Spatiotemporal modeling of molecular holograms.

Quantifying spatiotemporal dynamics during embryogenesis is crucial for understanding congenital diseases. We developed Spateo (https://github.com/aristoteleo/spateo-release), a 3D spatiotemporal modeling framework, and applied it to a 3D mouse embryogenesis atlas at E9.5 and E11.5, capturing eight million cells. Spateo enables scalable, partial, non-rigid alignment, multi-slice refinement, and mesh correction to create molecular holograms of whole embryos. It introduces digitization methods to uncover multi-level biology from subcellular to whole organ, identifying expression gradients along orthogonal axes of emergent 3D structures, e.g., secondary organizers such as midbrain-hindbrain boundary (MHB). Spateo further jointly models intercellular and intracellular interaction to dissect signaling landscapes in 3D structures, including the zona limitans intrathalamica (ZLI). Lastly, Spateo introduces "morphometric vector fields" of cell migration and integrates spatial differential geometry to unveil molecular programs underlying asymmetrical murine heart organogenesis and others, bridging macroscopic changes with molecular dynamics. Thus, Spateo enables the study of organ ecology at a molecular level in 3D space over time.