scSGL: Signed Graph Learning for Single-Cell Gene Regulatory Network Inference

Motivation Elucidating the topology of gene regulatory networks (GRNs) from large single-cell RNA sequencing (scRNAseq) datasets, while effectively capturing its inherent cell-cycle heterogeneity and dropouts, is currently one of the most pressing problems in computational systems biology. Recently, graph learning (GL) approaches based on graph signal processing (GSP) have been developed to infer graph topology from signals defined on graphs. However, existing GL methods are not suitable for learning signed graphs, which represent a characteristic feature of GRNs, as they account for both activating and inhibitory relationships between genes. They are also incapable of handling high proportion of zero values, which represent dropouts in single cell experiments. To this end, we propose a novel signed GL approach, scSGL , that learns GRNs based on the assumption of the smoothness and non-smoothness of gene expressions over activating and inhibitory edges, respectively. scSGL is then extended with kernels to take the nonlinearity of co-expressions into account and handle high proportion of dropouts. From GSP perspective, this extension corresponds to assuming smoothness/non-smoothness of graph signals in a higher dimensional space defined by the kernel. The proposed approach is formulated as a non-convex optimization problem and solved using an efficient ADMM framework. Results In our experiments on simulated and real single cell datasets, scSGL compares favorably with other single cell gene regulatory network reconstruction algorithms. Availability The scSGL code and analysis scripts are available at ( https://github.com/Single-Cell-Graph-Learning/scSGL ).