Deep dynamical modelling of developmental trajectories with temporal transcriptomics [SCIFATE_PILOT_DATA]
Developmental cell fate decisions are dynamic processes driven by the complex behaviour of gene regulatory networks. A challenge in studying these processes using single-cell genomics is that the data provides only a static snapshot with no detail of dynamics. Metabolic labelling and splicing can provide time-resolved information, but current methods have limitations. Here, we present experimental and computational methods that overcome these limitations to allow dynamical modelling of gene expression from single-cell data. We developed sci-FATE2, an optimised metabolic labelling method that substantially increases data quality, and profiled approximately 45,000 embryonic stem cells differentiating into multiple neural tube identities. To recover dynamics, we developed velvet, a deep learning framework that extends beyond instantaneous velocity estimation by modelling gene expression dynamics through a neural stochastic differential equation system within a variational autoencoder. Velvet outperforms current velocity tools across quantitative benchmarks, and predicts trajectory distributions that accurately recapitulate underlying dataset distributions while conserving known biology. Velvet trajectory distributions capture dynamical aspects such as decision boundaries between alternative fates and correlative gene regulatory structure. Using velvet to provide a dynamical description of in vitro neural patterning, we highlight a process of sequential decision making and fate-specific patterns of developmental signalling. Together, these experimental and computational methods recast single-cell analyses from  descriptions of observed data distributions to models of the dynamics that generated them, providing a new framework for investigating developmental gene regulation and cell fate decisions. Overall design: sci-FATE original protocol test, all mES differentiating celld, fixed in PFA, just to test protocol quality