Single Cell Universal Differential Equations: A Machine Learning Framework for Extracting Ordinary Differential Equations for Gene Regulatory Network Inference

Abstract

Over the past couple of decades, tools from synthetic and systems biology have been applied to understand gene regulatory motifs, the functional units of transcription. These regulatory motifs have been found to be generalizable across many biological systems and have been applied successfully in describing transcriptional dynamics. However, expert knowledge must be leveraged to model regulatory motifs embedded in gene regulatory networks. Here we propose to use data driven systems identification algorithms to extract significant transcriptional motifs from single cell data. Most algorithms that infer dynamical systems from data are constrained to linear regression of gene – gene interactions. Here we use a variant of the universal differential equations framework to extract a non-linear system of Hill equations that describes the gene regulatory network for the system. We demonstrate that neural ordinary differential equations (NODEs) can fit complex trajectories in single cell expression space. We also demonstrate that the SInDy-PI algorithm can use the output of NODEs to infer nonlinear interactions between genes on synthetic and real hematopoiesis datasets. These methods for inferring networks can serve as the basis for computational discovery of mode of action in drug discovery and adverse outcome pathways in risk assessment.