Gene regulation network prediction method and system based on explicit correlation modeling

Abstract

The invention discloses a gene regulatory network prediction method and system based on explicit correlation modeling, and the method comprises the steps: obtaining a gene expression matrix of single-cell RNA sequencing data and an adjacent matrix of a prior regulatory graph constructed based on prior knowledge, and inputting the matrixes into a graph neural network model; wherein the graph neural network model is configured to perform explicit modeling on a link in the prior regulation and control graph through an intra-layer message passing space and an inter-layer message passing space so as to obtain link representation; predicting whether a regulation relation exists between the gene pairs through a classifier on the basis of link characterization so as to deduce a gene regulation network; wherein the architecture of the graph neural network model is adaptively determined through an automatic architecture search algorithm according to input data. According to the framework provided by the scheme, modeling link representation is displayed in the message passing process, the regulation and control relation of the gene pair is inferred by MLP based on link embedding, utilization and organization of complex connection information of the prior regulation and control graph are enhanced from the source, and the inference accuracy is effectively improved.

Description

Technical Field

[0001] This invention belongs to the field of computer bioinformatics, and in particular relates to a method and system for predicting gene regulatory networks based on explicit association modeling. Background Technology

[0002] Gene regulatory networks reveal the interactions between genes and are key to understanding the core mechanisms of life activities. With the maturity of single-cell RNA sequencing technology, using computational models to inversely derive gene regulatory networks (GRNs) from scRNA-seq data has become a research hotspot in bioinformatics. Existing computational methods can be broadly classified into three categories: unsupervised / self-supervised learning, semi-supervised learning, and supervised learning. Unsupervised or self-supervised learning methods do not rely on known regulatory relationship labels; they infer gene regulatory networks by mining the intrinsic patterns in gene expression data. These methods show advantages in scenarios where label information is missing, but their reconstruction accuracy on real, complex biological data is often poor. Semi-supervised learning methods, while utilizing some known labels as guidance, offer limited performance improvements and also face accuracy bottlenecks.

[0003] Supervised learning methods formalize the GRN inference problem as a link prediction task, using known transcription factor-target gene regulatory relationships as training labels to train the model to predict unknown regulatory effects. However, these methods typically treat genes as independent node pairs, and their model design fails to fully consider and utilize the inherent graph topology of the gene regulatory network itself. Essentially, they learn statistical associations between gene pairs, ignoring the complex regulatory patterns formed by the interconnections of multiple genes in a local neighborhood. This leads to biases in their inference results in capturing the structural characteristics of the real GRN.

[0004] In recent years, graph neural networks (GNNs) have been introduced into GRN inference due to their powerful graph structure data modeling capabilities, resulting in advanced models such as GeneSpider and GENELink. These methods model genes and their interactions as graphs, using GNNs to learn gene representations, thus improving performance to some extent. However, these GNN models still have shortcomings. For example, existing GNN models generally follow a node-centric paradigm, performing information aggregation and representation learning at the node level. The regulatory relationships (i.e., links) between genes are implicit and indirect, inferred through the similarity or computation of node embeddings, failing to explicitly and directly model the links themselves. This prevents the full utilization of the rich semantics contained in the link information in the prior regulatory graph, limiting the model's ability to understand complex regulatory logic. Furthermore, existing GNN architecture designs rely on expert knowledge and lack adaptability. The inference model is fixed in specific, artificially designed GNN architecture instances. Given a graph learning task, a GNN architecture may perform well on a certain dataset, but this does not guarantee its effectiveness on other scRNA-seq datasets with different data distributions. Due to the diversity of single-cell datasets, manually designing and debugging GNN architectures for each new dataset is a laborious and challenging task, which greatly limits the general application and performance ceiling of the model. Summary of the Invention

[0005] The purpose of this invention is to propose a gene regulatory network prediction method and system based on explicit association modeling to address the problems existing in the prior art.

[0006] To achieve the above objectives, the present invention adopts the following technical solutions: A gene regulatory network prediction method based on explicit association modeling, the method comprising: Gene expression matrix from single-cell RNA sequencing data and adjacency matrix of prior regulatory graph constructed based on prior knowledge were obtained. The gene expression matrix and the adjacency matrix are input into the graph neural network model; The graph neural network model is configured to explicitly model the links in the prior control graph through intra-layer message passing space and inter-layer message passing space to obtain link representations. Based on the aforementioned link characterization, a classifier is used to predict whether there is a regulatory relationship between gene pairs, thereby inferring the gene regulatory network. The architecture of the graph neural network model is adaptively determined based on the input data using an automatic architecture search algorithm.

[0007] In the above-mentioned gene regulatory network prediction method based on explicit association modeling, the graph neural network model includes several information transmission network layers and a pooling layer, and the several information transmission network layers and the pooling layer are connected based on the inter-layer message passing space. The intra-layer message passing space is used for data processing within the information passing network layer.

[0008] In the gene regulatory network prediction method based on explicit association modeling described above, the intra-layer message passing space is processed in the following way to explicitly model the links: The neighborhood information of node v is aggregated by formula (1), and the representation of node v is updated by formula (2). in, This represents the l-th level aggregation operation; It is a neighborhood-type specific weight matrix; v represents the target node, and u represents the neighboring nodes of node v. This represents the set of all neighboring nodes directly connected to node v. It belongs to the set {𝑠𝑒l𝑓,𝑛𝑒𝑖𝑔ℎ𝑏𝑜𝑟} and is used to distinguish the connection between the node itself and its neighborhood; The weight matrix represents the node itself; It is the embedded representation of node u at level l; It is the embedded representation of the l-th layer node v; This represents the combined function operation of the l-th layer; This represents the activation function operation of the l-th layer.

[0009] In the gene regulatory network prediction method based on explicit association modeling mentioned above, this method includes a neighborhood aggregation candidate set containing several candidate aggregation patterns, a combination function candidate set containing several candidate combination patterns, and an activation function candidate set containing several candidate activation patterns. The aggregation operation, combination function operation, and activation function operation in the intra-layer message passing space are selected and determined by the automatic architecture search algorithm from the neighborhood aggregation candidate set, combination function candidate set, and activation function candidate set, respectively.

[0010] In the gene regulatory network prediction method based on explicit association modeling described above, in the inter-layer message passing space, the output and input of the upper layer of the information passing network are fused and used as the input of the lower layer of the information passing network, and the fusion method is selected and determined by the automatic architecture search algorithm from the inter-layer connection candidate set containing several candidate connection patterns.

[0011] In the gene regulatory network prediction method based on explicit association modeling described above, in the inter-layer message passing space, the outputs of all information passing network layers are aggregated as candidate information sources and input to the pooling layer, and the aggregation method is selected and determined by the automatic architecture search algorithm from the inter-layer aggregation candidate set containing several candidate aggregation patterns.

[0012] In the gene regulatory network prediction method based on explicit association modeling described above, this method includes a candidate set of link pooling operations containing several candidate pooling modes, and the automatic architecture search algorithm is further configured to select pooling operations for the pooling layer from the candidate set of link pooling operations.

[0013] In the gene regulatory network prediction method based on explicit association modeling described above, the automatic architecture search algorithm adaptively determines the architecture of the graph neural network model in the following manner: By optimizing the structured parameters Parameterized distribution Search the search space for the optimal combination of graph neural network model operations. ; This is an evaluation function used to measure the combination of operations. and a specific set of model weights Given a priori control map On the predictive performance; The search space covers the message passing space within the layer, the message passing space between layers, and the pooling layer operations.

[0014] A gene regulatory network prediction system based on explicit association modeling, comprising: The data acquisition module is used to acquire the gene expression matrix of single-cell RNA sequencing data and the adjacency matrix of the prior regulatory graph constructed based on prior knowledge; The model processing module includes a graph neural network model, which is used to receive the gene expression matrix and the adjacency matrix, and to explicitly model the links in the prior regulatory graph through the intra-layer message passing space and the inter-layer message passing space to obtain the link representation. The prediction module is used to predict whether there is a regulatory relationship between gene pairs based on the link characterization described above, so as to infer the gene regulatory network. An architecture search module is used to adaptively determine the architecture of the graph neural network model based on the input data using an automatic architecture search algorithm.

[0015] In the aforementioned system for inferring gene regulatory networks using graph neural networks based on explicit association modeling, the intra-layer message passing space in the model processing module is configured to process data to explicitly model the links in the following manner: The neighborhood information of node v is aggregated by formula (1), and the representation of node v is updated by formula (2). The aggregation operation of the intra-layer message passing space Combinatorial function operations Activation function operation They are configured to select from the neighborhood aggregation candidate set, the combination function candidate set, and the activation function candidate set, respectively. The inter-layer messaging space is configured to include connection operations selected from the inter-layer connection candidate set and aggregation operations selected from the inter-layer aggregation candidate set. The connection operation is used to merge the output and input of the upper information transmission network layer as the input of the lower information transmission network layer. The aggregation operation is used to aggregate the outputs of all information transmission network layers and input them into the pooling layer; The pooling layer is configured to include pooling operations selected from a candidate set of link pooling operations; The architecture search module is configured to execute a stochastic differentiable search algorithm based on a specific distribution. It searches the search space for the optimal combination of graph neural network model operations θ by optimizing the distribution ρβ(θ) parameterized by the structured parameter β. This search space covers the intra-layer message passing space, inter-layer message passing space, and pooling layer operations to determine the corresponding aggregation operations from the neighborhood aggregation candidate set, the combination function candidate set, and the activation function candidate set. Combinatorial function operations Activation function operation The system selects a determined aggregation mode from the inter-layer aggregation candidate set, a determined connection mode from the inter-layer connection candidate set, and a determined pooling mode from the link pooling operation candidate set.

[0016] The advantages of this invention are: the framework proposed in this solution displays the modeling link representation during message passing, and uses MLP to infer the regulatory relationship of gene pairs based on link embedding, thereby strengthening the utilization and organization of complex connection information of prior regulatory graphs from the source and improving the inference accuracy; The design employs a dual-space message passing mechanism, simultaneously modeling intra-layer and inter-layer spaces to capture multi-level regulatory dependencies. Furthermore, it re-aggregates the outputs of all layers, explicitly using the outputs of all layers as candidate information sources, and then performs searchable aggregation through various methods, effectively improving the model's flexibility and representational capabilities. By introducing an architecture search strategy, the optimal GNN structure can be automatically adapted to different single-cell RNA-seq datasets, including inter-layer, intra-layer, and pooling layer operations, reducing the burden of manual parameter tuning.

[0017] The three technical approaches of explicit link modeling, dual-space message passing, and automatic architecture search are creatively integrated and applied to the specific bioinformatics problem of gene regulatory network inference, and the results are significantly better than those of existing technologies. Attached Figure Description

[0018] Figure 1 This is a flowchart of the gene regulatory network prediction method based on explicit association modeling of the present invention. Figure 2 This is a diagram illustrating the overall framework of the gene regulatory network prediction method based on explicit association modeling of this invention. Figure 3 This is a system block diagram of the gene regulatory network prediction system based on explicit association modeling of the present invention; Figure 4 The performance of the AutoGERN model implemented in this invention on single-cell RNA sequencing datasets of seven real organisms is presented. Detailed Implementation

[0019] Given gene expression data from single-cell RNA sequencing and prior regulatory knowledge, the objective is to predict unobserved gene regulatory associations within a prior regulatory graph constructed based on this prior knowledge. The prior regulatory graph itself is highly incomplete, containing only a small subset of gene regulatory associations; the vast majority of potential gene regulatory associations remain unobserved, i.e., they are missing. Therefore, this task can be transformed into predicting missing links in the prior regulatory graph, also known as the link prediction problem.

[0020] This solution proposes a gene regulatory network prediction method based on explicit association modeling. A specific embodiment is provided below, and the method includes the following steps: (1) Data collection This embodiment evaluates the model's performance on the gene regulatory network inference task according to the testing standards of the BEELINE benchmark framework. Seven real single-cell RNA sequencing datasets were collected from the BEELINE benchmark framework, including two human cell lines and five mouse cell lines: human embryonic stem cells (hESC), human mature hepatocytes (hHEP), mouse dendritic cells (mDC), mouse embryonic stem cells (mESC), and three mouse hematopoietic stem cell (mHSC) lineages: erythroid lineage mHSC-E, lymphoid lineage mHSC-L, and granulocyte-macrophage lineage mHSC-GM. Detailed information on the above seven datasets is shown in Table 1.

[0021] Table 1. Statistical information from seven real single-cell RNA sequencing datasets. (2) Data preprocessing Seven real-world single-cell RNA sequencing datasets were preprocessed using the Scanpy tool. First, genes expressed in less than 90% of cells and low-quality cells with unacceptable gene expression were filtered out. Next, library size differences were corrected using TPM (transcriptional per million reads) and CPM (counts per million reads). Finally, the data were standardized and converted to logarithmic form. Bonferroni correction with an K-value threshold of 0.01 was used to identify the top 500 and 1000 significantly variable genes for each benchmark dataset. Furthermore, this embodiment used the TRRUST and RegNetwork databases to screen transcription factors for each benchmark dataset, and all screened transcription factors were included in the analysis. After removing duplicate genes, highly variable transcription factors and the top 500 and 1000 non-transcriptional genes with cell type specificity for each benchmark dataset were further screened. Simultaneously, gene regulatory networks derived from ChIP-Atlas chromatin immunoprecipitation sequencing ChIP-seq data were used as a real-world standard to evaluate the performance of the gene regulation inference method.

[0022] A hold-out validation strategy is adopted, in which the true standard regulatory effects of each benchmark dataset are randomly divided, with 80% of the regulatory relationships assigned as training set labels, 10% as test set labels, and the remaining 10% as validation set labels. This strategy is used to select the optimal training model and avoid model overfitting.

[0023] In link prediction tasks, the number of negative samples (unobserved regulatory effects) often far exceeds the number of positive samples (observed regulatory effects), leading to class imbalance when predicting the existence of regulatory interactions. To address this, a common strategy is to randomly sample an equal number of negative samples as positive samples during training—a process known as negative sampling. This helps maintain the unbiasedness of the classification model but may miss a significant amount of valuable discriminative information contained in the unobserved negative samples. Therefore, this embodiment retains all negative samples and divides them into the training and test sets along with the positive samples according to the aforementioned ratio. Meanwhile, to avoid data leakage, this embodiment further clarifies the segmentation conditions of the training set and the test set, and standardizes the sampling strategy for negative samples: unobserved gene pairs (𝑇𝑖, 𝐺𝑛𝑡) are defined as negative samples, where 𝐺𝑛𝑡 represents non-target genes; observed regulatory effects (𝑇𝑖, 𝐺𝑗) are defined as positive samples, where 𝑇𝑖 represents transcription factor 𝑖, and 𝐺𝑗 represents target gene 𝑗.

[0024] (3) Construction of graph neural network model framework like Figure 1 and Figure 2 As shown, this model uses the gene expression matrix *k* and the adjacency matrix *k* of the prior regulatory graph from single-cell RNA sequencing data as inputs to explicitly model and learn the link representations within the message-passing space. Furthermore, the link representations in this embodiment iterate alternately in two different message-passing spaces: intra-layer and inter-layer spaces. After multiple iterations and information aggregation, the learned link embeddings are further input into a classifier-multilayer perceptron (MLP) to infer the regulatory interactions of gene pairs. In addition, this method employs a robust search algorithm from graph neural networks to adapt the graph neural network architecture to different single-cell RNA sequencing datasets.

[0025] Figure 2 As can be seen, the model provided by this scheme consists of multiple stacked information transmission network layers. The input features and output link representations of each layer are connected and combined to form the input features of the next layer. Finally, the outputs of all layers are aggregated again, explicitly using the outputs of all layers as candidate information sources. Finally, the link representations predict whether gene pairs are regulatory associations through a pooling layer (Pool) and a multilayer perceptron (MLP). The bottom part shows the internal structure of the information transmission layer provided by this scheme.

[0026] Intra-layer message passing space implementation Traditional graph neural network models typically focus on node-level representation learning, relying primarily on connections between nodes to propagate information. These models update their feature representations by aggregating information from the neighborhood of the target node. While they capture the relationships between nodes to some extent, their processing of connection relationships and link information is relatively limited. They emphasize modeling the attributes of the nodes themselves, failing to fully explore the semantic information inherent in complex links, such as functional modules in protein-protein interaction networks and regulatory structures in gene regulatory networks.

[0027] This scheme proposes an intra-layer message passing framework that explicitly models the links between nodes in the graph, as shown in equations (1) and (2): Agg represents the aggregation operation, and equation (1) aggregates nodes. v The neighborhood information is given, where v represents the target node and u represents the neighboring nodes of node v. It is a feature of node u in the l-th layer, corresponding to Figure 2 middle ; It is a neighborhood-specific weight matrix for encoding link information (edges) in the graph, which introduces the edge parameter (weight) matrix for information transmission within the layer; Belongs to the set {𝑠𝑒l𝑓,𝑛𝑒𝑖𝑔ℎ𝑏𝑜𝑟}, and These represent the weight matrices of a node itself and its neighborhood, respectively, used to distinguish edges of the same type from those of its neighborhood. This represents the combination operation at level l. This represents the activation function of the l-th layer; It is the representation of node v in the l-th layer, corresponding to Figure 2 middle .

[0028] The above describes the characteristics of the neighboring node u of node v based on formula (1). Using the weight matrix with introduced edges After transformation, aggregation is performed to obtain the neighborhood aggregation result. , The characteristics of node v themselves are determined by formula (2). Weighted After transformation, the result is aggregated with the domain. The updated features of node v are obtained by fusing the features through a combination function and then processing them through an activation function. This means updating its own node.

[0029] Inter-layer message passing space implementation Traditional information relay networks (IRNs) are constructed by simply stacking layers to form graph neural network models, where the output of each IRN serves as the input for the next layer. However, due to vanishing gradients and oversmoothing issues, this approach is typically limited to very shallow models with very limited predictive performance.

[0030] This approach incorporates the concepts of residual connections and dense connections into the information transfer network, which helps alleviate the vanishing gradient problem in graph neural networks, effectively trains deeper networks, and better captures complex information and patterns in the graph. Simultaneously, through residual connections, the representation of each layer can retain information from previous layers, accelerating convergence, making the model more stable, and reducing the risk of overfitting. This approach defines this problem as inter-layer information transfer.

[0031] In particular, this scheme proposes an adaptive operation for the inter-layer search space, which adaptively searches for the optimal graph neural network architecture for different datasets. The inter-layer search space mainly consists of two important modules: layer connectivity and layer aggregation.

[0032] The layer connectivity module is used to fuse the output and input of the upper information transmission network layer as the input of the lower information transmission network layer. The fusion method is determined by an automatic architecture search algorithm from a set of inter-layer connection candidates containing several candidate connection modes. In this embodiment, three candidate connection modes are gathered for selection: stacked connection, skip summation connection, and skip splicing connection.

[0033] The inter-layer aggregation module is used to aggregate the outputs of all information transmission network layers and input them into the pooling layer. The aggregation method is determined by an automatic architecture search algorithm from an inter-layer aggregation candidate set containing several candidate aggregation modes. In this embodiment, three candidate aggregation modes are available for selection: skip aggregation, splicing aggregation, and maximizing aggregation.

[0034] Pooling layer After alternating intra-layer and inter-layer information transfer, the model employs pooling operations to represent the link embeddings at a higher level. For link prediction problems on prior regulatory graphs, the pooling operation ultimately outputs the link representations between gene nodes. In other autograph neural network models, subgraph-level ranking pooling methods are used to read information from the entire closed subgraph of the target link. Joint prediction tasks only require the joint structural representation of the target node set, thus eliminating the need for complex subgraph-level pooling methods. This scheme learns link representations solely from the target node set by reading information, and also proposes an adaptive operation for the pooling layer search space. This is determined by an automatic architecture search algorithm from a candidate set of link pooling operations containing several candidate pooling modes. This embodiment offers three pooling operations for selection: summation pooling, max pooling, and concatenation pooling.

[0035] Search space implementation The performance of graph neural network (Graph Neural Network) models is typically influenced by the characteristics and structure of the data. Different real-world single-cell sequencing datasets exhibit varying distribution characteristics and data structures, thus requiring different Graph Neural Network architectures. Single-cell RNA sequencing datasets are generally highly sparsity, which can interfere with the capture of gene-gene regulatory interactions. Furthermore, the topological structures of gene regulatory networks differ significantly across cell types, tissue types, and even species. Some datasets have simple topologies, while others have highly complex ones, particularly where gene-gene connections often extend beyond local connections. For these complex datasets, more complex Graph Neural Network (Graph Neural Network) structures are often better suited for capturing intricate global regulatory features between genes. Therefore, an automatic architecture search algorithm is employed to automatically select the optimal Graph Neural Network (Graph Neural Network) architecture for different datasets.

[0036] The search space of the model provided by this solution involves three parts: The adaptive operation of the intra-layer search space involves the selection of specific operations for operators such as aggregation functions, combination functions, and activation functions in the intra-layer message passing space. The specific operations of each function are determined by the automatic architecture search algorithm from the neighborhood aggregation candidate set, combination function candidate set, and activation function candidate set, respectively. The adaptive operation of the inter-layer search space involves the selection of specific operations for operators such as inter-layer join functions and inter-layer aggregation functions in the inter-layer message passing space. The specific operations of each function are selected and determined by the automatic architecture search algorithm from the inter-layer join candidate set and the inter-layer aggregation candidate set, respectively. The adaptive operation of the pooling layer search space involves the selection of specific operations for the pooling operators in the pooling layer. These specific operations are determined by an automatic architecture search algorithm from the candidate set of link pooling operations.

[0037] In this embodiment, each of the above operators provides multiple operation modes to adaptively select the appropriate operation to implement the corresponding operator.

[0038] Taking the inter-layer connection function as an example, in this embodiment, its candidate set 𝒪 has three candidate operations—connection modes: stacked connection, skip summation connection, and skip concatenation connection. For the hidden feature vectors that need to be connected... Assuming the selected connection operation The weight is Therefore, the output of this interlayer connection function can be expressed by formula 3: In the formula Furthermore, when one candidate operation is 1, the other two candidate operations are 0. Assuming that ᵃ represents the set of operations selected from all candidate operations in the model, the search task of the graph neural network model can be formalized as shown in formula (4): In the formula, 𝐸𝑣𝑎l(∙) represents the predictive performance of the model operation combination 𝜃 with weights 𝜔 on the prior control graph 𝒢.

[0039] Existing model adaptation algorithms generally suffer from drawbacks: some methods treat the operation combination 𝜃 directly as a continuous variable, thus making the objective function 𝐸𝑣𝑎l(𝜃,𝜔;𝒢) deterministically differentiable. However, with further research, researchers have found that such hybrid strategies often lead to performance inconsistencies. After the operation set search phase, the performance of the derived sub-network is significantly lower than that of its parent network before derivation. Analysis shows that the root cause of this phenomenon is that the relaxed operation combination 𝜃 cannot converge to a one-hot vector. Therefore, when redundant operations are removed after the operation set search, the actual structure obtained deviates from the final expected adaptive structure. At the same time, this hybrid strategy needs to maintain all operators in the entire large network during the adaptation process, consuming far more computational resources than the strategy corresponding to the one-hot vector.

[0040] To address this, this scheme employs a stochastic differentiable algorithm based on a specific distribution. Through reparameterization techniques, the objective function of the search space becomes differentiable, thereby achieving adaptive search for the graph neural network model. Specifically, assuming that the operation space φ of the graph neural network model is sampled from a certain distribution φ(φ), which is parameterized by the structured parameter φ, as shown in formula (5): In the formula, 𝜊 represents a specific operation in the candidate operation set; Indicates a uniformly distributed sample; 𝜏 represents the temperature parameter of the softmax activation function.

[0041] The above formula first guarantees the probability that 𝜊 will be sampled (i.e. ) and its weight It is directly proportional; secondly, its unique heat property. This ensures that the stochastic differentiable relaxation strategy is unbiased after convergence.

[0042] Therefore, the adaptation problem of graph neural network models is reformulated as Equation (6): Thus, the mathematical expression (6) of the automatic architecture search algorithm of the AutoGERN model of this scheme is obtained. This algorithm maximizes the expected predictive performance of the model on the gene regulation prior map under parameter constraints.

[0043] Furthermore, such as Figure 3 As shown, this embodiment further provides a gene regulatory network prediction system based on explicit association modeling, including: Data acquisition module 1 is used to acquire the gene expression matrix of single-cell RNA sequencing data and the adjacency matrix of the prior regulatory graph constructed based on prior knowledge; Model processing module 2, implemented through a graph neural network model, is used to receive the gene expression matrix and the adjacency matrix, and to explicitly model the links in the prior regulatory graph through intra-layer message passing space and inter-layer message passing space to obtain link representations; Prediction module 3, implemented through a classifier, is used to predict whether there is a regulatory relationship between gene pairs based on the link characterization, so as to infer the gene regulatory network. Architecture search module 4 is used to adaptively determine the architecture of the graph neural network model based on the input data using an automatic architecture search algorithm.

[0044] The overall model implementation in this embodiment is as follows: The number of information transmission network layers is set to four; the dimension of the hidden vector output by each layer is set to 100; the model uses the Adam optimizer by default to update parameters, and its learning rate is set to 0.0001; in addition, the model in this embodiment uses Dropout with a range of {0,0.2} to prevent overfitting; the batch size for model training is defined as 128, and the number of epochs is set to 100; while the number of epochs for model adaptation is set to 50.

[0045] The settings of hyperparameters in the model are summarized in Table 2 below.

[0046] Table 2 Summary of hyperparameters in the AutoGERN model To verify the potential of the AutoGERN model implemented by this method in gene regulation inference tasks, we used single-cell RNA sequencing datasets from seven real biological systems to comprehensively evaluate and analyze the performance of the AutoGERN model in gene regulation network inference and its robustness to the problem of imbalanced positive and negative samples from multiple perspectives.

[0047] The evaluation process summarized the following: ChIP-seq data was used as the true standard for performance validation, and a corresponding cell type-specific reference gene regulatory network standard was constructed for each real single-cell RNA sequencing dataset. The inferred gene regulatory network was then compared with the true standard gene regulatory network, and the area under the ROC curve (AUROC) and area under the PR curve (AUPRC) values ​​of the predicted results were calculated. The values ​​of AUROC and AUPRC range from 0 to 1, with higher values ​​indicating better performance. A UUROC value of 0.5 indicates that the model performance is equivalent to a random predictor.

[0048] Meanwhile, to further verify the superiority of the AutoGERN model, its performance was compared with five advanced supervised learning-based single-cell RNA sequencing data gene regulatory network inference algorithms. The specific comparison results are as follows: Figure 4 As shown.

[0049] from Figure 4 As can be seen, the prediction performance of the AutoGERN model on seven real single-cell RNA sequencing datasets (measured by AUROC and AUPRC values) is all above 0.98, and its overall performance is stable.

[0050] Among the datasets, the model achieved the best predictive performance on the datasets corresponding to the three mouse hematopoietic stem cell (mHSC) cell types, with both AUROC and AUPRC values ​​exceeding 0.99. We speculate that this result is mainly due to the denser prior regulatory network structure corresponding to these datasets, providing the model with more sufficient prior information support. However, the model's predictive performance was relatively the lowest on the mouse dendritic cell (mDC) dataset, with both AUROC and AUPRC values ​​below 0.99. This may be because the mDC dataset has the least available prior regulatory knowledge, resulting in insufficient prior information to aid the model's learning and thus a certain degree of performance degradation.

[0051] To further evaluate the performance of the AutoGERN model, this embodiment compares it with five supervised learning-based gene regulatory network inference models. The comparison results are shown in Table 3. Table 3 shows the AUROC performance of the AutoGERN model and the comparison methods on real datasets.

[0052] The bold text indicates the data for the first and second place performance rankings.

[0053] As shown in Table 3, the AutoGERN model significantly outperformed the other five methods on all seven real single-cell datasets. Specifically, compared to the second-ranked model on each dataset, the AutoGERN model achieved an average AUROC improvement of 21.3%. The improvement was smallest (8.5%) on the mouse hematopoietic stem cell erythroid lineage mHSC-E dataset, while the largest (28%) was achieved on the mouse dendritic cell mDC dataset. We speculate that this difference is related to the degree of influence of prior regulatory knowledge on different models. The performance of the other five models is more easily constrained by the amount of prior regulatory knowledge corresponding to the single-cell dataset, while the AutoGERN model is less affected by this factor. This result further demonstrates that the AutoGERN model has a wide range of applicability scenarios, especially when the available prior regulatory knowledge in the single-cell dataset is limited, the model can still maintain good inference performance.

[0054] The specific embodiments described herein are merely illustrative of the spirit of the invention. Those skilled in the art to which this invention pertains may make various modifications or additions to the described specific embodiments or use similar methods to substitute them, without departing from the spirit of the invention or exceeding the scope defined by the appended claims.

Claims

1. A gene regulatory network prediction method based on explicit association modeling, characterized in that, The method includes: Gene expression matrix from single-cell RNA sequencing data and adjacency matrix of prior regulatory graph constructed based on prior knowledge were obtained. The gene expression matrix and the adjacency matrix are input into the graph neural network model; The graph neural network model is configured to explicitly model the links in the prior control graph through intra-layer message passing space and inter-layer message passing space to obtain link representations. Based on the aforementioned link characterization, a classifier is used to predict whether there is a regulatory relationship between gene pairs, thereby inferring the gene regulatory network. The architecture of the graph neural network model is adaptively determined based on the input data using an automatic architecture search algorithm.

2. The gene regulatory network prediction method based on explicit association modeling according to claim 1, characterized in that, The graph neural network model includes several information passing network layers and a pooling layer, and the several information passing network layers and the pooling layer are connected based on the inter-layer message passing space. The intra-layer message passing space is used for data processing within the information passing network layer.

3. The gene regulatory network prediction method based on explicit association modeling according to claim 2, characterized in that, The intra-layer message passing space processes data to explicitly model the link in the following ways: （1） （2） The neighborhood information of node v is aggregated by formula (1), and the representation of node v is updated by formula (2). in, This represents the l-th level aggregation operation; It is a neighborhood-type specific weight matrix; v represents the target node, and u represents the neighboring nodes of node v. This represents the set of all neighboring nodes directly connected to node v. Belongs to the set {𝑠𝑒l𝑓, 𝑛𝑒𝑖𝑔ℎ𝑏𝑜𝑟}, used to distinguish the connections between a node itself and its neighborhood; The weight matrix represents the node itself; It is the embedded representation of node u at level l; It is the embedded representation of the l-th layer node v; This represents the combined function operation of the l-th layer; This represents the activation function of the l-th layer.

4. The gene regulatory network prediction method based on explicit association modeling according to claim 3, characterized in that, This method includes a neighborhood aggregation candidate set containing several candidate aggregation patterns, a combination function candidate set containing several candidate combination patterns, and an activation function candidate set containing several candidate activation patterns. The aggregation operation, combination function operation, and activation function operation in the intra-layer message passing space are selected and determined by the automatic architecture search algorithm from the neighborhood aggregation candidate set, combination function candidate set, and activation function candidate set, respectively.

5. The gene regulatory network prediction method based on explicit association modeling according to claim 2, characterized in that, In the inter-layer message passing space, the output and input of the upper-layer message passing network are fused and used as the input of the lower-layer message passing network, and the fusion method is selected and determined by the automatic architecture search algorithm from the inter-layer connection candidate set containing several candidate connection patterns.

6. The gene regulatory network prediction method based on explicit association modeling according to claim 5, characterized in that, In the inter-layer message passing space, the outputs of all information passing network layers are aggregated as candidate information sources and input to the pooling layer, and the aggregation method is selected and determined by the automatic architecture search algorithm from the inter-layer aggregation candidate set containing several candidate aggregation patterns.

7. The gene regulatory network prediction method based on explicit association modeling according to claim 2, characterized in that, This method includes a candidate set of link pooling operations containing several candidate pooling modes, and the automatic architecture search algorithm is further configured to select a pooling operation for the pooling layer from the candidate set of link pooling operations.

8. The gene regulatory network prediction method based on explicit association modeling according to claim 2, characterized in that, The automatic architecture search algorithm adaptively determines the architecture of the graph neural network model in the following manner: （3） By optimizing the structured parameters Parameterized distribution Search the search space for the optimal combination of graph neural network model operations. ; This is an evaluation function used to measure the combination of operations. and a specific set of model weights Given a priori control map On the predictive performance; The search space covers the message passing space within the layer, the message passing space between layers, and the pooling layer operations.

9. A gene regulatory network prediction system based on explicit association modeling, characterized in that, include: The data acquisition module (1) is used to acquire the gene expression matrix of single-cell RNA sequencing data and the adjacency matrix of the prior regulatory graph constructed based on prior knowledge; The model processing module (2) includes a graph neural network model, which is used to receive the gene expression matrix and the adjacency matrix, and to explicitly model the links in the prior regulation graph through the intra-layer message passing space and the inter-layer message passing space to obtain the link representation; The prediction module (3) is used to predict whether there is a regulatory relationship between gene pairs based on the link characterization described above, so as to infer the gene regulatory network. Architecture search module (4) is used to adaptively determine the architecture of the graph neural network model based on the input data through an automatic architecture search algorithm.

10. The system for inferring gene regulatory networks based on explicit association modeling using graph neural networks according to claim 9, characterized in that, The intra-layer message passing space in the model processing module (2) is configured to perform data processing to explicitly model the link in the following manner: （1） （2） The neighborhood information of node v is aggregated by formula (1), and the representation of node v is updated by formula (2). The aggregation operation of the intra-layer message passing space Combinatorial function operations Activation function operation They are configured to select from the neighborhood aggregation candidate set, the combination function candidate set, and the activation function candidate set, respectively. The inter-layer messaging space is configured to include connection operations selected from the inter-layer connection candidate set and aggregation operations selected from the inter-layer aggregation candidate set. The connection operation is used to merge the output and input of the upper information transmission network layer as the input of the lower information transmission network layer. The aggregation operation is used to aggregate the outputs of all information transmission network layers and input them into the pooling layer; The pooling layer is configured to include pooling operations selected from a candidate set of link pooling operations; The architecture search module (4) is configured to execute a random differentiable search algorithm based on a specific distribution, which searches for the optimal combination of graph neural network model operations θ from the search space by optimizing the distribution ρβ(θ) parameterized by the structured parameter β, the search space covering the operations of the intra-layer message passing space, the inter-layer message passing space and the pooling layer.

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