild type and mutant, and the stability change is predicted from the differential representation by MLP; Finally, the stability change is predicted by the multi-layer perceptron: ； in is the change in protein stability, expressed in kcal / mol. A positive value indicates that the mutation reduces stability, while a negative value indicates that the mutation enhances stability. The entire model includes the BiMamba module, the CoGNN module, the multi-scale feature fusion module, and the two-stream network framework, and is trained in an end-to-end manner by minimizing the mean absolute error loss: ； in represents the number of training samples, Indicates the The predicted value of the sample, Indicates the The true labels of samples, is a classifier consisting of three fully connected linear layers.

2. The method according to claim 1, characterized in that In step 1, the construction of the protein structure subgraph is achieved through the following steps: First, the protein structure is modeled as Contact diagram of atomic distances ,in Represents a set of nodes in the graph, each node corresponds to an amino acid residue; Atom refers to the central carbon atom in the amino acid backbone. Represents the set of edges between nodes. When the two residues A connection is established when the distance between atoms is less than the preset threshold of 8 Å, which is used to represent the spatial interaction between residues; is the node feature matrix, where is the number of nodes, each node has dimensional features; is the edge feature matrix, where is the number of nodes, and each edge has dimensional features; The mutation site located As the center, obtain the local subgraph through k-hop sampling: ； Among them, the subgraph Maintain the structural characteristics of the original image, and Represent the node set and edge set in the local subgraph respectively, is the node feature matrix of the subgraph, is the subgraph edge feature matrix; Starting from the mutation site, neighbor residues within k hops in the contact graph are collected to form a node subset; ； in, Indicates the mutation site, which refers to the residue position where the amino acid substitution occurs. Representation node and The shortest path length in the graph is less than , collect all nodes that meet the requirements Constituting a subgraph node set ; Then retain the edges between subgraph nodes and construct edge subsets: ； in, Represents a connected node and , collect all and All in the subgraph node set The edges in the subgraph form the edge set ; Accordingly, construct the feature matrix of the subgraph and the adjacency matrix .

3. The method according to claim 2, characterized in that Mutation site vmut: ； in Calculate the similarity of two amino acid one-hot encoded vectors, Indicates the wild-type protein The feature vector of the residues, Indicates the mutant protein The feature vector of the residues.

4. The method according to claim 2, characterized in that Node Features By sequence characteristics and structural characteristics composition: ； in Represents feature concatenation operation; Sequence characteristics Combine three types of information: 1) One-hot encoding of amino acid types: represents the identity information of 20 standard amino acids; 2) Evolutionary information including PSSM matrix and conservation score: including position-specific score matrix PSSM 20 dimensions and conservation score 1 dimension; 3) 12 dimensions of physicochemical properties: including hydrophilicity, volume, charge, and other properties that have an important impact on protein folding and stability; Structural characteristics Integrates structural properties of residues, including: 1) Secondary structure element 3D: indicates the type of secondary structure to which the residue belongs, such as α-helix, β-sheet or random coil; 2) Solvent accessibility 2D: indicates the degree of exposure of residues to solvent, which is closely related to protein stability; 3) Local environment descriptor 8-dimensional: describes the chemical environment around the residue, such as polarity, hydrophobicity and hydrogen bond formation ability characteristics.

5. The method according to claim 4, characterized in that When calculating edge features, distance-based position encoding is used to construct edge features, considering a pair of residues Euclidean distance between , edge eigenvector The build is as follows: ； ； in is the total dimension of edge features, is the frequency at position k, Residue pairs The Euclidean distance between Represents the position encoding function, when k is an even number , otherwise ,This design based on sinusoidal position encoding can capture the multi-scale spatial relationships between ,residue pairs through a combination of trigonometric functions of different frequencies, ,while maintaining the monotonicity and continuity of the distance.

6. The method according to claim 1, characterized in that Step 2 is as follows: First, for each node Calculate its degree: ； in, and Represents a node, Represents a collection of nodes, Representation and Node The number of connected edges; In order to make the serialization process more flexible, the Gumbel-Softmax mechanism is introduced: ； in Is an activation function that normalizes the numerical vector into a probability distribution vector. is the degree vector of all nodes, where each element Representation node The value of g is the noise sampled from a Gumbel distribution for random sampling, is the temperature parameter, which controls the smoothness of the softmax operation. It is the degree vector after softening based on Gumbel-Softmax. represents the field of real numbers, Represents an n-dimensional real vector space; based on the Gumbel-Softmax softened degree value, construct the sorting map π, and then obtain the rearranged feature sequence: ； in, is the input feature after layer normalization and linear projection, The features are sorted by degree value, and the length is the number of nodes , the feature dimension is ; The serialized features are processed through a selective state-space layer to model long-range dependencies: ； in is the SiLU activation function, defined as , yes The activation function is defined as , represents the linear projection layer, is the time step parameter in the state space model, which controls the speed of information flow. 、 denote the input and output projection matrices in the state-space model, respectively, represents the feature sequence in the state space model, It is a gate, which is used to control the ratio of information passing through; Then, forward and backward selective state-space transformations are performed; the forward scan processes the sequence of nodes from low to high degree values, while the backward scan processes the sequence of nodes from high to low degree values; finally, the forward and backward features are fused through an adaptive gating mechanism: ； in represents the gate value, yes The activation function is defined as , used to map variables to between [0, 1], is a multi-layer perceptron used to map sequence features to gate dimensions. and represent the sequence features after forward and backward selective state space transformation, Indicates flipping along the sequence dimension to align it with the forward direction for easy subsequent fusion processing. represents the Hadamard product, Represents feature splicing.

7. The method according to claim 1, characterized in that In step 3, CoGNN treats each node as an intelligent agent that can adaptively select four information interaction strategies: STANDARD (sending and receiving messages at the same time), LISTEN (receiving messages only), BROADCAST (sending messages only), and ISOLATE (neither sending nor receiving messages). (1) Action selection stage: using a two-layer graph convolutional network to build a policy network and , respectively predicting the node’s receiving and sending actions: ； ； in is a node The neighbor set of Indicates adding a self-loop node The degree, is the learnable weight matrix in CoGNN, Map features to a two-dimensional action space; Then, the action probability is generated through the Gumbel-Softmax mechanism: ； in is the noise sampled from a Gumbel distribution, , is the temperature parameter that controls the discreteness of sampling; (2) Update node features, after generating action probabilities, determine the edge based on the combination of two action probability vectors. Weight: ； in Indicates that the edge is reserved for message passing, Indicates temporary masking of the edge; Then update the node features according to the edge weights: ； in It is an environment network that updates the representation of the central node by aggregating features from active neighbor nodes and corresponding edge information; when the node has no active input edge ( ), it is updated only based on its own features; Finally, the local structure features are obtained through residual connections as shown below: ； Where LN represents layer normalization, MLP represents multi-layer perceptron, represents the features before updating, represents the updated features, Residual Jump to Updated representation through MLP.

8. The method according to claim 1, characterized in that In step 4, multi-scale feature fusion is achieved through the following methods: (1) First, the features output by the two modules and , apply channel attention respectively: ； in and The channel attention weights corresponding to the output features of BiMamba and CoGNN, represents the Sigmoid activation function, It is a multi-layer perceptron; After obtaining the attention weights, the features are reweighted by the Hadamard product: ； in Represents Hadamard product, i.e. element-wise multiplication, used for weighted features; (2) Then, a learnable gating mechanism is used to dynamically fuse the two types of features: ； Thus, dynamic fusion features are obtained ;in is the normalized exponential function, is a multi-layer perceptron, is the feature concatenation operation, is the weight of BiMamba and CoGNN, and satisfies ; (3) Finally, the final output is obtained through the feature enhancement network and residual connection: ； in Normalization of the representative layer, It is a multi-layer perceptron used to enhance features. Represents the final output of the previous layer, Represents the final output of this layer.

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