  Embryogenesis is a multiscale process during which developmental symmetry
breaking transitions give rise to complex multicellular organisms. Recent
advances in high-resolution live-cell microscopy provide unprecedented insights
into the collective cell dynamics at various stages of embryonic development.
This rapid experimental progress poses the theoretical challenge of translating
high-dimensional imaging data into predictive low-dimensional models that
capture the essential ordering principles governing developmental cell
migration in complex geometries. Here, we combine mode decomposition ideas that
have proved successful in condensed matter physics and turbulence theory with
recent advances in sparse dynamical systems inference to realize a
computational framework for learning quantitative continuum models from
single-cell imaging data. Considering pan-embryo cell migration during early
gastrulation in zebrafish as a widely studied example, we show how cell
trajectory data on a curved surface can be coarse-grained and compressed with
suitable harmonic basis functions. The resulting low-dimensional representation
of the collective cell dynamics enables a compact characterization of
developmental symmetry breaking and the direct inference of an interpretable
hydrodynamic model, which reveals similarities between pan-embryo cell
migration and active Brownian particle dynamics on curved surfaces. Due to its
generic conceptual foundation, we expect that mode-based model learning can
help advance the quantitative biophysical understanding of a wide range of
developmental structure formation processes.
