Abstract: The rapid development of single-cell RNA sequencing(scRNA-seq) technology has led to an exponential increase in single-cell gene expression data,thereby resulting in the accumulation of extensive gene expression datasets.Therefore,there is a pressing need for computational methods capable of leveraging these datasets to uncover potential regulatory relationships between genes.In recent years,the advancements in deep learning and the expansion of known regulatory relationship datasets have facilitated the development of numerous supervised inference methods,particularly those based on graph neural networks(GNNs).However,most of these current methods model the prior regulatory network as an undirected graph,neglecting the directed nature of regulatory relationships between genes,which makes it impossible to extract directional information.In addition,due to the limited availability of known regulatory information,genes with similar or correlated expression patterns may not ne-cessarily have known direct connections.Most current methods rely solely on extracting first-order neighborhood information,which may hinder the ability to fully capture the richer information contained in prior networks and expression data.To address these challenges,this paper proposes a gene regulatory inference method based on second-order multi-channel directed graph convolution.By leveraging prior regulatory networks,the method constructs a first-order adjacency matrix,a second-order in-degree adjacency matrix,and a second-order out-degree adjacency matrix.Additionally,it employs a directional Laplacian matrix to more accurately represent the structure of directed graphs,thereby enhancing the performance of network inference and the ability to model complex regulatory patterns.Experimental results with multiple datasets and evaluation metrics demonstrate that the proposed method can more accurately predict potential regulatory relationships between genes compared to existing work.Meanwhile,extensive ablation studies confirm that these different modules of the proposed method contribute to improving model performance.

Key words: Graph, Directed graph neural network, Gene regulatory network, Second-order neighborhood, Graph convolution