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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. 

Abstract Different cell types aggregate and sort into hierarchical architectures during the formation of animal tissues. The resulting spatial organization depends (in part) on the strength of adhesion of one cell type to itself relative to other cell types. However, automated and unsupervised classification of these multicellular spatial patterns remains challenging, particularly given their structural diversity and biological variability. Recent developments based on topological data analysis are intriguing to reveal similarities in tissue architecture, but these methods remain computationally expensive. In this article, we show that multicellular patterns organized from two interacting cell types can be efficiently represented through persistence images. Our optimized combination of dimensionality reduction via autoencoders, combined with hierarchical clustering, achieved high classification accuracy for simulations with constant cell numbers. We further demonstrate that persistence images can be normalized to improve classification for simulations with varying cell numbers due to proliferation. Finally, we systematically consider the importance of incorporating different topological features as well as information about each cell type to improve classification accuracy. We envision that topological machine learning based on persistence images will enable versatile and robust classification of complex tissue architectures that occur in development and disease.