  When a dynamical system can be modeled as a sequence of observations, Granger
causality is a powerful approach for detecting predictive interactions between
its variables. However, traditional Granger causal inference has limited
utility in domains where the dynamics need to be represented as directed
acyclic graphs (DAGs) rather than as a linear sequence, such as with cell
differentiation trajectories. Here, we present GrID-Net, a framework based on
graph neural networks with lagged message passing for Granger causal inference
on DAG-structured systems. Our motivating application is the analysis of
single-cell multimodal data to identify genomic loci that mediate the
regulation of specific genes. To our knowledge, GrID-Net is the first
single-cell analysis tool that accounts for the temporal lag between a genomic
locus becoming accessible and its downstream effect on a target gene's
expression. We applied GrID-Net on multimodal single-cell assays that profile
chromatin accessibility (ATAC-seq) and gene expression (RNA-seq) in the same
cell and show that it dramatically outperforms existing methods for inferring
regulatory locus-gene links, achieving up to 71% greater agreement with
independent population genetics-based estimates. By extending Granger causality
to DAG-structured dynamical systems, our work unlocks new domains for causal
analyses and, more specifically, opens a path towards elucidating gene
regulatory interactions relevant to cellular differentiation and complex human
diseases at unprecedented scale and resolution.
