The rapid advancement of single-cell technologies has shed new light on the complex mechanisms of cellular heterogeneity. However, compared to bulk RNA sequencing (RNA-seq), single-cell RNA-seq (scRNA-seq) suffers from higher noise and lower coverage, which brings new computational difficulties. Based on statistical independence, cell-specific network (CSN) is able to quantify the overall associations between genes for each cell, yet suffering from a problem of overestimation related to indirect effects. To overcome this problem, we propose the c-CSN method, which can construct the conditional cell-specific network (CCSN) for each cell. c-CSN method can measure the direct associations between genes by eliminating the indirect associations. c-CSN can be used for cell clustering and dimension reduction on a network basis of single cells. Intuitively, each CCSN can be viewed as the transformation from less “reliable” gene expression to more “reliable” gene–gene associations in a cell. Based on CCSN, we further design network flow entropy (NFE) to estimate the differentiation potency of a single cell. A number of scRNA-seq datasets were used to demonstrate the advantages of our approach. 1) One direct association network is generated for one cell. 2) Most existing scRNA-seq methods designed for gene expression matrices are also applicable to c-CSN-transformed degree matrices. 3) CCSN-based NFE helps resolving the direction of differentiation trajectories by quantifying the potency of each cell. c-CSN is publicly available at https://github.com/LinLi-0909/c-CSN .
Gene regulatory networks (GRNs) reveal the complex molecular interactions that govern cell state. However, it is challenging for identifying causal relations among genes due to noisy data and molecular nonlinearity. Here, we propose a novel causal criterion, neighbor cross-mapping entropy (NME), for inferring GRNs from both steady data and time-series data. NME is designed to quantify ‘continuous causality’ or functional dependency from one variable to another based on their function continuity with varying neighbor sizes. NME shows superior performance on benchmark datasets, comparing with existing methods. By applying to scRNA-seq datasets, NME not only reliably inferred GRNs for cell types but also identified cell states. Based on the inferred GRNs and further their activity matrices, NME showed better performance in single-cell clustering and downstream analyses. In summary, based on continuous causality, NME provides a powerful tool in inferring causal regulations of GRNs between genes from scRNA-seq data, which is further exploited to identify novel cell types/states and predict cell type-specific network modules.
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