Optimal transport reveals dynamic gene regulatory networks via gene velocity estimation

Inferring gene regulatory networks from gene expression data is an important and challenging problem in the biology community. We propose OTVelo, a methodology that takes time-stamped single-cell gene expression data as input and predicts gene regulation across two time points. It is known that the rate of change of gene expression, which we will refer to as gene velocity, provides crucial information that enhances such inference; however, this information is not always available due to the limitations in sequencing depth. Our algorithm overcomes this limitation by estimating gene velocities using optimal transport. We then infer gene regulation using time-lagged correlation and Granger causality via regularized linear regression. Instead of providing an aggregated network across all time points, our method uncovers the underlying dynamical mechanism across time points. We validate our algorithm on 13 simulated datasets with both synthetic and curated networks and demonstrate its efficacy on 9 experimental data sets.Author summary: Understanding how genes interact to regulate cellular functions is crucial for advancing our knowledge of biology and disease. We present OTVelo, a method that uses single-cell gene expression data collected at different time points to infer gene regulatory networks. By leveraging the mathematical framework of optimal transport, OTVelo first reconstructs likely trajectories of gene expression changing over time, then infers the regulatory interactions from the rate of change along these trajectories. This approach allows OTVelo to offer a dynamic view of how gene interactions change over time, providing deeper insights into cellular processes. Unlike traditional methods, which often rely on static network assumptions, OTVelo captures temporal information through ancestor-descendant transitions without assuming a specific underlying regulatory model. We validate our approach using both simulated and real-world data, demonstrating its effectiveness in revealing complex gene regulation patterns. This method could lead to new discoveries in understanding biological systems and developing disease treatments.