Abstract
Gene regulatory network (GRN) refers to the complex network formed by regulatory interactions between genes in living cells. In this paper, we consider inferring GRNs in single cells based on single-cell RNA sequencing (scRNA-seq) data. In scRNA-seq, single cells are often profiled from mixed populations, and their cell identities are unknown. A common practice for single-cell GRN analysis is to first cluster the cells and infer GRNs for every cluster separately. However, this two-step procedure ignores uncertainty in the clustering step and thus could lead to inaccurate estimation of the networks. Here, we consider the mixture Poisson log-normal model (MPLN) for network inference of count data from mixed populations. The precision matrices of the MPLN are the GRNs of different cell types. To avoid the intractable optimization of the MPLN's log-likelihood, we develop an algorithm called variational mixture Poisson log-normal (VMPLN) to jointly estimate the GRNs of different cell types based on the variational inference method. We compare VMPLN with state-of-the-art single-cell regulatory network inference methods. Comprehensive simulation shows that VMPLN achieves better performance, especially in scenarios where different cell types have a high mixing degree. Benchmarking on real scRNA-seq data also demonstrates that VMPLN can provide more accurate network estimation in most cases. Finally, we apply VMPLN to a large scRNA-seq dataset from patients infected with severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) and find that VMPLN identifies critical differences in regulatory networks in immune cells between patients with moderate and severe symptoms. The source codes are available on the GitHub website (github.com/XiDsLab/SCVMPLN).