Discovering governing equations of biological systems through representation learning and sparse model discovery

Understanding the governing rules of complex biological systems remains a significant challenge due to the nonlinear, high-dimensional nature of biological data. In this study, we present CLERA, a novel end-to-end computational framework designed to uncover parsimonious dynamical models and identify active gene programs from single-cell RNA sequencing data. By integrating a supervised autoencoder architecture with Sparse Identification of Nonlinear Dynamics, CLERA leverages prior knowledge to simultaneously extract related low-dimensional representation and uncover the underlying dynamical systems that drive the processes. Through the analysis of both synthetic and biological data, CLERA demonstrates robust performance in reconstructing gene expression dynamics, identifying key regulatory genes, and capturing temporal patterns across distinct cell types. CLERA's ability to generate dynamic interaction networks, combined with network rewiring using Personalized PageRank to highlight central genes and active gene programs, offers new insights into the complex regulatory mechanisms underlying cellular processes.