CycleGRN: Inferring Gene Regulatory Networks from Cyclic Flow Dynamics in Single-Cell RNA-seq

Oscillatory processes such as the cell cycle play critical roles in cell fate determination and disease development, yet existing gene regulatory network (GRN) inference methods often fail to account for their dynamic nature. We propose CycleGRN , a novel framework that treats cell cycle gene expression observations as an invariant measure of a stochastic differential equation and learns from data a dynamical system that fits cycling biological processes. Using a directed graph constructed along the inferred flow field in the cell space, we estimate Lie derivatives for all genes, enabling velocity inference beyond the cell cycle subspace. To quantify regulatory interactions, we introduce a time-lagged correlation operator between any pair of genes supported on the flow-aligned directed graph, which respects the intrinsic geometry of the data manifold and allows temporal ordering consistent with the underlying oscillatory process. The method requires only raw gene expression data at single-cell resolution and a list of cycle genes, without temporal binning or splicing dynamics. We evaluate our method on four synthetic datasets generated from mechanistic models with known network structures with oscillatory subnetworks, and on a mouse retinal progenitor single-cell RNA-seq dataset spanning three cell types and a knockout condition. Across all settings, our method outperforms existing methods, demonstrating its ability to recover causal and oscillatory interactions from static single-cell RNA-seq datasets.