Interpretable gene network inference with nonlinear causality

Interactions among genes orchestrate the growth and survival of all living systems. Such interactions are mediated by vast networks of time-dependent couplings, yet existing strategies for inferring gene networks from omics data do not account for the strong causal constraints acting on nonlinear dynamical systems. As a result, we show here that current gene network inference approaches fail when applied to time series from physical systems. We thus introduce RiCE, a physics-based algorithm for inferring causal interaction graphs using geometric information embedded within time series. We benchmark RiCE against 30 other gene network inference methods, including recent probabilistic machine learning methods, and obtain leading results across 15 datasets spanning diverse experimental modalities and tissue types. RiCE learns physically-interpretable parameters of complex biological systems, requiring low overhead to achieve leading performance. We show diverse applications of RiCE: identifying transition states during the epithelial-mesenchymal transition, classifying cell subtypes during immune cell activation, and determining transcriptional dynamics during endocrinogenesis. Our work demonstrates nonlinearity as a critical inductive bias to accurately infer gene-gene interactions, as well as a key quantitative metric for understanding the dynamic biology of the cell.