Hybrid deep learning-mechanistic modeling of cellular dynamics from a spatiotemporal single-cell atlas

Single-cell measurement technologies provide a powerful framework for studying cellular heterogeneity, transitions, and regulatory networks, yet reconstructing the underlying dynamical processes governing these transitions remains a major challenge due to the high dimensionality of gene expression data. To address this, we develop a variational autoencoder (VAE)-latent neural ordinary differential equation (ODE) approach that learns a low-dimensional latent representation of cellular states and models their temporal evolution. We apply our framework to the single-cell fluorescence imaging spatiotemporal atlas of Drosophila melanogaster blastoderm embryos via spatial registration, which comprises six registered developmental time points prior to gastrulation. In our approach, gene expression profiles are encoded into a latent space where a neural ordinary differential equation (ODE) is trained to capture the continuous dynamics of cellular states over time, and a decoder subsequently maps these evolving latent representations back to the original high-dimensional gene expression space, enabling accurate reconstruction of observed transcriptional patterns. While such black-box deep learning approaches excel at capturing complex dynamical trajectories, they are inherently limited in their ability to predict the effects of combinatorial perturbations. To overcome this limitation, we leverage the inferred latent dynamics as a foundation for fitting a mechanistic Hill-function model of gene regulation, which--guided by the black-box representations--enables interpretable predictions by systematically perturbing couplings between specific gene pairs and thus provides mechanistic insight into developmental regulatory programs. Author summaryWe set out to learn how genes interact over time during early development using data measured from individual cells. Many powerful deep learning models can fit complex patterns, but they are hard to edit or use for "what-if" genetic changes. Classical mechanistic models are easier to interpret but struggle when the data are sparse. We built a hybrid approach that combines both strengths. First, we trained a deep learning model to place each cells gene activity into a smooth, low-dimensional space and to estimate how these states change over time. We then used those estimates to fit a simple, editable model of gene regulation based on standard biochemical response curves. This second model lets us turn specific regulatory connections on or off and predict the effects without retraining the whole system. Using a spatiotemporal atlas of the fruit fly embryo, we show that the hybrid model makes accurate short-term predictions and yields clear, testable hypotheses about which genes control others. Our study demonstrates a practical way to turn flexible deep learning into interpretable, mechanistic insight for dynamic single-cell data.