A method for mining plant lncRNAs associated with abiotic stress responses based on graph neural networks

Abstract

This invention discloses a method for mining plant lncRNAs related to abiotic stress responses based on graph neural networks, comprising the following steps: obtaining semantic features of abiotic stress and features of plant lncRNAs and miRNAs; constructing corresponding similarity networks; generating interaction networks of lncRNAs and miRNAs; and obtaining association networks between lncRNAs, miRNAs, and abiotic stress, thereby constructing a lncRNA-miRNA-abiotic stress heterogeneous network; inputting the lncRNA-miRNA-abiotic stress heterogeneous network into a trained heterogeneous graph neural network model using causal walking to predict the association between plant lncRNAs and abiotic stress. This invention utilizes causal walking graph neural networks to accurately predict the association between lncRNAs and abiotic stress, thereby mining potential lncRNAs related to abiotic stress.

Description

Technical Field

[0001] This invention relates to the field of bioinformatics, specifically to a method for mining plant lncRNAs related to abiotic stress responses based on graph neural networks. Background Technology

[0002] For a long time, some ncRNAs, such as long non-coding RNAs (lncRNAs) and microRNAs (miRNAs), have been regarded by researchers as "junk" products of the transcription process. However, recent studies have increasingly uncovered a large number of ncRNAs and confirmed their important roles in regulating gene expression and plant responses to abiotic stresses (such as drought, low temperature, and high salinity). Currently, research on uncovering ncRNAs related to abiotic stress responses typically employs traditional biological experiments and classical statistical methods for verification and analysis, which leads to a significant waste of human and financial resources and may face the risk of unreliable experimental results. With the development of network models, represented by graph neural networks (GNNs), in bioinformatics, particularly their successful application in complex biological networks such as protein-protein interaction networks, gene regulatory networks, and disease-drug association networks, researchers' research costs and time have been significantly reduced, while simultaneously creating higher academic value.

[0003] Current research on graph neural networks faces the following technical challenges that need to be overcome:

[0004] (1) In terms of data, the usual method of biological network modeling is to collect data manually and construct biological networks, and then build a model based on these networks. Therefore, artificially constructed biological networks often contain noisy data, which reduces the prediction accuracy of the model.

[0005] (2) In terms of model construction, the typical GNN model lacks good interpretability and cannot provide intermediate explanations for its results. Summary of the Invention

[0006] The technical problem to be solved by this invention is to provide a method for mining plant lncRNAs related to abiotic stress responses based on graph neural networks, addressing the aforementioned problems in the prior art. Starting from plant ncRNA association data and ncRNA-abiotic stress association data, an improved GNN model is developed by introducing causal reasoning techniques to reduce the impact of noise data on the model in artificially constructed biological networks and improve the interpretability of the model in mining plant lncRNAs corresponding to abiotic stresses.

[0007] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows:

[0008] A method for mining plant lncRNAs associated with abiotic stress responses based on graph neural networks includes the following steps:

[0009] To obtain the characteristics of plant lncRNAs and miRNAs, and to obtain semantic features of abiotic stress;

[0010] Similarity networks corresponding to lncRNA features, miRNA features, and abiotic stress semantic features were constructed respectively. Interaction networks of lncRNA and miRNA were generated based on the features of lncRNA and miRNA. The association networks of lncRNA and abiotic stress and miRNA and abiotic stress were obtained from the specified database respectively.

[0011] Based on the similarity networks corresponding to lncRNA features, miRNA features, and abiotic stress semantic features, the interaction network between lncRNA and miRNA, the association network between lncRNA and abiotic stress, and the association network between miRNA and abiotic stress, a lncRNA-miRNA-abiotic stress heterogeneous network was constructed.

[0012] The lncRNA-miRNA-abiotic stress heterogeneous network is input into a trained heterogeneous graph neural network model utilizing causal walks. The heterogeneous graph neural network model first generates a causal walk path corresponding to each node from the lncRNA-miRNA-abiotic stress heterogeneous network, and integrates the causal walk paths using the adjacency matrix method to obtain different causal walk subgraphs. Then, the heterogeneous mutual attention vector and heterogeneous message passing vector of the nodes in the causal walk subgraphs are calculated, and the embeddings of the nodes are updated using the heterogeneous mutual attention vector and heterogeneous message passing vector, thereby obtaining the embeddings of lncRNA, miRNA and abiotic stress. Finally, the lncRNA embedding and abiotic stress embedding are subjected to a dot product operation to obtain the reconstructed lncRNA-abiotic stress association matrix, so as to realize the prediction of the association between plant lncRNA and abiotic stress.

[0013] Furthermore, when constructing similarity networks corresponding to lncRNA features, miRNA features, and abiotic stress semantic features, specifically, the following methods are used: The nearest neighbor algorithm constructs similarity networks for lncRNA features, miRNA features, and abiotic stress semantic features based on cosine similarity scores.

[0014] Furthermore, when generating the interaction network of lncRNAs and miRNAs based on their characteristics, the specific steps include:

[0015] A lncRNA-miRNA heterogeneous network was constructed based on the characteristics of lncRNAs and miRNAs. The lncRNA-miRNA heterogeneous network includes a similarity network of lncRNA characteristics, a similarity network of miRNA characteristics, and a lncRNA-miRNA interaction network.

[0016] The lncRNA-miRNA heterogeneous network is input into a trained counterfactual heterogeneous graph attention model to learn the embeddings of lncRNA and miRNA. The counterfactual heterogeneous graph attention model learns the embeddings of nodes in the lncRNA-miRNA heterogeneous network through a heterogeneous graph attention neural network, and enhances the ability of the heterogeneous graph attention neural network to learn node embeddings through counterfactual links.

[0017] The lncRNA and miRNA embedded by the counterfactual heterogeneous graph attention model are input into the MLP to predict the interaction scores between lncRNA and miRNA.

[0018] Furthermore, when generating the causal travel path corresponding to each node from the lncRNA-miRNA-abiotic stress heterogeneous network, the specific steps include:

[0019] Community labels were assigned to each node in the lncRNA-miRNA-abiotic stress heterogeneous network. The set of neighboring nodes of each node was obtained and the corresponding graph structure was generated. The causal relationship between each node and its graph structure and community label was analyzed to obtain an initial causal model. Perturbations were introduced into the graph of the lncRNA-miRNA-abiotic stress heterogeneous network and abstracted as confounding factors to obtain the final causal model.

[0020] The backdoor criterion is used to identify direct causal effects in the causal model and obtain the causal weights between the target node and its neighboring nodes.

[0021] The transition weight of each neighbor node of the target node is calculated based on the causal weight. Among the neighbor nodes of the target node, the node with the largest transition weight is selected as the node for the next traversal, until the specified causal traversal length is reached. The mathematical expression for the transition weight is as follows:

[0022]

[0023] in, Indicates the current node To the next node The transfer weights, This is the current step. and the next step Causal weights between them and These are two hyperparameters that control the breadth and depth of the walk, respectively. This represents the number of hops between two nodes.

[0024] Furthermore, when calculating the heterogeneous mutual attention vector and heterogeneous message passing vector of nodes in the causal walk subgraph, the mathematical expression of the heterogeneous mutual attention vector is as follows:

[0025]

[0026] in, This represents the heterogeneous mutual attention vector between the target node and its neighboring nodes. It is the source node and target node In meta-relations The next The mathematical expression for an attention head is as follows:

[0027]

[0028]

[0029]

[0030] in, It is the prior vector for attention-adaptive scaling. express The total vector dimension of each attention head. and These are the source node and the target node's... A linear projection function, Indicates the first Source node embedding of the layer Is it a meta-relation? The relevant weight matrix.

[0031] Furthermore, when calculating the heterogeneous mutual attention vector and heterogeneous message passing vector of the nodes in the causal walk subgraph, the mathematical expression of the heterogeneous message passing vector is as follows:

[0032]

[0033]

[0034] in, Indicates by Heterogeneous message passing vector composed of individual message vectors Indicates the number of messages. Represents the source node's... A linear projection function, Represented as meta-relation The weight matrix is ​​set.

[0035] Furthermore, when updating the embedding of the node using heterogeneous mutual attention vectors and heterogeneous message passing vectors, the mathematical expression is as follows:

[0036]

[0037]

[0038] in, This indicates the update embedding of the target node. Represents the target node The set of neighboring nodes, and Representing the target node respectively In the Layer and first Layer embedding, This represents a linear projection function that embeds the target node into its node type distribution.

[0039] Furthermore, the method also includes: optimizing the model parameters of the heterogeneous graph neural network model using a composite loss function combining an interval loss function and a cross-entropy function. The mathematical expression of the composite loss function is as follows:

[0040]

[0041] in, Represents the cross-entropy function. This represents the interval loss function.

[0042] Furthermore, the mathematical expression for the cross-entropy function is as follows:

[0043]

[0044] in, This represents the reconstructed lncRNA-abiotic stress association matrix. , It is lncRNA embedding. It is an embedding of non-biological stress. It is a non-linear activation function. This represents the network linking lncRNAs to abiotic stresses, where N represents the number of lncRNAs.

[0045] Furthermore, the mathematical expression for the interval loss function is as follows:

[0046]

[0047] in, Indicates and The positive sample prediction matrix corresponding to the known edge is given. Indicates and The negative sample prediction matrix related to the unknown edge.

[0048] Compared with the prior art, the advantages of the present invention are as follows:

[0049] (1) Integrate multi-source lncRNA, miRNA and abiotic stress databases to construct lncRNA-miRNA-abiotic stress heterogeneous network.

[0050] (2) Innovatively, causal weights are integrated with the walking algorithm to perform causal weighting on the walking process, improve the causality of the walking path, and further filter out non-causal edges, i.e. noise edges, in heterogeneous networks, providing high-quality modeling objects for GNN.

[0051] (3) In GNN, heterogeneous mutual attention, message passing and aggregation mechanisms are used to automatically obtain key meta-paths in heterogeneous networks, provide intermediate explanations for model decision-making, and reveal the core association between lncRNA and abiotic stress. Attached Figure Description

[0052] Figure 1 This is a flowchart of a method according to an embodiment of the present invention.

[0053] Figure 2 This is a schematic diagram illustrating the framework and process of the CW-HGT heterogeneous graph neural network model utilizing causal walks in an embodiment of the present invention. Figure 2 (a) indicates that the LMS heterogeneous network is input into the CW-HGT model. Figure 2 (b) represents the process by which the CW-HGT model constructs a causal walking subgraph using the causal walking algorithm. Figure 2 (c) represents the process by which the CW-HGT model calculates the heterogeneous mutual attention vector and heterogeneous message passing vector of nodes in the causal walk subgraph to update the node embedding. Figure 2 (d) represents the process by which the CW-HGT model predicts the association between plant lncRNAs and abiotic stresses based on the lncRNA embedding and abiotic stress embedding in the node embedding.

[0054] Figure 3 This is a flowchart illustrating the extraction of causal models from the lncRNA-miRNA-abiotic stress isomorphic network. Figure 3 (a) represents the general causal relationships and connections in LMS heterogeneous networks. Figure 3 (b) represents the causal path and the construction of the initial causal model in the LMS heterogeneous network. Figure 3 (c) represents the final causal model after adding perturbations to the yellow area. Detailed Implementation

[0055] The present invention will be further described below with reference to the accompanying drawings and specific preferred embodiments, but this does not limit the scope of protection of the present invention.

[0056] In biological networks, the relationships between entities are strongly causal. However, current network construction methods often fail to incorporate these causal relationships, resulting in numerous irrelevant and redundant edges. Furthermore, improving the interpretability of GNN models helps in understanding their decision-making mechanisms, aiming to provide insights into biological mechanisms beyond prior knowledge.

[0057] Based on this, this embodiment proposes a method for mining plant lncRNAs related to abiotic stress responses using graph neural networks. Starting from plant ncRNA data, a heterogeneous network of ncRNAs related to abiotic stress is constructed. Based on graph neural networks, a graph neural network utilizing causal walks is developed to mine potential lncRNAs related to abiotic stress, providing a new perspective for understanding the response mechanisms of plant abiotic stresses. At the same time, it provides a theoretical basis and practical guidance for crop breeding and stress resistance improvement.

[0058] like Figure 1 As shown, the method includes the following steps:

[0059] Step 1: Feature Construction. Specifically, this involves acquiring the features of plant lncRNAs and miRNAs, and obtaining semantic features related to abiotic stresses.

[0060] Step 2: Construct the lncRNA-miRNA-abiotic stress heterogeneous network, hereinafter referred to as the LMS heterogeneous network. Specifically, this involves constructing similarity networks (including the lncRNA similarity network) corresponding to lncRNA features, miRNA features, and abiotic stress semantic features. miRNA similarity network Abiotic stress semantic similarity network Furthermore, based on the characteristics of lncRNAs and miRNAs, an interaction network between lncRNAs and miRNAs was generated. Furthermore, the association networks between lncRNAs and abiotic stresses were obtained from the PncStress database. miRNA and abiotic stress association network Finally, based on the above network, a lncRNA-miRNA-abiotic stress heterogeneous network was constructed, and the adjacency matrix of this heterogeneous network is shown below:

[0061]

[0062] in, Representing similar networks; , and These represent the quantities of lncRNAs, miRNAs, and abiotic stresses, respectively; a 1 in the adjacency matrix indicates a connection between two nodes, and vice versa.

[0063] Step 3: Implement lncRNA-abiotic stress prediction using a graph neural network based on causal walks. Specifically, input the lncRNA-miRNA-abiotic stress heterogeneous network into a pre-trained heterogeneous graph neural network model CW-HGT using causal walks, such as... Figure 2 As shown, the CW-HGT model first generates causal walk paths for each node from the lncRNA-miRNA-abiotic stress heterogeneous network. It then integrates these causal walk paths using the adjacency matrix method to obtain different causal walk subgraphs. Next, it calculates the heterogeneous mutual attention vector and heterogeneous message passing vector for each node in the causal walk subgraph and updates the node embeddings using these vectors, thereby obtaining the embeddings of lncRNA, miRNA, and abiotic stress. Finally, it performs a dot product operation on the lncRNA and abiotic stress embeddings to obtain the reconstructed lncRNA-abiotic stress association matrix, enabling the prediction of the association between plant lncRNA and abiotic stress.

[0064] The following provides a detailed explanation of each step.

[0065] In step S1 of this embodiment, when obtaining the characteristics of plant lncRNA and miRNA, the RNA Chaotic Game Representation (CGRNA) method is specifically used. The secondary structure of RNA is used as additional information to project the RNA sequence onto a two-dimensional plane, and the projection information is used as the RNA sequence characteristics to obtain the characteristics of plant lncRNA and miRNA. This is a conventional method for converting nucleotide sequences (letters) into numerical sequences. The specific implementation steps are well known to those skilled in the art and are not the focus of this solution, so they will not be described in detail here.

[0066] In step S1 of this embodiment, when acquiring the semantic features of abiotic stress, a pre-trained FastText model is used to generate semantic word vectors for abiotic stress. The FastText model is based on the Continuous Bag of Words (CBOW) model, and its training corpus covers a large amount of text data related to abiotic stress. Therefore, the pre-trained FastText model can provide high-quality semantic representations of abiotic stress. In this embodiment, each abiotic stress word vector has a dimension of 100, i.e. .

[0067] In step S2 of this embodiment, when constructing similar networks corresponding to lncRNA features, miRNA features, and abiotic stress semantic features, specifically using... Nearest neighbor algorithm ( (NN) Construct a similarity network corresponding to lncRNA features, miRNA features, and abiotic stress semantic features. For each node, select the node with the highest cosine similarity score. Each node is designated as a neighbor, and the corresponding entry in the adjacency matrix is ​​set to 1, thereby constructing a lncRNA similarity network. miRNA similarity network Abiotic stress semantic similarity network .

[0068] In step S2 of this embodiment, when generating the interaction network of lncRNA and miRNA based on the characteristics of lncRNA and miRNA, the interaction data between lncRNA and miRNA is obtained using the Heterogeneous Graph Attention Model (CFHAN) based on counterfactual links, including the following steps:

[0069] Step S21: Construct a lncRNA-miRNA heterogeneous network, hereinafter referred to as the LM heterogeneous network, based on the characteristics of lncRNAs and miRNAs. In this embodiment, the similarity network of lncRNA characteristics, the similarity network of miRNA characteristics, and the lncRNA-miRNA interaction network are integrated to form the LM heterogeneous network. The LM heterogeneous network is defined as follows: ,in Represents a set of nodes. Represents the edge set. A subnetwork is defined as... ,in Indicates the type of metapath; metapath is defined as follows: The adjacency matrix of a heterogeneous network is represented as follows:

[0070]

[0071] in, , and These are the adjacency matrices corresponding to the metapaths LL, MM, and LM, respectively. Represents a node and nodes A connection exists if one connection is present, and vice versa.

[0072] Step S22: Input the lncRNA-miRNA heterogeneous network into the trained counterfactual heterogeneous graph attention model CFHAN to predict lncRNA-miRNA interactions. In this embodiment, the counterfactual heterogeneous graph attention model CFHAN learns the node embeddings in the lncRNA-miRNA heterogeneous network through a heterogeneous graph attention neural network, and enhances the learning ability of the heterogeneous graph attention neural network through counterfactual links. This enables it to accurately predict real plant lncRNA-miRNA interactions (LncRNA-miRNA Interactions, LMIs), as detailed below:

[0073] (1) Heterogeneous Graph Attention Neural Network. The initial node embeddings are obtained by learning the topology and semantic information of the lncRNA-miRNA heterogeneous network through feature projection, node-level attention (NA), and semantic-level attention (SA). Since the lncRNA-miRNA heterogeneous network contains two types of ncRNAs: lncRNA and miRNA, the features of lncRNA and miRNA are first projected into the same feature space using residuals and linear transformation matrices. Specifically, for lncRNAs belonging to type... nodes The projected eigenvectors are represented as follows:

[0074]

[0075] in, This represents the projected feature vector. Represents a linear transformation matrix. Representation type nodes Features This represents the residual term.

[0076] To understand the importance of connections between lncRNAs / miRNAs and their neighboring nodes, CFHAN employs an attention mechanism (NA) to obtain attention scores between the target node and its neighbors within a metapath. Specifically, GAT is used to learn the attention scores of neighboring nodes towards the target node within a specific metapath. The feature representation of the target node is updated by aggregating the features of its neighbors and itself based on these attention scores. For metapath-based... subgraph ,node and Edge weights between This can be expressed by the following formula:

[0077]

[0078]

[0079] in, Represents node-level attention; ReLU is the activation function. and These represent the features of the node pairs after projection. It is a vector concatenation operation. This is the node-level attention vector. To ensure the comparability of attention values ​​between different nodes, the attention values ​​are further normalized using the softmax function:

[0080]

[0081] Finally, CFHAN implements different attention mechanisms for nodes within each metapath to reduce the impact of a single self-attention mechanism and stabilize the learning process of attention scores; this is known as the multi-head attention mechanism. The final node-level embedding representation is as follows:

[0082]

[0083] in, Represents a node exist The first-order neighbor set in the middle, This represents the number of heads in the attention mechanism. CFHAN further applies the SA mechanism to learn the semantic importance between metapaths and target nodes. Specifically, The node-level embedding is represented as Multi-head attention mechanism is used to learn each metapath subgraph pair. The importance of simultaneous computation and metapath Corresponding subgraph and node-level embedding The attention scores between nodes are then aggregated. Then, the different meta-path embeddings of nodes of the same type are aggregated with the attention scores.

[0084]

[0085]

[0086] in, It is the weight of each metapath. This represents semantic-level attention operations. This indicates node-level embedding of the same type of node under different metapaths. These are the attention weights between nodes on different meta-paths. It is a counting operation. It is a semantic-level attention vector. Represents a node In metapath Subgraph Node-level embedding within. Similarly, A softmax function needs to be applied to ensure that attention scores at different semantic levels are comparable:

[0087]

[0088]

[0089] in, This represents the normalized semantic-level attention value. Indicates the number of node-level embeddings. Represents a node The final embedding.

[0090] (2) Counterfactual Heterogeneous Graph Attention Neural Network. CFHAN introduces counterfactual causal reasoning and enhances the data by constructing counterfactual links in the network, guiding the heterogeneous graph attention neural network to learn more realistic associations, thereby further improving the quality of node embedding and providing richer and more accurate input for predicting the association scores between lncRNA and miRNA.

[0091] Counterfactual reasoning aims to identify causal relationships between treatments and outcomes by posing counterfactual questions. In CFHAN, the counterfactual question is defined as "If the network structure changes, will the relationship between lncRNAs and miRNAs change?" Based on this counterfactual question, CFHAN constructs and utilizes counterfactual links to enhance graph data and improve node embedding learning, ultimately improving CFHAN's robustness to noise in heterogeneous networks.

[0092] CFHAN uses the final feature as context The heterogeneous network structure is represented as a binary processing variable. The lncRNA-miRNA interaction relationship is expressed as the result. ,and This indicates the output given the context and processing variables. For example, the true lncRNA-miRNA interaction does not change with changes in the graph structure. Therefore, when tending towards 1 and As the graph attention network of CFHAN approaches zero, it should appropriately adjust the embedding of the current lncRNA and miRNA until, theoretically, it reaches zero. and All equal 1.

[0093] In CFHAN, the fact link is the observed lncRNA-miRNA interaction. This example utilizes the Louvain algorithm to discover network structures in the observed lncRNA-miRNA interactions. Each node is assigned to a specific subnetwork. Then, we transform the network structure into a fact-based processing mechanism by distinguishing whether two nodes belong to the same subnetwork. The formula is as follows:

[0094]

[0095]

[0096] However, counterfactual links cannot be directly obtained. Therefore, CFHAN identifies node pairs in lncRNA-miRNA interactions that meet the following criteria as counterfactual links: they are the nearest neighbors of the factual links, and their processing is the opposite of that of the factual links. Formally, for each node pair... Its counterfactual links Defined as:

[0097]

[0098] in, The final characteristics of lncRNA The final characteristics of miRNA The Euclidean distance between them This is the threshold for similarity between two nodes. The formula for calculating counterfactual processing is as follows:

[0099]

[0100] in, and They represent lncRNAs respectively and miRNA The counterfactual processing and counterfactual linking are performed. After obtaining the counterfactual processing, CFHAN concatenates it as additional information with the node embeddings and guides the update of node embeddings in the heterogeneous graph attention neural network message passing, as shown below:

[0101]

[0102] in, This indicates the node pair embedding after introducing counterfactual processing. Indicates lncRNA with miRNA Hadamard product of node embeddings.

[0103] Step S23: Input the lncRNA and miRNA embeddings learned by the Counterfactual Heterogeneous Graph Attention Model (CFHAN) into the MLP to predict the interaction scores between lncRNAs and miRNAs. To further capture the nonlinear relationship between counterfactual link-based node embeddings and lncRNA-miRNA interactions, this embodiment uses an MLP as the predictor to predict the interaction scores between lncRNAs and miRNAs. CFHAN obtains node embeddings by applying node-level attention and semantic-level attention. It further enhances the node embeddings through counterfactual links, and the enhanced embeddings are fed into the MLP as input.

[0104] Specifically, when training using counterfactual links, CFHAN first performs a Hadamard product operation on the embeddings of lncRNA and miRNA through a message-passing mechanism, and then concatenates the product embeddings with either factual or counterfactual processing. During the prediction phase, CFHAN utilizes two MLP predictors to obtain the predicted factual results and the predicted counterfactual results, respectively. The formula is as follows:

[0105]

[0106] in, and These represent the predicted factual outcome and the predicted counterfactual outcome, respectively. Indicates lncRNA and miRNA The result of the embedded Hadamard product. and They represent lncRNAs respectively and miRNA The factual processing value and the counterfactual processing value.

[0107] Training a CFHAN presents two challenges: covariate bias risk and prediction optimization. In this embodiment, the predicted factual outcome is defined. And predicting counterfactual outcomes The Kullback-Leibler (KL) divergence between variables was analyzed, and minimizing the KL divergence effectively reduced covariate bias and mitigated risk.

[0108]

[0109]

[0110] in, The KL divergence represents the distance between two distributions. and Representing the original distributions respectively and approximate distribution Furthermore, this embodiment employs the cross-entropy loss function and the Adam optimizer to optimize the MLP output. and to bring it close and :

[0111]

[0112]

[0113] in, and These represent the quantities of lncRNAs and miRNAs, respectively. The weighted sum of the three loss functions is used as the global loss function for CFHAN, as shown in the following formula:

[0114]

[0115] in, and These are hyperparameters (usually set to 0.5), which respectively affect... and The loss values ​​are weighted.

[0116] In step S3 of this embodiment, the CW-HGT process framework is as follows: Figure 2 As shown, the input of CW-HGT includes node features and LMS heterogeneous network ( Figure 2 (a)), and then through the process of causal walks and the construction of subgraphs, learning objects are provided for CW-HGT ( Figure 2 (b)), and then through Figure 2 The node embedding update process shown in (c) updates the target node embedding based on the target node embedding and the embeddings of its neighboring nodes, and finally... Figure 2 As shown in (d), the association probability between lncRNA and abiotic stress is calculated. This includes the following steps:

[0117] Step S31: Construct a causal walking subgraph.

[0118] like Figure 2 As shown in (b), in this embodiment, the construction of the causal walking subgraph involves two main processes: obtaining causal walking paths; and then integrating these paths into the subgraph.

[0119] When obtaining causal walk paths, a causal walk algorithm is specifically used to generate the causal walk path corresponding to each node in the lncRNA-miRNA-abiotic stress heterogeneous network. The causal walk algorithm aims to discover causal relationships between nodes in the network using causal inference learning, generate causal weights between nodes and their neighbors, and apply these weights to the walk algorithm to eliminate non-causal edges (noise edges) in the network, thereby providing clean and reliable data and learning objects for downstream models. Specifically, the causal walk algorithm mainly consists of two steps: First, according to the definition of causal inference learning, discover causal relationships in the network to form a general causal model; second, use the backdoor criterion to quantify the causal strength in the causal model, i.e., the causal weights between nodes, and deploy them in the walk algorithm. Therefore, generating the causal walk path corresponding to each node in the lncRNA-miRNA-abiotic stress heterogeneous network specifically includes:

[0120] Step S311: Assign community tags to each node in the lncRNA-miRNA-abiotic stress heterogeneous network, obtain the neighbor node set of each node and generate the corresponding graph structure, analyze the causal relationship between each node and its graph structure and community tags to obtain the initial causal model, and introduce perturbations into the graph of the lncRNA-miRNA-abiotic stress heterogeneous network and abstract them as confounding factors to obtain the final causal model.

[0121] In complex biological networks, nodes are typically interconnected through causal relationships that reflect the network topology. Notably, ncRNA molecules with similar functions or regulatory roles tend to cluster together. Based on this understanding, this embodiment employs the Louvain community detection algorithm to segment these clusters in the LMS heterogeneous network, thereby assigning different community tags to each node. Figure 3 As shown, a causal model is used to describe the causal relationships between the target node, its neighboring nodes, and the target node's community label. Figure 3 middle, Figure 3 (a) represents the general causal relationships and connections in LMS heterogeneous networks; Figure 3 (b) represents the causal path and the construction of the initial causal model in the LMS heterogeneous network; Figure 3 (c) represents the final causal model after adding perturbations to the yellow area. The black arrows indicate the causal direction, red nodes represent the target node, yellow nodes represent the target node's neighbor nodes, and green nodes represent potential causal nodes.

[0122] like Figure 3 As shown in (a), the LMS heterogeneous network is defined as follows: ,in and These represent the node set and the edge set, respectively. This represents the set of community tags assigned to a node. This indicates the type of each node. Define as a node The set of neighboring nodes, Indicates in The potential causal nodes that need to be analyzed. Analysis from the following perspectives. , Graph structure as well as The causal relationship between them. First, and All nodes are with There is a direct causal relationship, forming two causal paths: and Secondly, for Community tags , It can directly affect Thus change This introduces another causal path: .

[0123] Based on the three causal paths mentioned above, an initial causal model can be constructed, such as... Figure 3 As shown in (b). Furthermore, by introducing a perturbation throughout the figure and abstracting it as a confounding factor... The final causal model is obtained, such as Figure 3 As shown in (c).

[0124] Step S312: Use the backdoor criterion to identify direct causal effects in the causal model and obtain the causal weights between the target node and its neighboring nodes;

[0125] In the causal model described above, there exists a backdoor path. It does not pass Direct impact Instead, through Indirect impact. Furthermore... , and The three causal paths between them satisfy the backdoor criterion condition: (a) when When dealing with variables, There is no (b) descendants; Blocked and All causal paths between them. Therefore, utilizing Operator recognition and The direct causal relationship between them is determined, and the backdoor criterion is applied to cut it off. All backdoor paths between them. This process can be represented by an intervention distribution:

[0126]

[0127] in, express Operators Indicates in and under conditions The conditional probability. For ease of causal reasoning, the above formula is approximated as follows:

[0128]

[0129]

[0130] in, The kernel density estimate is obtained from the joint and marginal reproducing kernel Hilbert space (RKHS) function. It is causal weight.

[0131] Step S313: Calculate the transition weight of each neighbor node of the target node based on the causal weight. Among the neighbor nodes of the target node, select the node with the largest transition weight as the node to be traversed next, until the specified causal traversal length is reached.

[0132] The causal walk algorithm in CW-HGT is based on a causal model and mainly consists of two parts: it uses the backdoor criterion to identify direct causal effects in the causal model, especially by calculating the causal weights between the target node and its neighboring nodes; it combines the causal weights with the transition probabilities to guide the walk process.

[0133] like Figure 2 As shown in (b), the current node is defined as The next hop node is defined as The previous hop node is defined as Then from the current node To the next node Transfer weights for:

[0134]

[0135] in, Indicates the current node To the next node The transfer weights, This is the current step. and the next step Causal weights between them and These are two hyperparameters that control the breadth and depth of the walk, respectively. This represents the number of hops between two nodes.

[0136] By continuously selecting the node with the largest transition weight among the neighboring nodes as the next node to be traversed, the specified causal traversal length is reached, ultimately resulting in a causal traversal path about the starting node. For example, in an LMS heterogeneous network containing 724 nodes (including lncRNA, miRNA, and abiotic stress nodes), a causal walk is initiated from each of these 724 nodes. This process generates 724 distinct causal walk paths, each representing a sequence of node identifiers of a specified length in the LMS heterogeneous network.

[0137] Step S314: Generate a causal walking subgraph based on the causal walking path.

[0138] This embodiment uses a formula similar to the adjacency matrix of the lncRNA-miRNA-abiotic stress heterogeneous network described above to integrate the multiple causal walk paths generated through the above steps, ultimately obtaining a causal walk subgraph. It is worth noting that the causal walk algorithm is specifically applied to the three similarity networks (lncRNA, miRNA, and abiotic stress similarity networks) and the lncRNA-miRNA interaction network. This strategic implementation ensures that the associations between lncRNA, miRNA, and abiotic stress verified in experiments are preserved in the causal walk subgraph, while effectively reducing noise in the LMS heterogeneous network.

[0139] A causal walking subgraph can be defined as follows: ,in and Let represent the set of nodes and the set of edges in the subgraph, respectively. Since the causal walk subgraph is also a heterogeneous graph, given an edge in the subgraph... Meta-relations can be abstractly defined as follows: ,in and These represent the source node and the target node, respectively. and These represent the distribution of nodes and edges of a specific type in the subgraph, respectively. The adjacency matrix of the causal walk subgraph is represented as follows:

[0140]

[0141] Step S32: Calculate the heterogeneous mutual attention vector and heterogeneous message passing vector of the node, and then aggregate the heterogeneous mutual attention vector and heterogeneous message passing vector through the heterogeneous aggregation mechanism to update the node embedding.

[0142] In this embodiment, a heterogeneous mutual attention mechanism is used to calculate the heterogeneous mutual attention vectors of nodes in the causal walking subgraph. Unlike traditional attention-based GNN models, the heterogeneous mutual attention mechanism uses meta-relations. The mutual attention values ​​between nodes are calculated. Specifically, in the heterogeneous mutual attention mechanism, the target node is first mapped to a Query vector, the source node is mapped to a Key vector, and a meta-relation is set. Related weight matrix Secondly, regarding the Query vector, Key vector, and... Perform a dot product operation to obtain the attention values ​​of the target node and the source node under different meta-relations, that is, the projection weight of the target node under each meta-relation.

[0143]

[0144]

[0145]

[0146] in, It is the source node and target node In meta-relations The next One's attention, It is the prior vector for attention-adaptive scaling. express The total vector dimension of each attention head. and These are the source node and the target node's... A linear projection function. Indicates that CW-HGT is in the Embed the source node of the layer. Head attention values ​​according to meta-relations The attention vectors are concatenated and then aggregated using softmax to represent the heterogeneous mutual attention vectors between the target node and its neighboring nodes.

[0147]

[0148] In this embodiment, a heterogeneous message passing mechanism is used when calculating the heterogeneous message passing vectors of nodes in the causal walk subgraph. While calculating heterogeneous mutual attention, edge relationships are incorporated into the message passing process of CW-HGT to reduce the distribution differences of different types of nodes and edges. Specifically, different meta-relationships are included... All source nodes are mapped to Message Value vectors, and this is a meta-relation. Set the weight matrix For any meta-relation, its heterogeneous message passing vector is calculated using the following formula:

[0149]

[0150]

[0151] in, Indicates the number of messages. Represents the source node's... A linear projection function, Indicates by A heterogeneous message passing vector composed of individual message vectors.

[0152] In this embodiment, when updating the embedding of the node using heterogeneous mutual attention vectors and heterogeneous message passing vectors, the heterogeneous mutual attention vectors and heterogeneous message passing vectors are aggregated through a heterogeneous aggregation mechanism, and the embedding of the target node is updated. Specifically, This determines the importance of different meta-paths, and Adaptive weights are assigned to meta-paths based on their message-passing importance in continuous learning iterations. This dual mechanism promotes dynamic updates of node embeddings through iterative learning. For example, when the meta-relation "lncRNA-abiotic stress" plays a crucial role, It will automatically assign higher weight coefficients to them, so that CW-HGT can identify key metapath types during the learning process.

[0153] Furthermore, the heterogeneous mutual attention vector is used as a weight and weighted with the heterogeneous message passing vector to obtain the updated embedding of the target node. At the same time, introducing a linear projection function will... Map back to target node The corresponding type distribution is expressed as follows:

[0154]

[0155]

[0156] in, Represents the target node The set of neighboring nodes, and Representing the target node respectively In CW-HGT's Layer and first Layer embedding. This represents a linear projection function that embeds the target node into its node type distribution.

[0157] Step S33: Predict plant lncRNA-abiotic stress associations.

[0158] CW-HGT utilizes the CGRNA algorithm and a pre-trained FastText model to acquire features of lncRNAs, miRNAs, and abiotic stresses. The LMS heterogeneous network is constructed, including similarity and association networks for lncRNAs, miRNAs, and abiotic stresses. Subsequently, CW-HGT filters out noisy edges in the LMS heterogeneous network to obtain a causal walking subgraph. CW-HGT automatically learns the key-meta paths and topological information in the causal walking subgraph to obtain the embeddings of lncRNAs, miRNAs, and abiotic stresses. CW-HGT then performs lncRNA embedding. Abiotic stress embedding Performing a dot product operation yields the reconstructed lncRNA-abiotic stress correlation matrix. This allows us to obtain the association probability between each pair of lncRNAs and abiotic stress in the matrix. The calculation formula is as follows:

[0159]

[0160] in, It is a non-linear activation function.

[0161] In this embodiment, 10-fold cross-validation (10-CV) is used to obtain experimental metrics. In 10-CV, known... Edges are treated as positive samples and divided into 10 equal-sized subsets (in CW-HGT, ...). The known edges in the sample are defined as positive samples. ,and The unknown edge in the sample is defined as a negative sample. In each iteration, one subset is used as the test set, and the remaining nine subsets constitute the training set. This process is repeated until each subset has been used as the test set once, resulting in a trained CW-HGT model. Furthermore, the mean of all predictions is used as a threshold.

[0162] The reconstructed lncRNA-abiotic stress association matrix was obtained. Next, the values ​​of each pair of lncRNAs and abiotic stresses in the matrix are compared with a threshold. If the value is greater than the threshold, it is considered that there is an association between the lncRNA and abiotic stress; otherwise, there is no association.

[0163] Furthermore, in the prediction of lncRNA-abiotic stress association, CW-HGT aims to enhance the ability to distinguish between positive and negative samples. Therefore, in this embodiment, a composite loss function combining interval loss and cross-entropy function is used to optimize the model parameters during model training. The mathematical expression of this loss function is as follows:

[0164]

[0165]

[0166]

[0167] in, Represents the cross-entropy function. Represents the interval loss function. This represents the reconstructed lncRNA-abiotic stress association matrix. This represents the network linking lncRNAs to abiotic stresses, where N represents the number of lncRNAs. Indicates and The positive sample prediction matrix corresponding to the known edge is given. Indicates and The negative sample prediction matrix related to the unknown edge.

[0168] The following model comparison experiments and case study experiments were designed to verify the predictive ability of CW-HGT for plant lncRNA-abiotic stress associations. In the model comparison experiments of CW-HGT, its performance was evaluated by comparing it with six state-of-the-art models from two perspectives: walk-based algorithms and heterogeneous GNN-based models. In the walk-based comparison, three models were constructed: RW-HGT, N2VRW-HGT, and MHRWR. Among them, random walk (RW) and Node2Vec (Node2Vec-Random walk, N2VRW) are classic walk algorithms used to replace the causal walk in CW-HGT. MHRWR is an algorithm based on restarted random walk, originally designed to predict lncRNA-human disease associations. In addition, due to the limited research on lncRNA-abiotic stress association prediction, two lncRNA-human disease association prediction models (GCLMTP and CSGLMD) and one miRNA-abiotic stress association prediction model (MFGNN) were selected for comparison. The results are shown in Table 1. CW-HGT's predictive ability is superior to other models.

[0169]

[0170] In the case study experiment of CW-HGT, salt stress and drought stress were selected as case studies. Specifically, the optimal CW-HGT was trained using the complete dataset. Furthermore, associations between lncRNAs and salt stress, lncRNAs and drought stress, and lncRNAs and intense light stress were excluded from the dataset. Subsequently, the optimized CW-HGT was used to predict the association scores of all unknown lncRNAs associated with these three abiotic stresses. For ease of analysis, the top 5 lncRNA-intense light stress and lncRNA-salt stress association predictions for Arabidopsis thaliana, and the top 5 lncRNA-drought stress and lncRNA-salt stress association predictions for rice were extracted from the entire prediction results and validated through literature search and in the PLncDB database. The prediction results of CW-HGT and their evidence are shown in Table 2.

[0171]

[0172] In summary, this invention proposes a method for mining plant lncRNAs associated with abiotic stress responses based on graph neural networks. It utilizes a causal walk-based heterogeneous graph transformer model (CW-HGT) to apply the causal walk algorithm to a lncRNA-miRNA-abiotic stress heterogeneous network, filtering out noisy edges and thus enhancing the causal correlation of edges in the network. On the denoised heterogeneous network, CW-HGT uses heterogeneous mutual attention, mutual message passing, and aggregation mechanisms to learn node embeddings and automatically obtains key meta-paths. It then performs a dot product on the embeddings of lncRNAs and abiotic stresses to obtain their association scores. Finally, the mean of all association prediction results is used as a threshold to determine whether an association exists. Experimental results show that CW-HGT outperforms six other benchmark models in predicting lncRNA-abiotic stress associations and possesses good noise resistance and predictive ability. Furthermore, by selecting Arabidopsis thaliana and rice as case studies of predicted lncRNAs under common abiotic stresses, the effectiveness of this method in mining key lncRNAs was further validated.

[0173] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-readable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code. This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create a machine for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to operate in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The functions specified in one or more boxes. These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable apparatus for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0174] The above description is merely a preferred embodiment of the present invention. The scope of protection of the present invention is not limited to the above embodiments. All technical solutions falling within the scope of the present invention's concept are within the scope of protection of the present invention. It should be noted that for those skilled in the art, any improvements and modifications made without departing from the principles of the present invention should also be considered within the scope of protection of the present invention.

Claims

1. A method for mining plant lncRNA associated with abiotic stress response based on graph neural network, characterized in that, Includes the following steps: To obtain the characteristics of plant lncRNAs and miRNAs, and to obtain semantic features of abiotic stress; Similarity networks corresponding to lncRNA features, miRNA features, and abiotic stress semantic features were constructed separately. Interaction networks between lncRNA and miRNA were generated based on their features. The association networks between lncRNA and abiotic stress and between miRNA and abiotic stress were obtained from specified databases. Based on the similarity networks corresponding to lncRNA features, miRNA features, and abiotic stress semantic features, the interaction networks between lncRNA and miRNA, the association networks between lncRNA and abiotic stress, and the association networks between miRNA and abiotic stress, a lncRNA-miRNA-abiotic stress heterogeneous network was constructed. The lncRNA-miRNA-abiotic stress heterogeneous network is input into a trained heterogeneous graph neural network model utilizing causal walks. The heterogeneous graph neural network model first generates a causal walk path corresponding to each node from the lncRNA-miRNA-abiotic stress heterogeneous network, and integrates the causal walk paths using the adjacency matrix method to obtain different causal walk subgraphs. Then, the heterogeneous mutual attention vector and heterogeneous message passing vector of the nodes in the causal walk subgraphs are calculated, and the embeddings of the nodes are updated using the heterogeneous mutual attention vector and heterogeneous message passing vector, thereby obtaining the embeddings of lncRNA, miRNA and abiotic stress. Finally, the lncRNA embedding and abiotic stress embedding are subjected to a dot product operation to obtain the reconstructed lncRNA-abiotic stress association matrix, so as to realize the prediction of the association between plant lncRNA and abiotic stress.

2. The method for mining plant lncRNAs related to abiotic stress responses based on graph neural networks according to claim 1, characterized in that, When constructing the similarity network corresponding to the lncRNA feature, the miRNA feature and the abiotic stress semantic feature respectively, specifically, the cosine similarity score is used to construct the similarity network of the lncRNA feature, the similarity network of the miRNA feature and the similarity network of the abiotic stress semantic feature. The cosine similarity score is used to construct the similarity network of the lncRNA feature, the similarity network of the miRNA feature and the similarity network of the abiotic stress semantic feature.

3. The method for mining plant lncRNAs related to abiotic stress responses based on graph neural networks according to claim 1, characterized in that, The generation of the lncRNA and miRNA interaction network specifically includes: A lncRNA-miRNA heterogeneous network was constructed based on the characteristics of lncRNAs and miRNAs. The lncRNA-miRNA heterogeneous network includes a similarity network of lncRNA characteristics, a similarity network of miRNA characteristics, and a lncRNA-miRNA interaction network. The lncRNA-miRNA heterogeneous network is input into a trained counterfactual heterogeneous graph attention model to learn the embeddings of lncRNA and miRNA. The counterfactual heterogeneous graph attention model learns the embeddings of nodes in the lncRNA-miRNA heterogeneous network through a heterogeneous graph attention neural network, and enhances the ability of the heterogeneous graph attention neural network to learn node embeddings through counterfactual links. The lncRNA and miRNA embedded by the counterfactual heterogeneous graph attention model are input into the MLP to predict the interaction scores between lncRNA and miRNA.

4. The method for mining plant lncRNAs related to abiotic stress responses based on graph neural networks according to claim 1, characterized in that, When generating the causal travel path corresponding to each node in the lncRNA-miRNA-abiotic stress heterogeneous network, the specific steps include: Community labels were assigned to each node in the lncRNA-miRNA-abiotic stress heterogeneous network. The set of neighboring nodes of each node was obtained and the corresponding graph structure was generated. The causal relationship between each node and its graph structure and community label was analyzed to obtain an initial causal model. Perturbations were introduced into the graph of the lncRNA-miRNA-abiotic stress heterogeneous network and abstracted as confounding factors to obtain the final causal model. The backdoor criterion is used to identify direct causal effects in the causal model and obtain the causal weights between the target node and its neighboring nodes. The transition weight of each neighbor node of the target node is calculated based on the causal weight. Among the neighbor nodes of the target node, the node with the largest transition weight is selected as the node for the next traversal, until the specified causal traversal length is reached. The mathematical expression for the transition weight is as follows: in, Indicates the current node To the next node The transfer weights, This is the current step. and the next step Causal weights between them and These are two hyperparameters that control the breadth and depth of the walk, respectively. This represents the number of hops between two nodes.

5. The method for mining plant lncRNAs related to abiotic stress responses based on graph neural networks according to claim 1, characterized in that, When calculating the heterogeneous mutual attention vector and heterogeneous message passing vector of nodes in the causal walk subgraph, the mathematical expression of the heterogeneous mutual attention vector is as follows: in, This represents the heterogeneous mutual attention vector between the target node and its neighboring nodes. It is the source node and target node In meta-relations The next The mathematical expression for an attention head is as follows: in, It is the prior vector for attention-adaptive scaling. express The total vector dimension of each attention head. and These are the source node and the target node's... A linear projection function, Indicates the first Source node embedding of the layer Is it a meta-relation? The relevant weight matrix.

6. The method for mining plant lncRNAs related to abiotic stress responses based on graph neural networks according to claim 5, characterized in that, When calculating the heterogeneous mutual attention vector and heterogeneous message passing vector of nodes in the causal walk subgraph, the mathematical expression of the heterogeneous message passing vector is as follows: in, Indicates by Heterogeneous message passing vector composed of individual message vectors Indicates the number of messages. Represents the source node's first... A linear projection function, Represented as meta-relation The weight matrix is ​​set.

7. The method for mining plant lncRNAs related to abiotic stress responses based on graph neural networks according to claim 6, characterized in that, When updating the embedding of the node using heterogeneous mutual attention vectors and heterogeneous message passing vectors, the mathematical expression is as follows: in, This indicates the update embedding of the target node. Represents the target node The set of neighboring nodes, and Representing the target node respectively In the Layer and first Layer embedding, This represents a linear projection function that embeds the target node into its node type distribution.

8. The method for mining plant lncRNAs related to abiotic stress responses based on graph neural networks according to claim 1, characterized in that, The method further includes: optimizing the model parameters of the heterogeneous graph neural network model using a composite loss function that combines an interval loss function and a cross-entropy function. The mathematical expression of the composite loss function is as follows: in, Represents the cross-entropy function. This represents the interval loss function.

9. The method for mining plant lncRNAs related to abiotic stress responses based on graph neural networks according to claim 8, characterized in that, The mathematical expression for the cross-entropy function is as follows: in, This represents the reconstructed lncRNA-abiotic stress association matrix. , It is lncRNA embedding. It is an embedding of non-biological stress. It is a non-linear activation function. This represents the network linking lncRNAs to abiotic stresses, where N represents the number of lncRNAs.

10. The method for mining plant lncRNAs related to abiotic stress responses based on graph neural networks according to claim 9, characterized in that, The mathematical expression for the interval loss function is as follows: in, Indicates and The positive sample prediction matrix corresponding to the known edge is given. Indicates and The negative sample prediction matrix related to the unknown edge.

Images