Abstract
Singlecell RNA sequencing provides highthroughput gene expression information to explore cellular heterogeneity at the individual cell level. A major challenge in characterizing highthroughput gene expression data arises from challenges related to dimensionality, and the prevalence of dropout events. To address these concerns, we develop a deep graph learning method, scMGCA, for singlecell data analysis. scMGCA is based on a graphembedding autoencoder that simultaneously learns cellcell topology representation and cluster assignments. We show that scMGCA is accurate and effective for cell segregation and batch effect correction, outperforming other stateoftheart models across multiple platforms. In addition, we perform genomic interpretation on the key compressed transcriptomic space of the graphembedding autoencoder to demonstrate the underlying gene regulation mechanism. We demonstrate that in a pancreatic ductal adenocarcinoma dataset, scMGCA successfully provides annotations on the specific cell types and reveals differential gene expression levels across multiple tumorassociated and cell signalling pathways.
Introduction
Singlecell RNA sequencing (scRNASeq)^{1} allows the investigation of transcriptomic landscapes; it is an increasingly popular platform for characterizing cellular heterogeneity^{2}, discovering complex tissues and diseases^{3,4}, and inferring cell trajectories^{5} at the singlecell level. Recently, many computational models have been developed to distinguish and annotate cell types, enabling efficient downstream analysis^{6}. However, these computational models often suffer from various challenges due to the high dimensionality of data and high probability of dropout events from the low capture rate and insufficient sequencing depth^{7,8,9,10}. There is an urgent need to develop effective computational models that capture the relationships between cells and identify the highprobability dropout events in scRNAseq data.
As an unsupervised learning method, cluster analysis has become a key step in defining cell types based on transcriptome data as well as the basis for downstream analyses. Accordingly, clustering methods have been welldeveloped to address the challenges over the past years; for instance, five very popular toolkits including SC3^{11}, Seurat^{12}, SCANPY^{13}, SINCERA^{14} and SingleR^{15} have been developed for the downstream analysis of scRNAseq data. SC3 is a consensus clustering algorithm using genetic filtering and PCA and Laplacian transformation^{11}. Seurat integrates scRNAseq data with insitu RNA patterns to infer cell locations and clusters^{12} while SCANPY is a scalable toolkit for analyzing singlecell gene expression data built jointly with anndata^{13}, both using shared nearest neighbor (SNN) modular optimization and Leiden for clustering. SINCERA converts the data to a zscore before clustering and then cell types are identified in the hierarchical structure^{14}. In general, these algorithms provide fast analysis and presentation to users’ lacking prior scRNAseq knowledge.
While these toolkits provide valuable information, it is apparent that current dimensionality reduction methods often either suffer from multiple simultaneous techniques and biological variability or ignore the intrinsic data distribution, resulting in the issue of overcrowding in the latent space and thus inaccurate cell clustering. To address these limitations, deep embedding clustering approaches have been successfully developed to model the highdimensional and sparse scRNAseq data; for example, deep count autoencoder network (DCA) uses an autoencoder based on negative binomial loss, with or without zero expansion to denoise scRNAseq count data^{16}. On this basis, scDeepCluster learns the feature representation and clustering simultaneously in the autoencoder from the zeroinflated negative binomial distribution model^{17}. A year later, scDeepCluster was extended to scDCC, with a prior exploitation of the domain knowledge in a semisupervised manner. In addition, other deep embedding models have been proposed to enhance the clustering results from diverse perspectives such as, DESC^{18}, scVI^{19}, scCAEs^{20}, scDHA^{21} and SCA^{22}. However, these deep embedding clustering methods typically ignore cell topological information and the heterogeneity among cell populations. Recently, emerging graph neural networks (GNNs) have been shown to naturally model heterogeneous cellcell relationships and the complex gene expression patterns from compressed latent spaces^{23,24}.
Here, motivated by these discoveries, we propose a graph convolutional autoencoder framework, called scMGCA, to analyze scRNAseq datasets. scMGCA adopts the graph convolutional network (GCN) as an encoder to extract the key structural information of the scRNAseq gene expression count matrix and cell graph; it is paired with a multinomialbased decoder to capture the global probability structure of the data. Then, selfoptimized embedded clustering is applied to cluster the lowdimensional representation by adopting the KullbackLeibler (KL) divergence. In addition, three training losses including the clustering loss, multinomialbased loss and cell graph reconstruction loss, are simultaneously optimized to discover the cell clustering label assignment and to protect the cellcell topological representation. Moreover, to formulate the cellcell relationships, we propose the cellPPMI graph with a positive pointwise mutual information (PPMI) matrix and random surfing to aggregate adjacent cells in the cooccurrence probability PPMI matrix. We evaluate the clustering performance of scMGCA by comparing it with the stateoftheart clustering methods on several real scRNAseq datasets, and reveal that scMGCA is superior to these scRNAseq clustering methods for cell segregation and visualization. In particular, scMGCA is also able to correct for the batch effect of data coming from different scRNAseq protocols. We then analyze the functional genomic interpretation of the principal compressed transcription space in the graphembedding autoencoder to provide robust understanding of the functional significances of scMGCA. To further demonstrate the potential of scMGCA in tumor disease research, we apply it to the pancreatic ductal adenocarcinoma (PDAC) dataset and identify the cell types which elucidated PDACrelated regulatory mechanisms and PDAC cellular communication.
Results
scMGCA can learn the lowdimensional representation from highdimensinal and sparse scRNAseq data by providing a global view of the entire cell graph and count matrix (Fig. 1) to aid in the downstream analysis of scRNAseq data. It has five main steps to learn the graphembedding representation. (1) A cellPPMI matrix is generated on the normalized singlecell gene expression matrix to capture the cellcell topology. (2) We established the framework of graph convolution autoencoder. GCN is used to integrate the expression matrix and cell graph (cellPPMI) to extract the main gene information and cell topology, and to preserve it in a latent embedded representation. (3) High probability dropout events of the singlecell data are simulated by multinomial distribution, and a multinomialbased decoder is developed to characterize multimodal distribution. (4) A selfoptimized clustering task based on KullbackLeibler (KL) divergence is performed on the embedded representation, which is simultaneously trained with the loss functions in the graph convolution autoencoder. (5) The latent embedded representation learned by scMGCA enables clustering, dimensionality reduction, and visualization of the singlecell data. In addition, it is possible to interpret the biological significance of genes and discover disease regulatory mechanisms.
We first normalized the scRNAseq gene expression matrix and selected the highly variable genes, and then built a cell graph that represents the cellcell relationships of the normalized data. For the construction of cell graph, we used a random surfing algorithm based on KNN graph to aggregate neighboring cells. Intuitively, the random surfing algorithm captures the transition probability between different vertices from the unweighted KNN graph structure information. After that, the positive pointwise mutual information (PPMI) matrix was calculated to describe similar cells by assigning a cooccurrence attention mechanism, which further enhances the cell graph. Finally, the cell graph, an undirected weighted graph, can be fed into the model.
Under the framework of graph convolution autoencoder, scMGCA uses two layers of GCN to effectively extract the gene expression information and cellcell topological structure from the scRNAseq data matrix and cell graph, which is then preserved in a lowdimensional embedded representation. To capture the global probabilistic structure of the data, a multinomialbased decoder was developed to characterize scRNAseq data distribution and simulate dropout events using the multinomial distribution. It should be noted that the zeroinflated distribution was not used here as recent studies have shown that singlecell count matrices largely follow a multinomial distribution^{25}. In addition, we adopted an inner product decoder to reconstruct the content and structural information of the cell graph from the lowdimensional representation.
Finally, we perform the KullbackLeibler (KL) divergence on the latent representations to selfoptimize the clustering task by enhancing the auxiliary target distribution. Then, by simultaneously revising clustering loss, multinomialbased loss and cellgraph reconstruction loss, scMGCA can jointly evaluate the clustering label assignment and feature learning of topological structures by training the entire graph convolution autoencoder, which promptly compensates for model deviations from the correct clustering distribution. After that, we can directly obtain the predicted cluster labels from the final optimized result. In particular, we selected the best strategy from Kmeans and spectral clustering to initialize the clustering centers, resulting in the robust clustering performance of the overall model. In addition to its significant clustering performance, the lowdimensional latent representation learned by scMGCA also provides good reduction and visualization effects of the original data. In terms of application, we transferred the standard deviation rank of the weight matrix into the network to screen for genes with biological interpretability in the latent embedded representation, providing new marker genes for the singlecell datasets. Further, scMGCA was able to identify cell types in cancer datasets and explore disease regulatory mechanisms.
scMGCA provides better performance than other singlecell clustering methods across multiple platforms
We compared scMGCA with 12 other singlecell clustering methods on 20 real scRNAseq datasets across multiple platforms to evaluate the clustering performance of scMGCA. These benchmark methods are divided into three main categories, namely deep embedded clustering methods (scziDesk^{26}, scDeepCluster^{17}, DCA^{16}, DEC^{27}, DESC^{18}, scVI^{19}, scCAEs^{20}), deep graph embedded clustering methods (scGNN^{23}, scGAE^{28}, GraphSCC^{24}) and basic singlecell clustering methods (Seurat^{12}, SHARP^{29}).
The ground truth cell type labels for these datasets are available, and we used normalized mutual information (NMI), adjusted rand index (ARI) and average silhouette width (ASW) as the evaluation metrics of the clustering performance (Fig. 2a and Supplementary Figs. 1–2). As shown in those figures, for the 20 datasets, scMGCA has the highest NMI, ARI and ASW values for 15 of them, respectively. Overall, across the 20 datasets, scMGCA has the highest mean NMI, ARI and ASW values, reaching 0.8304, 0.8278, and 0.5827, respectively. After scMGCA, scziDesk has superior NMI and ARI values, while scVI has superior ASW values. In addition, we also compared the overall clustering performance (by NMI, ARI and ASW) of the methods across various data platforms, including platebased platform, flowcellbased platform, SmartSeq2, SMARTer, 10X Genomics, and Dropseq. The experimental results indicated that scMGCA outperformed the other 12 clustering algorithms on across multiple platforms, and demonstrating the effectiveness and precision of scMGCA in clustering across multiple platforms. In particular, we optimize the compared deep learning methods and take their best case as the final result (Supplementary Tables 1–18).
In addition, we visualized the lowdimensional embedded representations of scMGCA and 10 of the other embedded clustering methods in two dimensions using UMAP^{30} (Fig. 2b). Overall, scMGCA and scziDesk outperformed the other methods for cell clustering on the ‘Qx Limb Muscle’ dataset, confirming the results with NMI. However, scziDesk had a few cell clustering results that are confounded in the skeletal muscle cell and macrophage clusters, while scMGCA successfully clustered almost all of the cells on the ‘Qx Limb Muscle’ dataset. This may indicate that the latent embedded representation of scMGCA effectively preserves the key information and data distribution learned from the scRNAseq gene expression matrix and cell graph. We performed UMAP visualization comparisons on all datasets (Supplementary Figs. 3–7). In addition, to investigate whether scMGCA can detect rare cell types and small clusters that cannot be detected by other methods, we compared scMGCA with other deep learning methods including scziDesk, scDeepCluster, DCA, DEC, scGNN, scGAE, and GraphSCC on four datasets (‘QS heart’, ‘Muraro’, ‘Qx limb Muscle’, and ‘Adam’) that contain rare cell types and small clusters for indepth examination (Supplementary Note 3 and Supplementary Fig. 8).
We also compared the running time of scMGCA with other clustering algorithms. For the test dataset, we adopted 20 smallscale datasets with 30025,000 cells, and a largescale dataset called ‘Tabula Muris’ with 70,118 cells from 20 organs and tissues. The experimental results are depicted in Fig. 2c. It is worth noting that scMGCA divides the data into multiple batches for learning when clustering datasets with >25,000 cells. Figure 2c shows that the running time of the traditional methods, including Seurat and SHARP, is always faster than all deep learning methods. Compared to other GNNbased methods, our proposed model can provide shorter running time. We also found that scGAE cannot be run on the datasets with >12k cells. We observe that the running time curve of scMGCA drops and is within reasonable ranges (i.e. all less 1.5 h) as a result of the use of batch learning for the ‘Tabula Muris’. To explore the specific changes in the running time of scMGCA with the number of cells and genes, we tested the respective running time of scMGCA for different numbers of cells and different numbers of genes on ‘Tabula Muris’ (Supplementary Fig. 9). It can be observed that scMGCA demonstrates a monotonically linear increase in running time along with the number of cells and genes, demonstrating its potential as the computing power increases in the future. Further, scMGCA still has good clustering performance on ‘Tabula Muris’ (Fig. 2d).
Finally, to further demonstrate the scalability of scMGCA, we applied scMGCA to the dataset composed of 1,306,127 mouse brain cells (Supplementary Note 5 and Supplementary Fig. 10). Most comparison algorithms failed or produced no results within 24 h for such a big dataset. Ultimately, only scMGCA, DEC, DESC, and traditional methods were able to run successfully. Therefore, we compared their running time and memory usage at different numbers of cells (Supplementary Fig. 11). From the experimental results, we observe that, excluding the extra time and memory consumption from the cell graph computation, there is not much difference between scMGCA and the deep learning methods. Moreover, it is worth noting that, among several graph neural networks compared in this paper, scMGCA is the only one that can run successfully; it can also be regarded as an advancement in deep graph learning method development on largescale scRNAseq datasets.
scMGCA effectively performs dimensionality reduction correction and improves visualization of scRNAseq data
Dimensionality reduction and visualization of highthroughput data have always been the main goals of scRNAseq data clustering to facilitate downstream analysis and cell type discovery. Here, we compared scMGCA with three other dimensionality reduction methods, namely PCA^{31}, tSNE^{32}, and UMAP^{30}. We adopted the average silhouette width (ASW) as the evaluation metric that measures true cell labels and the reduced matrix. ASW reflects the degree of aggregation of the same cell type and the extent of separation between different cell types, and a value close to 1 indicates good performance. Since tSNE and UMAP have many parameters which can greatly affect the 2D embedding, we compared scMGCA with tSNE and UMAP in wider parameter space; and the experimental results demonstrated that scMGCA is superior to tSNE and UMAP (Supplementary Note 6 and Supplementary Tables 19–21). We then compared the best case of tSNE and UMAP with PCA and scMGCA (Fig. 3a). Figure 3a depicts that scMGCA has the highest ASW on ‘QS Trachea’ and ‘QS Heart’ datasets, and the performance of dimensionality reduction correction and visualization significantly outperforms the other compared methods. Furthermore, the overall average ASW obtained on the 20 datasets is much higher than that of the other methods in Fig. 3b. The ASW values and visualization performance of all datasets are shown in Supplementary Figs. 12–15.
We also carried out a comprehensive comparison between scMGCA and two stateoftheart singlecell transcriptome analysis methods (SCANPY and Seurat), measuring their clustering performance, dimensionality reduction, and visual comparison (Fig. 3c). scMGCA performs dimensionality reduction correction and clustering based on critical gene expression information and topology captured by a graph neural network. SCANPY and Seurat utilize PCA to reduce the dimensionality of the gene expression matrix, and then cluster in a lowdimensional space. The functions and parameter settings used in SCANPY and Seurat are shown in Supplementary Note 8. We used the UMAP embedded scatter plot to grade the three methods and compared the predicted labels with the true labels on three datasets, ‘QS Limb Muscle’, ‘QS Diaphram’ and ‘Qx Bladder’. In Fig. 3c, we certainly observe that scMGCA performs better than SCANPY and Seurat in terms of effectiveness and clustering performance when dimensionality reduction correction, and it separates most of the cells correctly. Specifically, on the ‘QS Diaphram’ dataset, scMGCA identifies better the compacted mesenchymal and skeletal muscle cell clusters compared to the other methods. On the ‘Qx Bladder’ dataset, scMGCA is able to distinguish urothelial cells from mixed bladder cells. For comprehensive analysis, we chose five evaluation metrics (DaviesBouldin, ASW, NMI, ARI and VMeasure) to assess the three models (Fig. 3d). We observed that scMGCA surpasses SCANPY and Seurat for all metrics on the three datasets, demonstrating scMGCA’s strong clustering performance. Comparisons on all the datasets are presented in Supplementary Figs. 16–18.
scMGCA can remove the batch effect in human pancreatic data from different scRNAseq protocols
Batch effect correction and clustering of data generated by multiple different scRNAseq protocols is challenging due to the strong batch differences among different scRNAseq protocols. To investigate the batch effect of data generated by different scRNAseq protocols, we combined four publicly available human pancreas datasets generated from CELseq^{33}, CELseq2^{34}, Fluidigm C1^{35}, and Smartseq2^{36}. For benchmark comparison, we selected five stateoftheart batch effect correction methods including DECS^{18}, Harmony^{37}, MNN^{38}, scVI^{19}, and Scanorama^{39}.
In Fig. 4a, we observe that scMGCA can effectively merge datasets from different scRNAseq protocols and remove the batch effect. Compared to other batch effect correction methods, both DESC and Harmony can substantially complete correction of the batch effect, but they do not mix all cells uniformly. scVI could only mix the datasets from CELseq and CELseq2, with no correction of Fluidigm C1 and Smartseq2. Scanorama did not remove the batch effect from Smartseq2, while MNN completely separated the data generated by the four scRNAseq protocols. Furthermore, Fig. 4a also reveals that scMGCA can effectively aggregate cells of the same type and separate cells of different types. DESC also aggregated most cells, with the exception of beta cells which were mixed with alpha cells, acinar cells, and ductal cells. Harmony mixed alpha cells are mixed with acinar cells, delta cells, and beta cells. The three methods (MNN, scVI, and Scanorama), failed in effectively seperating the different cell types, resulting in downstream confusion. These findings are also confirmed by the comparison of the clustering performance as depicted in Fig. 4b. Overall, scMGCA and DESC are superior to other batch effect correction methods, whereas MNN, scVI, and Scanorama perform poorly across those three metrics: NMI, ARI, and ASW.
To explore the process by which scMGCA removes batch effects, we visualize the latent embedding representation of scMGCA at different epochs. As shown in Fig. 4c, scMGCA is capable of aggregating the cells and gradually mixing the datasets generated by the various scRNAseq protocols. This demonstrates that scMGCA not only accurately clusters cells but also simultaneously corrects for batch effect in multiple datasets with strong batch differences.
Evaluation of hyperparameter selection and ablation study
We evaluated the impact of different numbers of cell clusters, transfer steps, numbers of selected genes and diverse cluster center initialization methods on scMGCA, as well as the effectiveness of each component in scMGCA of the 20 real scRNAseq datasets.
For the cluster number effect, we compared the clustering performance of scMGCA after perturbing the cluster number, that is, we set the number of experimental clusters to {K − 2, K − 1, K, K + 1, K + 2}, where K is the true cluster number. The heatmap of Fig. 5a indicates that, for most datasets, a better NMI value is achieved for the true number of clusters. The datasets with a low number of clusters, such as ‘Qx Bladder’ (K = 4), ‘QS Trachea’ (K = 4) and ‘QS Diaphragm’ (K = 5), are more affected by disturbance than others. The reason may be that they contain less cell populations and unstable structures. On the whole, scMGCA is insensitive to the number of clusters. The heatmap of the ARI measures is depicted in Supplementary Fig. 19.
Figure 5b shows the clustering performance of scMGCA with different numbers of transfer steps (s) and different numbers of selected genes (d). The results demonstrate that scMGCA has the best overall clustering performance when s = 2 and d = 500 compared to other conditions. The initialization of the clustering centers is very critical to the clustering process and will influence the final clustering performance. As scMGCA’s clustering center initialization method is based on the optimal strategy in kmeans and spectral clustering, we conducted correlation analysis in the context of purely kmeans, spectral or random initialization methods, respectively (Fig. 5c). We observed that kmeans and spectral clustering models are indeed more relevant to scMGCA than random initialization methods. The kmeans has the highest correlation, which also implies that scMGCA chooses more clustering centers initialized by kmeans on the 20 scRNAseq datasets. Further, we elaborated on the conditions and reasons under which the two initialization methods, kmeans and spectral clustering, can be effective, respectively (Supplementary Note 10 and Supplementary Table 22). We also analyzed other parameters in detail, including the weights of loss function, the parameters of cellPPMI graph, the number of network layers, and different network frameworks (Supplementary Note 11), so as to give users an effective guide.
We performed an ablation study on scMGCA to investigate if the cellPPMI graph augments the traditional KNN graph, and whether the multinomialbased decoder is more effective than ZINB in modeling singlecell data distribution. Specifically, we compared the clustering performance of scMGCA, scMGCA with KNN graph and scMGCA with ZINB decoder, using NMI (Fig. 5d) and ARI measures (Supplementary Fig. 25). The experimental results showed that scMGCA had the best clustering performance on most datasets; and that removing the cellPPMI graph and multinomialbased decoder reduced the performance of scMGCA for cell clustering. In particular, we further verified that the cellPPMI graph is more suitable for singlecell data than the KNN graph (Supplementary Note 12). In addition, we also compared the performance of scMGCA with other clustering algorithms for dropout correction (Supplementary Note 13 and Supplementary Figs. 27–28). From the experimental results, it was observed that both NMI and ARI values of scMGCA decrease slightly on most datasets and it outperforms all the other comparison methods. These experimental findings confirm that scMGCA is sufficiently stable and robust to provide promising performance in dropout event correction.
Functional genomics interpretability of the latent embedded characterization of scMGCA
We conducted a functional genomics interpretability analysis of the latent embedded representation of scMGCA on the ‘Qx Limb Muscle’ dataset, and validated that it preserves the key information of the scRNAseq gene expression data and thus has the capacity of functional genomics interpretation.
First, we used the tSNE algorithm to project the latent embedded representation into a twodimensional space at different stages of training and up to the end (Fig. 6a). The results show that, as the training progresses, cells on the latent representation gradually cluster together; and the cell clusters become more and more obvious, reflecting that the training and learning of the latent embedded representation is meaningful and effective. Moreover, to illustrate that the lowdimensional latent representation of scMGCA preserves the cellcell topology of the original data, we calculated the paired Pearson correlations between each pair of cells in the original scRNAseq data and the data reduced by scMGCA, PCA, tSNE, and UMAP (Fig. 6b). Obviously, the experimental results indicate that the latent representation of scMGCA on the ‘Qx Limb Muscle’ preserves the cellcell topological information and the structure of the original data better than PCA, tSNE, and UMAP (Fig. 6b).
To explore the functional significances of the latent embedded representation, we selected the top 200 highly expressed genes using the standard deviation and weight of the latent embedded representation (specific selection strategy in Methods), and then performed Gene Ontology (GO) enrichment analysis to detect enriched functional attributes based on geneassociated GO terms (Fig. 6c). The GO terms are mainly enriched in the chemotaxis and migration of neutrophils in the biological processes (BPs). Neutrophils are the frontline cells of the innate immune system with an important role in inflammation and tissue wound healing^{40,41}. We also performed KEGG pathway analysis to investigate the molecular pathways behind the selected genes (Fig. 6d). We observe that the pathway with the most of the selected genes is Cytokinecytokine receptor interaction that corresponds to the molecular function (MF) predominantly enriched in cytokine receptor and ligand activity in the GO enrichment analysis results. Muscle cells produce cytokines into the circulation during exercise, and the control of cytokine production depends on the interactions between various local and systemic factors^{42}. Therefore, the results of the KEGG and GO analysis indicate that the genes selected in the latent embedded representation are essential for the binding of receptor ligands in the circulation. Furthermore, we employed STRING^{43} to construct the PPI network for the selected genes, and then visualized the network structure showing an interaction score > 0.7 through Cytoscape^{44} (Fig. 6e). In particular, Molecular Complex Detection (MCODE)^{45} was adopted to identify the most important modules.
On this basis, to explore whether there are marker genes among the selected genes, we used the gene expression matrix of the ‘Qx Limb Muscle’ dataset and the predicted cluster label of scMGCA to analyze the expression levels of the selected genes in each cell cluster via SCANPY. Fig. 6f depicts the stacked violin plots of the top 10 genes expressed in each cluster, and we provide the detailed distribution of gene expression values of the top most genes of each cell cluster (Fig. 6g). We found that many selected genes serve as cell marker genes, such as Bcr for B cells^{46} and Pdcd1 for T cells^{47}, which further proves that the 200 genes selected in the latent embedded representation have meaningful functional interpretation. In addition, some genes that have not yet been discovered have the potential as new cellular markers for biologists; for instance, Egr4 has the highest gene expression level in mesenchymal cells, but not enough studies have been done to determine whether it is actually a cellular marker; therefore, Egr4 may represent a marker gene for these cells. Similarly, Pmaip1 could be a candidate marker gene for mouse skeletal muscle cells. In addition, we employed other clustering methods and used the same method to extract functional genes to compare with scMGCA (Supplementary Note 14 and Supplementary Figs. 29, 30). From the experimental results, we observed that scMGCA is able to selects genes that are highly expressed in each cell cluster, while the other clustering algorithms appeared confused or not found. scMGCA identified differentially expressed genes closer to the genes according to the annotated labels. Furthermore, we also compared scMGCA with SCANPY and Seurat and found that scMGCA was able to detect genomic features which have not been detected by the standard methods (Supplementary Note 15 and Supplementary Fig. 31).
Finally, we applied the Monocle3^{48} algorithm to the gene expression matrix consisting of these 200 interpretable genes to analyze the developmental trajectory of the timeseries ‘Klein’^{9} and hESC dataset^{49} in pseudotime (Supplementary Note 16 and Supplementary Fig. 32). From Supplementary Fig. 32, it can be observed that the raw data does not lead to the trajectory path well and reveals the wrong stage of cell differentiation, whereas the cell trajectories inferred by the interpretable genes picked by scMGCA were closely related to the true stages of cell differentiatio accurately. The cell and time trajectories inferred from the interpretable genes selected by scMGCA accurately tracked the stages of cell differentiation, demonstrating that these genes can effectively infer the cell and time trajectories, and further elaborating the effectiveness for selecting interpretable genes.
scMGCA can elucidate the underlying regulatory mechanisms of pancreatic ductal carcinoma
We applied scMGCA to a pancreatic ductal carcinoma (PDAC) dataset to illustrate its capability for singlecell analysis. The dataset was obtained from a primary PDAC tumor and a control pancreas from CRA001160, and contained a total of 57,530 cells and 18,008 genes^{50}. The PDAC data were first preprocessed and clustered by scMGCA (Supplementary Note 17), and then cell types were annotated with marker genes in each cell cluster, as summarized in Supplementary Table 23. Finally, we identified 10 types of cells, including acinar cells, B cells, type 1 ductal cells, type 2 ductal cells, endocrine cells, endothelial cells, fibroblasts, macrophages, stellate cells, and T cells (Fig. 7a). Among them, the largest proportion of type 2 duct cells and the smallest proportion of endocrine cells were found. Notably, type 2 ductal cells were all detected in tumor cells as seen in Fig. 7b. We then visualized the expression levels of the top 10 differential genes in each cell cluster (Fig. 7c). We observe from the heatmap, that differential genes are clearly expressed in each cell cluster, demonstrating that scMGCA is effective in clustering and annotating the dataset. Specially, we also checked for transcription factors (TF) among these genes using RcisTarget^{51}, and obtained the DNA binding motif with the highest enrichment score for each cell cluster. Further, we interpreted the significant marker gene of each cell cluster in detail, including its expression distribution in all cells (Fig. 7d) and the difference in its expression levels between the cell clusters (Fig. 7e). We also performed pseudotime analysis of the top 10 genes of each cell cluster and visualized them for 4 clusters (Fig. 7f). We see that the genes of clusters 3 and 4 are highly expressed at the start point and middle point of the pseudotime course, respectively, while the genes of clusters 1 and 2 are highly expressed at the end point.
Then, we performed pathway enrichment analysis (Fig. 7g). Among all the cell types, the highest enrichment score was for pancreatic secretion; it is consistent with the fact that dysregulated pancreatic duct fluid secretion is the main process related to PDAC. The digestion and absorption of proteins and fats are also the processes significantly enriched in PDAC, as evidenced by other PDAC studies^{52,53,54}. The pancreas contains different cells that produce enzymes important for digestion, including trypsin and chymotrypsin that digest protein, and lipase that breaks down fats. Therefore, the abnormality of the pancreas will indirectly or directly affect the digestion and absorption of proteins and fats. In addition, protein digestion and absorption have been reported to be associated with the development of pancreatic neuroendocrine tumors^{55}. Other pathways, such as natural killer cellmediated cytotoxicity and complement and coagulation cascades, have been confirmed in PDACrelated research^{56,57}. Systematically, we used CellChat^{58} to infer cellcell communication detected by scMGCA. A variety of signaling pathways were found by CellChat, of which the insulin signaling pathway had the highest level of signaling. Due to the plethora of metabolic derangements caused by hyperinsulinemia, researchers believe that insulin signaling plays a potentially decisive role in tumors, including PDAC^{59}. From the hierarchical plot of cell interactions of the insulin signaling pathway in Fig. 7h, we observe that endothelial cells, fibroblasts, macrophages, and stellate cells in addition to duct cells, have a high percentage of cells that serve as sources of the insulin signaling pathway. Meanwhile, several studies have indeed demonstrated that the insulin signaling pathway active in these cells plays an important role in the progression of PDAC^{60}.
To verify whether the signaling pathways identified by the singlecell PDAC data are clinically relevant, we conducted a cohort study adopting TCGA’s database public of invasive pancreatic ductal adenocarcinomas and its variants (PAAD) to validate their consistency. Specifically, since the type 2 ductal cells identified by scMGCA were all derived from tumor cells, it is reasonable to assume that type 2 ductal cells and tumors are correlated. On this basis, we performed GSVA enrichment on the type 2 ductal cells identified by scMGCA and 178 tumor samples from the TCGA data, respectively, and then compared them (Supplementary Fig. 33). It can be observed that the pathways enriched from PAAD tumor samples are mostly the same as those enriched from the type 2 ductal cells identified by scMGCA, and these pathways are essentially associated with PDAC. Among them, the coenriched p53 (signaling) pathway is an important pathway in PDAC. As a sequencespecific transcription factor, the p53 protein is a major tumor suppressor^{61}. Under oncogenic stress, p53 is activated to induce multiple programs, including cell cycle exit, apoptosis and replicative senescence, aiming to limit malignant cell proliferation^{62}. In addition to this, it was mainly enriched for tumorrelated functions such as glycolysis, protein secretion and pathways in cancer, further supporting the malignant state of the type 2 ductal cells. In conclusion, the experimental results indicate that the results of scMGCA analysis of PDAC can be validated by another independent cohort study and that scMGCA can elucidate the potential regulatory mechanisms of PDAC.
Discussion
scRNAseq enables the highthroughput measurements on gene expression patterns at the level of individual cells, accounting for cellular heterogeneity. However, the effective cell type annotation from highdimensional and sparse sequencing data is still challenging by AI or even human. Therefore, it is worth exploring effective extraction and dissemination of cellcell topology in the data. In this paper, we proposed scMGCA to address these problems. Specifically, we propose a cellPPMI graph to aggregate neighboring cells through random surfing and a cooccurrence probability PPMI matrix, capturing critical cellcell topology. Secondly, we employ GCNs under the framework of graph autoencoder to extract and integrate the gene expression information and cell topology, and to preserve the key information in lowdimensional latent embedded representations. Thirdly, we propose a multinomialbased decoder to decode the latent embedded representation and to train the network by optimizing a multinomialbased loss function. This step simulates the dropout events that lead to sparse scRNAseq data through multinomial distribution, so that the overall model always follows the multimodal distribution for learning. Finally, we propose selfoptimizing embedded clustering based on KL divergence on the lowdimensional representations, and simultaneously optimize the clustering loss and the other loss functions in the network.
To demonstrate that scMGCA can accurately cluster cells, we compared it with 12 singlecell clustering methods. The experimental results show that scMGCA has the best clustering performance and outperforms the other 12 comparison methods for data across multiple platforms, demonstrating the crossplatform capability of scMGCA in the wetlab sense. In particular, some rare cell types and small clusters that cannot be picked up by other methods can be detected by scMGCA. For model scalability, scMGCA is able to successfully cluster 1.3 million datasets with reasonable time and memory consumption, which can be seen as an advancement in deep graph learning on largescale datasets. scMGCA can also effectively reduce dimensionality and visualize blue the singlecell data. In experiments compared with three dimensionality reduction methods and two singlecell analysis packages, the ASW obtained for dimensionality reduction by scMGCA is the highest and the visualized results are close to the distribution of the real clusters. In addition, scMGCA is able to correct for the batch effect generated by data from different scRNAseq protocols, outperforming other stateoftheart batch effect correction methods.
Meanwhile, scMCGA presents a new interpretable approach for functional genomics. We propose a ranking and screening method based on the standard deviation of the parameter matrix in the GCN encoder to select 200 highly expressed genes from the latent embedding representation in scMGCA. Through the functional analysis of these genes, we found that the latent embedding representation of scMGCA is biologically interpretable without any major sacrifices on its cell clustering performance. In addition, scMGCA is able to discover significantly expressed differential genes in each cell cluster, which other deep learning methods cannot, and discover potential marker genes in some cell clusters that were not detected by standard methods. These experimental results not only verify that the underlying embedding representation of scMGCA is biologically interpretable, but also provide a new way for deep graph clustering to explore biological interpretability.
Moreover, scMGCA can also elucidate the underlying regulatory mechanisms of pancreatic ductal carcinoma (PDAC). We applied scMGCA to PDAC data for cell clustering and defined cell types by marker genes in the cell clusters. Interestingly, all type 2 ductal cells identified by scMGCA were derived from tumor cells. Furthermore, we found that type 2 ductal cells were enriched for several pathways essentially associated with PDAC, and most of them were consistent with the pathways enriched in tumor samples from clinical data. This demonstrates the ability of scMGCA to elucidate the underlying regulatory mechanisms of complex diseases and deliver biologically meaningful results.
In summary, scMGCA discards the traditional way of constructing cell graphs and jointly analyzes singlecell data through graphembedding representation and multinomial distribution simulation. As a new graphlearning method for singlecell biology, can simultaneously perform cell clustering, dimensionality reduction, batch effect correction, millionlevel data analysis, interpretability analysis and singlecell data analysis of joint clinical data, which is rare in the current field of graph neural networks. In future work, we will continue to improve and expand scMGCA.
Methods
Data processing and normalization
We take the scRNAseq gene expression count matrix X ∈ R^{n×g} as input, where n and g denote the number of cells and genes, respectively. The first step is to filter out genes that are not expressed in cells, reducing the impact of the high dropout rates in scRNAseq data. Then, to facilitate training and optimization of the network, we convert the discrete data into continuous data and ensure the stability of the size factor, the normalization can be defined as follows:
where median(X) denotes the median of the total expression values of all cells. According to Eq. (1), the discrete data is smoothed and rescaled by natural log transformation. Finally, we adopt the SCANPY package^{13} to calculate the normalized dispersion values of each gene to rank them, and the top d highly variable genes with highlevel information are used in the study, that is, the final normalized matrix \(\widehat{{{{{{{{\bf{X}}}}}}}}}\in {{{{{{{{\bf{R}}}}}}}}}^{n\times d}\).
Cell graph
In this study, we develop a cell graph to represent the relationship between cells, inspired by a cooccurrence probability PPMI matrix^{63}. The cell graph is first constructed from a KNN graph, where each node represents a cell. Through computing the Euclidean distance between nodes, and setting the number of neighbors k, each node is connected to the node within k shortest distance including itself, and creates an edge between them, and the cell graph K can be defined below:
where \({{{{{{{{\mathcal{N}}}}}}}}}_{k}(i)\) represents the neighborhood containing the nearest k nodes with the ith node as the center. It can be clearly seen that the KNN graph determines the domain of each node and its neighbor nodes through a local search method, which is a more effective way to model biological networks^{64,65}.
After that, we apply the random surfing model^{66} to the KNN graph to further explore the potentially complex nonlinear relationships between nodes in the domain. We introduce a transition matrix \({{{{{{{{\mathcal{P}}}}}}}}}^{s}\), where \({{{{{{{{\mathcal{P}}}}}}}}}_{ij}^{s}\) represents the probability of the ith node reaching the jth node after s steps of transitions, and \({{{{{{{{\mathcal{P}}}}}}}}}^{0}\) is the initial transition matrix equal to the identity matrix (\({{{{{{{{\mathcal{P}}}}}}}}}^{0}={{{{{{{\mathcal{I}}}}}}}}\)). The probability of returning to the initial vertex and restarting the process is set to (1 − α), the transition matrix iteration process can be defined as follows:
Empirically, we set the transfer step s to two steps (s ≤ 3), where it has been proved that the thirdorder neighborhood covers almost the entire biological network, and the neighborhood was not very informative for nodes with more than three hops^{67,68}. To further explore Eq. (3), we can update the rule through the initial transition matrix \({{{{{{{{\mathcal{P}}}}}}}}}^{0}\):
After s steps, the probability matrix is \({{{{{{{\bf{U}}}}}}}}=\mathop{\sum }\nolimits_{s=1}^{S}{{{{{{{{\mathcal{P}}}}}}}}}^{s}\). To augment the graph, we transform the U after a random surfing model into a positive pointwise mutual information (PPMI) matrix. The main method of augmentation is based on calculating the pointwise mutual information (PMI) of each node and measuring their correlation, which is defined below.:
where ∣S∣ = ∑_{x}∑_{y}p(x, y), x, and y represent different nodes; p(x) and p(y) denote the probability of x and y, respectively; p(x, y) represents the cooccurrence probability of x and y. According to probability theory, if x and y are more related, the ratio of p(x, y) and p(x)p(y) is larger. Therefore, the cells of the same type in the biological network have higher weights in the cell graph. Finally, we can approximately yield the PPMI matrix as the cell graph A, which is defined below:
where Θ denotes the sum of all elements in U. row(U) and col(U) are the column vector of the sum of each row of U and the row vector of the sum of each column of U, respectively.
Multinomialbased graph convolutional autoencoder
To better capture the cell graph structure and node relationships of scRNAseq data, we propose a graph convolutional autoencoder based on multinomial distribution model. The pipeline of the model is to first preserve the main features and structure of the count matrix data and cell graph data into a lowdimensional space through graph convolution network (GCN), and then we use two parallel decoders to reconstruct the graph and extract the data information in the latent embedded representation; respectively, the inner product and multinomialbased decoder.
We take the preprocessed gene expression matrix \(\widehat{{{{{{{{\bf{X}}}}}}}}}\) and the cell graph A as inputs. The encoder performs convolution operation through twolayers of GCN, and preserves the important information of \(\widehat{{{{{{{{\bf{X}}}}}}}}}\) and A into the latent embedded representation Z, which is defined as follows:
where \(\sigma (\cdot )=\max (0,\cdot )\) denotes a RELU activation function; \(\overline{{{{{{{{\bf{A}}}}}}}}}={{{{{{{{\bf{D}}}}}}}}}^{\frac{1}{2}}{{{{{{{\bf{A}}}}}}}}{{{{{{{{\bf{D}}}}}}}}}^{\frac{1}{2}}\) is normalized cell graph, and D = diag{(I + A)1_{N}} is the degree matrix; W_{l} is the parameter matrix learned by lth layer. The inner product decoder decodes the reconstructed cell graph information from Z, which is defined as follows:
where \(\widehat{{{{{{{{\bf{A}}}}}}}}}\) is the reconstructed cell graph A, sigmoid( ⋅ ) = 1/(1 + e^{−⋅}) is sigmoid activation function. Therefore, we can define a reconstruction loss \({{{{{{{{\mathcal{L}}}}}}}}}_{r}\) to minimize it during training as follows:
where n represents the total number of nodes.
On the other hand, we employ a multinomialbased decoder to decode the data matrix information. We define \({n}_{i}=\mathop{\sum }\nolimits_{j=1}^{d}{\widehat{X}}_{ij}\) to represent the total gene expression of the ith cell and m_{ij} denotes the unknown true relative abundance of the jth gene expression in the total gene expression of the ith cell, that is, \(E({\widehat{X}}_{ij})={n}_{i}{m}_{ij}\). Therefore, the vector \({\widehat{X}}_{i}=({\widehat{X}}_{i1},{\widehat{X}}_{i2},...,{\widehat{X}}_{id})\) follows a multinomial distribution, which can be defined as follows:
To address dropout events, we propose using a binary random variable U_{ij} for simulation, where U_{ij} = 0 means that the jth gene is dropped in the ith cell. Let π_{ij} = P(U_{ij} = 1), we have U_{ij} ~ Bernoulli(π_{ij}). Theoretically, a high dropout rate implies low gene expression, and it can be inferred that π_{ij} is positively correlated with m_{ij}. Assuming that V_{ij} is the expected relative expression level of the jth gene in the ith cell, and m_{ij} should be multiplied by π_{ij} and V_{ij} during the dropout process and normalized as below:
Obviously, m cannot be calculated completely by statistical theory, hence we learn from the lowdimensional representation in the deep neural network according to Eq. (12), which is defined as follows:
where f_{d} is a threelayer fully connected neural network with 128, 256 and 512 nodes in the hidden layers, respectively; W_{m} represents the learned weights and M is the parameter matrix. Given the latent embedded representation \({{{{{{{\bf{Z}}}}}}}},\widehat{{{{{{{{\bf{X}}}}}}}}}\) can be regarded as conditionally independent, the negative loglikelihood of the multinomial distribution can be constructed as the loss of data matrix reconstruction as below:
Deep embedded clustering with latent representation
To obtain better clustering performance, we present a selftraining clustering method on the latent embedded representation of the graph convolutional autoencoder. The loss function takes the form of KullbackLeibler (KL) divergence, which is defined as follows:
where q_{iu} is the soft label of the embedded node z_{i}, using Student’s tdistribution to calculate the similarity between z_{i} and the cluster center μ_{u}, which can be described as follows :
For the initial clustering center {μ}, we use kmeans clustering based on data distribution and spectral clustering based on graph structure to obtain the results, and select the best ones for training. In addition, p_{iu} is an auxiliary target distribution, to improve the high confidence in q_{iu}, which can be formulated as follows:
Noticeably, the target distribution P is defined on the basis of Q, and Q approximates the target distribution P in a selfoptimizing manner to obtain better clustering performance.
Joint embedding and clustering optimization
The training strategy of scMGCA is to jointly optimize the latent embedded representation of the graph convolutional autoencoder and cluster tasks, minimizing the following objective function:
where \({{{{{{{{\mathcal{L}}}}}}}}}_{r}\) denotes the cell graph reconstruction loss; \({{{{{{{{\mathcal{L}}}}}}}}}_{m}\) represents the loss of multinomialbased decoder; \({{{{{{{{\mathcal{L}}}}}}}}}_{c}\) is the embedded clustering loss; γ_{1}, γ_{2} and γ_{3} are weight coefficients assigned to each loss to control the balance of the total objective function. Stochastic gradient descent (SGD) and back propagation are used jointly to optimize the graph autoencoder and clustering centers. The gradient of the clustering loss \({{{{{{{{\mathcal{L}}}}}}}}}_{c}\) relative to the potential embedded node z_{i} and the cluster center μ_{u} can be calculated as:
Given the learning rate l_{r}, the cluster center μ_{u} can be updated as follows:
where n denotes the total number of nodes. The polynomial coefficient matrix W_{e} of scMGCA in encoder and the weight matrix W_{d} in the multinomialbased decoder are updated as follows:
The stopping condition is that the maximum number of iterations is achieved. Then, we can obtain the predicted clustering assignment of each cell via the Q after model training.
Functional genomics interpretation of gene findings from latent embedded representations
In scMGCA, the normalized cell graph \(\overline{{{{{{{{\bf{A}}}}}}}}}\) and scRNAseq gene expression matrix \(\widehat{{{{{{{{\bf{X}}}}}}}}}\) preserve the cellcell topology information into a lowdimensional latent embedded representation Z through two layers of GCN, as shown in Equation (8). Among them, the ddimensional data is reduced to 15dimensional at the beginning, and d is the number of genes after preprocessing. Obviously, the weight matrix W contains the key information of these genes, as it plays a leading role in dimensionality reduction and is involved in model training. Therefore, we focus on the weight matrices W_{1} and W_{2}, extracting the key information through the variance from the direction of Z^{n×15} to \({\widehat{{{{{{{{\bf{X}}}}}}}}}}^{n\times d}\), and finally finding the biologically explanatory genes. In the remaining part, we introduce the specific computational process.
First, the latent embedded representation Z^{n×15} is derived from the weight matrix \({{{{{{{{\bf{W}}}}}}}}}_{2}^{128\times 15}\) and the firstlayer GCN output \({\widehat{{{{{{{{\bf{X}}}}}}}}}}_{1}^{n\times 128}\). At this time, the key information of all genes contained in 15 dimensions of Z can be captured from W_{2}. Therefore, we calculate the standard deviation of W_{2} and obtaine a 128dimensional result \({r}_{1}^{128\times 1}\). Then, we select the top 50% (128 × 50% = 64) of highest variance from \({r}_{1}^{128\times 1}\), and save their index \({I}_{1}^{1\times 64}\). The \({\widehat{{{{{{{{\bf{X}}}}}}}}}}_{1}^{n\times 128}\) is derived from the weight matrix \({{{{{{{{\bf{W}}}}}}}}}_{1}^{d\times 128}\) and the \({\widehat{{{{{{{{\bf{X}}}}}}}}}}^{n\times d}\). In this step, we filter and retain the columns with high variance in \({\widehat{{{{{{{{\bf{X}}}}}}}}}}_{1}^{n\times 128}\) (containing essential gene information) according to I_{1}, and finally we get \({\overline{{{{{{{{\bf{W}}}}}}}}}}_{1}^{d\times 64}\). We also perform the previous operation on \({\overline{{{{{{{{\bf{W}}}}}}}}}}_{1}^{d\times 64}\), that is, calculate the standard deviation, to obtain a ddimensional result \({r}_{2}^{d\times 1}\). Finally, we extract the top 200 highly variable genes from \({r}_{2}^{d\times 1}\) and save the index \({I}_{2}^{1\times 200}\), and then find 200 pivotal genes with biological explanations from \({\widehat{{{{{{{{\bf{X}}}}}}}}}}^{n\times d}\) based on the index \({I}_{2}^{1\times 200}\).
Implementation details and comparisons with existing methods
scMGCA is implemented in Python, and the core model is built on the Tensorflow framework that is publicly available at https://pypi.org/project/scMGCA. To evaluate the performance of our scMGCA against other current scRNA clustering methods, we compared scMGCA with the following methods:

Deep selftraining Kmeans clustering method (scziDesk, https://github.com/xuebaliang/scziDesk)^{26}. scziDesk combines the deep learning method and a soft selftraining Kmeans algorithm to aggregate scRNAseq data in a latent space.

Singlecell modelbased deep learning method (scDeepCluster, https://github.com/ttgump/scDeepCluster)^{17}. scDeepCluster is a deep clustering method based on a singlecell model that uses domain knowledge to learn clustering and feature representation simultaneously.

Deep count autoencoder network (DCA, https://github.com/theislab/dca)^{16}. DCA takes into account the overdispersion and count distribution of scRNAseq data and uses a zeroinflated negative binomial noise model.

Unsupervised deep embedding clustering method (DEC, https://github.com/XifengGuo/DECkeras)^{27}. DEC applies a deep neural network to simultaneously learn cluster assignments and feature representations in a lowerdimensional space.

Unsupervised deep embedding algorithm (DESC, https://github.com/eleozzr/desc)^{18}. DESC clusters scRNAseq data by iteratively optimizing the clustering objective function.

Singlecell variational inference (scVI, https://github.com/YosefLab/scVI)^{19}. scVI uses stochastic optimization and deep neural networks to aggregate information from similar cells and genes and approximate the distribution of the observed expression values, taking into account batch effects and limited sensitivity.

Deep scRNAseq clustering method via convolutional autoencoder and soft Kmeans (scCAEs, https://github.com/gushenweiz/scCAEs)^{20}. scCAEs learns feature representation and clustering for scRNAseq based on convolutional autoencoder embeddings and soft Kmeans.

Singlecell graph neural network (scGNN, https://github.com/juexinwang/scGNN)^{23}. scGNN provides a deep learning framework that formulates cellcell relationships and applies a mixture Gaussian model to learn gene expression patterns.

Singlecell graph autoencoder (scGAE, https://github.com/ZixiangLuo1161/scGAE)^{28}. scGAE applies a multitask oriented graph autoencoder to maintain the feature information and structural information of scRNAseq data.

GCNbased singlecell clustering model (GraphSCC, https://github.com/GeniusYx/GraphSCC)^{24}. GraphSCC clusters cells by using a graphical convolutional network to illustrate the structural relationships between cells.

R toolkit for singlecell genomics (Seurat, https://github.com/satijalab/seurat). Seurat is an R package design for the analysis and exploration of single cell RNAseq data.

Singlecell RNAseq hyperfast and accurate processing via ensemble random projection (SHARP, https://github.com/shibiaowan/SHARP). SHARP is a bioinformatics tool for processing and analyzing singlecell RNAseq (scRNAseq) data.
Benchmarking metrics for scMGCA clustering and visualization
In this paper, we employed two widely used evaluation measures, normalized mutual information (NMI) and adjusted rand index (ARI), to estimate the performance of the different computational methods. DaviesBouldin (DBI) and VMeasure are also introduced for a more comprehensive analysis when comparing to SCANPY and Seurat.
NMI measures the normalized mutual information between predicted labels and true labels. Let l denote the predicted cluster labels and l^{G} denote the groundtruth labels. The NMI is defined as:
ARI evaluates the similarity of two clustering results in a statistical way, which can be defined as:
where \({n}^{{\prime} }\) is the number of clusters in the predicted clustering l, n^{G} is the number of clusters in the groundtruth clustering \({l}^{G},\, {{n}_{i}}^{{\prime} }\) is the number of data objects in the ith cluster of \(l,{n}_{j}^{G}\) is the number of data objects in the jth cluster of l^{G}, and n_{ij} is the number of data objects that belong to both cluster i in l and cluster j in l^{G}.
We also adopt the average silhouette width (ASW) to test our method for dimensionality reduction and visualization, which is defined as below:
where a(i) denotes the average distance from x_{i} to all the other data points in the cluster to which x_{i} belongs, and b(i) denotes the minimum average distance from x_{i} to all other clusters to which o does not belong. The value of ASW is between [ − 1, 1]. If ASW is close to 1, it means that the clustering of the data object x is reasonable; if ASW is close to 1, it means that the division of x is inaccurate; if ASW is ~0, it implies that many data points in x are on the boundary of the two clusters. The ASW is a measure of the reasonableness and validity of the clustering results.
DBI measures the mean of the maximum similarity of each cluster, which can be formulated as:
where N is the number of clusters, \(\overline{{S}_{i}}\) represents the average distance from the data in the ith cluster to the cluster centroid, and E_{ij} is the Euclidean distance between the ith cluster and the jth cluster. The smaller the DBI value, the closer the clustering results are to the inside of the cluster, indicating that the clustering effect is better.
VMeasure is based entirely on the conditional entropy between two clusters, which can be defined as:
where \(\frac{H({{{{{{{\bf{C}}}}}}}}{{{{{{{\bf{K}}}}}}}})}{H({{{{{{{\bf{C}}}}}}}})}\) is the conditional entropy of class division given the cluster division condition. h and c represent homogeneity and completeness measures, respectively. The VMeasure value v is the harmonic mean of the h and c, and the value is larger when the two categories are closely separated.
Functional enrichment
We use the R package ClusterProfiler^{69} to perform KEGG and GO enrichment analysis on the 200 genes selected from the latent embedded representation. We utilize the function ‘enrichKEGG’ for the KEGG analysis, where the parameters are set to “pAdjustMethod = fdr, pvalueCutoff = 0.01, qvalueCutoff = 0.05”. The GO analysis is performed by function ‘enrichGO’, where the parameters are set to “ont = ALL, pAdjustMethod = BH, pvalueCutoff = 0.01, qvalueCutoff = 0.05”.
PPI network
We performed preliminary PPI network construction on the selected 200 genes using STRING^{43} and extracted the part of the network with high interaction scores (>0.7) as input to Cytoscape for visualization. To identify the most important modules in the PPI network, we adopt MCODE^{45} for the network and give the top three modules.
Trajectory inference
The trajectory analysis was performed in the R package, Monocle3 (http://coletrapnelllab.github.io/monoclerelease/monocle3/). In Supplementary Fig. 32, we extracted an expression matrix of 200 biologically interpretable genes as input and used the labels predicted by scMGCA clustering. After the monocle loads the data by function ‘new_cell_data_set’, the data is preprocessed by function ‘preprocess_cds’. Then, the data is dimensionally reduced by function ‘reduce_dimension’, where the parameters are set to “reduction_method = UMAP, preprocess_method = PCA”. Further, the cells are clustered by function ‘cluster_cells’, where the parameters are set to “reduction_method = UMAP”, and the principal graph is learned by function ‘learn_graph’, where the parameters are set to “use_partition = F, close_loop = F, learn_graph_control = NULL, verbose = FALSE”. Finally, the function ‘plot_cells’ is used to visualize the trajectory inference. In Fig. 7f, the heatmap of the pseudotime analysis adopted the function ‘plot_pseudotime_heatmap’. Monocle introduces a strategy of sorting individual cells in pseudotime, using the asynchronous process of individual cells to place them on corresponding trajectories for biological processes such as cell differentiation.
Identification of marker genes in cell clusters
We used the function ‘FindAllMarkers’ in the R package Seurat^{12} to identify marker genes, where the parameters are set to “only.pos = True, min.pct = 0.25”. Then, biological marker genes of each cell cluster were selected from the obtained genes with p_val_adj ⩽ 0.05 and avg_logFC ⩾ 0.5. Finally, the expression levels of biological marker genes in different cell clusters are visualized by the function ‘DoHeatmap’.
TFmotif analysis
TF motifs were found by the R package RcisTarget^{51} with default parameters. For the analysis of human cancer samples, hg19 was used as the reference TF. By inputting the marker genes of each cell cluster into the function ‘cisTarget’, where the parameters are set to “motifAnnot = motifAnnotations_hgnc”, the enriched motif corresponding to each cell cluster is obtained, and then the motif with the highest enrichment score is selected.
Gene set enrichment analysis (GSEA)
GSEA is performed on the basis of biological marker genes, and the main process adopts the R package ClusterProfiler^{69}. First, the genes obtained from the function ‘FindAllMarkers’ were converted by the function ‘bitr’, that is from SYMBOL to ENTREZID, and then the converted genes and their avg_log2FC are input into the function ‘gseKEGG’ for enrichment analysis. Finally, the visualization of the results is performed by the function ‘gseaplot2’.
Gene set variation analysis (GSVA)
We mainly use the function ‘gsva’ from the R package GSVA, where the parameters are set to “method = ssgsea, abs.ranking = T”. The related pathway analysis was used to assess the activation of hallmark and metabolic pathways, which is available in the MSigDB databases^{70}.
CellChat analysis
CellChat analysis was performed using the R package CellChat^{58}. First, we used the function ‘createCellChat’ to create a CellChat object for the overall gene expression matrix, and then addded the cell annotation information identified by scMGCA through the function ‘addMeta’. We used CellChatDB.human provided by CellChat as the human ligand receptor reference. Finally, the cellcell communication probability is inferred using the function ‘computeCommunProb’, and the communication probability at the level of each cell signaling pathway is inferred by the function ‘computeCommunProbPathway’. The figure is generated with the function ‘netVisual_aggregate’, where the parameter is set to “layout = hierarchy”.
Statistics and reproducibility
The detailed statistical tests were explained in each figure legend. Sample data were obtained from public repositories. Sample size was not predetermined and is the maximum number of samples available for each datasets. No data were excluded from the analyses. No experimental groups were assigned. Our study does not involve group allocation that requires blinding. To reproduce the results, please find the Source Data file we provided.
Reporting summary
Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.
Data availability
We collected 20 real and public scRNAseq datasets across multiple platforms. These datasets come from different organs in humans and mouse, such as the brain, pancreas, trachea, and other. These datasets include ‘Pollen’ (SRP041736), ‘CampBrain’ (GSE75140), ‘CampLiver’ (GSE81252), ‘Muraro’ (GSE85241), ‘Klein’ (GSE65525), ‘Romanov’ (GSE74672), ‘Adam’ (GSE94333), ‘Young’ (EGAS00001002171), ‘Plasschaert’ (GSE102580), ‘Chen’ (GSE87544), ‘Tosches turtle’ (PRJNA408230), ‘Bach’ (GSE106273), and so on. The remaining ‘QS’ and ‘Qx’ datasets are derived from mouse scRNAseq data generated by Smartseq2 sequencing and 10x Genomics sequencing, respectively, in the Stanford University study^{71}. The details of the 20 scRNAseq datasets including the number of cells, number of cell types, and organs are tabulated in Supplementary Table 24, and can be downloaded from https://github.com/Philyzh8/scMGCA and https://hemberglab.github.io/scRNA.seq.datasets. The dataset ‘Tabula Muris’ (GSE109774) can be downloaded from https://doi.org/10.6084/m9.figshare.5968960.v3. The 1.3 million mouse brain cells dataset contains 1,306,127 cells and 27,998 genes, downloaded from the 10x Genomics website: https://support.10xgenomics.com/singlecellgeneexpression/datasets/1.3.0/1M_neurons. The human pancreatic islet datasets are generated from four different scRNAseq protocols, including CELseq (GSE81076)^{33}, CELseq2 (GSE85241)^{34}, Fluidigm C1 (GSE86469)^{35}, and Smartseq2 (EMTAB5061)^{36}. The hESC dataset (GSE75748)^{49} can be downloaded from https://www.ncbi.nlm.nih.gov/geo/query/acc.cgi?acc=GSE75748. The accession number for the PDAC data reported in this paper is GSA: CRA001160. These data have been deposited in the Genome Sequence Archive under project PRJCA001063. The PAAD data comes from TCGA and can be downloaded from https://github.com/Philyzh8/scMGCA/tree/master/PAAD. The MSigDB databases for gene set analysis can be downloaded from https://www.gseamsigdb.org/gsea/msigdb. These datasets have been deposited in the Zenodo database (https://doi.org/10.5281/zenodo.7475687). All other relevant data supporting the key findings of this study are available within the article and its Supplementary Information files or from the corresponding author upon reasonable request. Source data are provided with this paper.
Code availability
scMGCA is released as a python package at: https://pypi.org/project/scMGCA. The source code and usage tutorial at GitHub: https://github.com/Philyzh8/scMGCA^{72}.
References
Kolodziejczyk, A. A., Kim, J. K., Svensson, V., Marioni, J. C. & Teichmann, S. A. The technology and biology of singlecell rna sequencing. Mol. Cell 58, 610–620 (2015).
Saliba, A.E., Westermann, A. J., Gorski, S. A. & Vogel, J. örg Singlecell rnaseq: advances and future challenges. Nucleic Acids Res. 42, 8845–8860 (2014).
Haghverdi, L., Büttner, M., Wolf, F. A., Buettner, F. & Theis, F. J. Diffusion pseudotime robustly reconstructs lineage branching. Nat. Methods 13, 845–848 (2016).
Stephenson, W. et al. Singlecell rnaseq of rheumatoid arthritis synovial tissue using lowcost microfluidic instrumentation. Nat. Commun. 9, 1–10 (2018).
Tran, T. N. & Bader, G. D. Tempora: cell trajectory inference using timeseries singlecell rna sequencing data. PLoS Comput. Biol. 16, e1008205 (2020).
Zheng, R. et al. An adaptive sparse subspace clustering for cell type identification. Front. Genet. 11, 407 (2020).
Macosko, E. Z. et al. Highly parallel genomewide expression profiling of individual cells using nanoliter droplets. Cell 161, 1202–1214 (2015).
Zheng, G. X. Y. et al. Massively parallel digital transcriptional profiling of single cells. Nat. Commun. 8, 1–12 (2017).
Klein, A. M. et al. Droplet barcoding for singlecell transcriptomics applied to embryonic stem cells. Cell 161, 1187–1201 (2015).
Han, X. et al. Mapping the mouse cell atlas by microwellseq. Cell 172, 1091–1107 (2018).
Kiselev, V. Y. et al. Sc3: consensus clustering of singlecell rnaseq data. Nat. Methods 14, 483–486 (2017).
Butler, A., Hoffman, P., Smibert, P., Papalexi, E. & Satija, R. Integrating singlecell transcriptomic data across different conditions, technologies, and species. Nat. Biotechnol. 36, 411–420 (2018).
Wolf, F. A., Angerer, P. & Theis, F. J. Scanpy: largescale singlecell gene expression data analysis. Genom. Biol. 19, 1–5 (2018).
Guo, M., Wang, H., Potter, S. S., Whitsett, J. A. & Xu, Y. Sincera: a pipeline for singlecell rnaseq profiling analysis. PLoS Comput. Biol. 11, e1004575 (2015).
Aran, D. et al. Referencebased analysis of lung singlecell sequencing reveals a transitional profibrotic macrophage. Nat. Immunol. 20, 163–172 (2019).
Eraslan, G., Simon, L. M., Mircea, M., Mueller, N. S. & Theis, F. J. Singlecell rnaseq denoising using a deep count autoencoder. Nat. Commun. 10, 1–14 (2019).
Tian, T., Wan, J., Song, Q. & Wei, Z. Clustering singlecell rnaseq data with a modelbased deep learning approach. Nat. Machine Intel. 1, 191–198 (2019).
Li, X. et al. Deep learning enables accurate clustering with batch effect removal in singlecell rnaseq analysis. Nat. Commun. 11, 1–14 (2020).
Lopez, R., Regier, J., Cole, M. B., Jordan, M. I. & Yosef, N. Deep generative modeling for singlecell transcriptomics. Nat. Methods 15, 1053–1058 (2018).
Hu, H., Li, Z., Li, X., Yu, M. & Pan, X. Sccaes: deep clustering of singlecell rnaseq via convolutional autoencoder embedding and soft kmeans. Brief. Bioinform. 23, bbab321 (2022).
Tran, D. et al. Fast and precise singlecell data analysis using a hierarchical autoencoder. Nat. Commun. 12, 1–10 (2021).
Alessandri, L. et al. Sparselyconnected autoencoder (sca) for single cell rnaseq data mining. NPJ Syst. Biol. Appl. 7, 1–10 (2021).
Wang, J. et al. scgnn is a novel graph neural network framework for singlecell rnaseq analyses. Nat. Commun. 12, 1–11 (2021).
Zeng, Y., Zhou, X., Rao, J., Lu, Y. & Yang, Y. Accurately clustering singlecell rnaseq data by capturing structural relations between cells through graph convolutional network. In 2020 IEEE International Conference on Bioinformatics and Biomedicine (BIBM), 519–522 (IEEE, 2020).
Townes, F. W., Hicks, S. C., Aryee, M. J. & Irizarry, R. A. Feature selection and dimension reduction for singlecell rnaseq based on a multinomial model. Genom. Biol. 20, 1–16 (2019).
Chen, L., Wang, W., Zhai, Y. & Deng, M. Deep soft kmeans clustering with selftraining for singlecell rna sequence data. NAR Genom. Bioinform. 2, lqaa039 (2020).
Xie, J., Girshick, R. & Farhadi, A. Unsupervised deep embedding for clustering analysis. In International Conference on Machine Learning, 478–487 (PMLR, 2016).
Luo, Z., Xu, C., Zhang, Z. & Jin, W. scgae: topologypreserving dimensionality reduction for singlecell rnaseq data using graph autoencoder. bioRxiv https://doi.org/10.1101/2021.02.16.431357 (2021).
Wan, S., Kim, J. & Won, K. J. Sharp: hyperfast and accurate processing of singlecell rnaseq data via ensemble random projection. Genom. Res. 30, 205–213 (2020).
McInnes, L., Healy, J. & Melville, J. Umap: Uniform manifold approximation and projection for dimension reduction. arXiv https://doi.org/10.48550/arXiv.1802.03426 (2018).
Ivosev, G., Burton, L. & Bonner, R. Dimensionality reduction and visualization in principal component analysis. Analytical Chem. 80, 4933–4944 (2008).
Van der Maaten, L. & Hinton, G. Visualizing data using tsne. J. Machine Learn. Res. 9, 11 (2008).
Grün, D. et al. De novo prediction of stem cell identity using singlecell transcriptome data. Cell Stem Cell 19, 266–277 (2016).
Muraro, M. J. et al. A singlecell transcriptome atlas of the human pancreas. Cell Syst. 3, 385–394 (2016).
Lawlor, N. et al. Singlecell transcriptomes identify human islet cell signatures and reveal celltype–specific expression changes in type 2 diabetes. Genom. Res. 27, 208–222 (2017).
Segerstolpe, Å et al. Singlecell transcriptome profiling of human pancreatic islets in health and type 2 diabetes. Cell Metabol. 24, 593–607 (2016).
Korsunsky, I. et al. Fast, sensitive and accurate integration of singlecell data with harmony. Nat. Methods 16, 1289–1296 (2019).
Haghverdi, L., Lun, A. T. L., Morgan, M. D. & Marioni, J. C. Batch effects in singlecell rnasequencing data are corrected by matching mutual nearest neighbors. Nat. Biotechnol. 36, 421–427 (2018).
Hie, B., Bryson, B. & Berger, B. Efficient integration of heterogeneous singlecell transcriptomes using scanorama. Nat. Biotechnol. 37, 685–691 (2019).
De Oliveira, S., Rosowski, E. E. & Huttenlocher, A. Neutrophil migration in infection and wound repair: going forward in reverse. Nat. Rev. Immunol. 16, 378–391 (2016).
Metzemaekers, M., Gouwy, M. & Proost, P. Neutrophil chemoattractant receptors in health and disease: doubleedged swords. Cell. Mol. Immunol. 17, 433–450 (2020).
Peake, J., Della Gatta, P., Suzuki, K. & Nieman, D. Cytokine expression and secretion by skeletal muscle cells: regulatory mechanisms and exercise effects. Exercise Immunol. Rev. 21, 8–25 (2015).
Szklarczyk, D. et al. String v11: protein–protein association networks with increased coverage, supporting functional discovery in genomewide experimental datasets. Nucleic Acids Res. 47, D607–D613 (2019).
Smoot, M. E., Ono, K., Ruscheinski, J., Wang, P.L. & Ideker, T. Cytoscape 2.8: new features for data integration and network visualization. Bioinformatics 27, 431–432 (2011).
Bader, G. D. & Hogue, C. W. V. An automated method for finding molecular complexes in large protein interaction networks. BMC Bioinform. 4, 2 (2003).
Vallat, L. D., Park, Y., Li, C. & Gribben, J. G. Temporal genetic program following bcell receptor crosslinking: altered balance between proliferation and death in healthy and malignant b cells. Blood 109, 3989–3997 (2007).
Shah, P. D., West, E. E., Whitlock, A. B., Orens, J. B. & McDyer, J. F. Cd154 deficiency uncouples allograft cd8+ tcell effector function from proliferation and inhibits murine airway obliteration. Am. J. Transplant. 9, 2697–2706 (2009).
Qiu, X. et al. Reversed graph embedding resolves complex singlecell trajectories. Nat. Methods 14, 979–982 (2017).
Chu, L.F. et al. Singlecell rnaseq reveals novel regulators of human embryonic stem cell differentiation to definitive endoderm. Genom. Biol. 17, 1–20 (2016).
Peng, J. et al. Singlecell rnaseq highlights intratumoral heterogeneity and malignant progression in pancreatic ductal adenocarcinoma. Cell Res. 29, 725–738 (2019).
Verfaillie, A., Imrichova, H., Janky, R. & Aerts, S. iregulon and icistarget: reconstructing regulatory networks using motif and track enrichment. Curr. Protoc. Bioinform. 52, 2–16 (2015).
Cho, K. C. et al. Abstract a60: Integrated proteogenomic characterization of pancreatic ductal adenocarcinoma. Cancer Res. 79, A60–A60 (2019).
He, Y. et al. Identification of key pathways and candidate genes in pancreatic ductal adenocarcinoma using bioinformatics analysis. Oncol. Lett. 17, 3751–3764 (2019).
Li, N., Zhao, X. & You, S. Identification of key regulators of pancreatic ductal adenocarcinoma using bioinformatics analysis of microarray data. Medicine 98, e14074 (2019).
Wang, D. D. et al. Microarray based analysis of gene expression patterns in pancreatic neuroendocrine tumors. Eur. Rev. Med. Pharmacol. Sci. 19, 3367–3374 (2015).
Van Audenaerde, J. R. M. et al. Interleukin15 stimulates natural killer cellmediated killing of both human pancreatic cancer and stellate cells. Oncotarget 8, 56968 (2017).
Yang, J. Integrated genomic and transcriptomic analysis reveals unique characteristics of hepatic metastases and prometastatic role of complement c1q in pancreatic ductal adenocarcinoma. Genom. Biol. 22, 1–20 (2021).
Jin, S. et al. Inference and analysis of cellcell communication using cellchat. Nat. Commun. 12, 1–20 (2021).
Pollak, M. Insulin and insulinlike growth factor signalling in neoplasia. Nat. Rev. Cancer 8, 915–928 (2008).
Mutgan, A. C. et al. Insulin/igfdriven cancer cellstroma crosstalk as a novel therapeutic target in pancreatic cancer. Mol. Cancer 17, 1–11 (2018).
Bieging, K. T. & Attardi, L. D. Deconstructing p53 transcriptional networks in tumor suppression. Trends Cell Biol. 22, 97–106 (2012).
Levine, A. J. & Oren, M. The first 30 years of p53: growing ever more complex. Nat. Rev. Cancer 9, 749–758 (2009).
Bullinaria, J. A. & Levy, J. P. Extracting semantic representations from word cooccurrence statistics: A computational study. Behavior Res. Methods 39, 510–526 (2007).
Goldenberg, A., Mostafavi, S., Quon, G., Boutros, P. C. & Morris, Q. D. Unsupervised detection of genes of influence in lung cancer using biological networks. Bioinformatics 27, 3166–3172 (2011).
Mostafavi, S., Goldenberg, A. & Morris, Q. Labeling nodes using three degrees of propagation. PloS One 7, e51947 (2012).
Cao, S., Lu, W. & Xu, Q. In Proc. AAAI Conference on Artificial Intelligence Vol. 30 (PKP Publishing Services Network, 2016).
Davis, D., Yaveroğlu, Ö. N., MalodDognin, N., Stojmirovic, A. & Pržulj, N. Topologyfunction conservation in protein–protein interaction networks. Bioinformatics 31, 1632–1639 (2015).
Cowen, L., Ideker, T., Raphael, B. J. & Sharan, R. Network propagation: a universal amplifier of genetic associations. Nat. Rev. Genet. 18, 551–562 (2017).
Yu, G., Wang, L.G., Han, Y. & He, Q.Y. clusterprofiler: an r package for comparing biological themes among gene clusters. OMICS 16, 284–287 (2012).
Liberzon, A. et al. Molecular signatures database (msigdb) 3.0. Bioinformatics 27, 1739–1740 (2011).
Schaum, N. et al. Singlecell transcriptomics of 20 mouse organs creates a tabula muris: The tabula muris consortium. Nature 562, 367 (2018).
Yu, Z. & Li, X. Topological identification and interpretation for singlecell gene regulation elucidation across multiple platforms using scMGCA. Zenodo https://doi.org/10.5281/zenodo.7515775 (2023).
Acknowledgements
The work described in this paper was substantially supported by the National Natural Science Foundation of China under Grant No. 62076109 (X.L.). The work described in this paper was substantially supported by a grant from the Health and Medical Research Fund, the Food and Health Bureau, The Government of the Hong Kong Special Administrative Region [07181426] (K.C.W.). This research was substantially sponsored by the research projects (Grant No. 32170654 and Grant No. 32000464) (K.C.W.) supported by the National Natural Science Foundation of China.
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X.L. conceived and supervised the project. Z.Y. developed and implemented the algorithms under the guidance of X.L., and Z.Y. wrote the manuscript. Z.Y. conducted the experiments. X.L., Z.Y. and K.C.W. did the biological interpretation. Z.Y., Y.S., and Y.Y. completed the figures and manuscript. Z.Y., X.L., and K.C.W. revised the manuscript. Y.L., F.W., S.Z., and Y.C. provided advice in method development. All authors approved the manuscript.
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Yu, Z., Su, Y., Lu, Y. et al. Topological identification and interpretation for singlecell gene regulation elucidation across multiple platforms using scMGCA. Nat Commun 14, 400 (2023). https://doi.org/10.1038/s41467023361347
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DOI: https://doi.org/10.1038/s41467023361347
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