Depicting pseudotime-lagged causality across single-cell trajectories for accurate gene-regulatory inference

Identifying the causal interactions in gene-regulatory networks requires an accurate understanding of the time-lagged relationships between transcription factors and their target genes. Here we describe DELAY (short for Depicting Lagged Causality), a convolutional neural network for the inference of gene-regulatory relationships across pseudotime-ordered single-cell trajectories. We show that combining supervised deep learning with joint probability matrices of pseudotime-lagged trajectories allows the network to overcome important limitations of ordinary Granger causality-based methods, for example, the inability to infer cyclic relationships such as feedback loops. Our network outperforms several common methods for inferring gene regulation and, when given partial ground-truth labels, predicts novel regulatory networks from single-cell RNA sequencing (scRNA-seq) and single-cell ATAC sequencing (scATAC-seq) data sets. To validate this approach, we used DELAY to identify important genes and modules in the regulatory network of auditory hair cells, as well as likely DNA-binding partners for two hair cell cofactors (Hist1h1c and Ccnd1) and a novel binding sequence for the hair cell-specific transcription factor Fiz1. We provide an easy-to-use implementation of DELAY under an open-source license at https://github.com/calebclayreagor/DELAY.