  Embryogenesis is a multiscale process during which hierarchical symmetry
breaking transitions give rise to a fully developed organism. Recent advances
in high-resolution live-cell microscopy provide unprecedented insights into the
collective cell dynamics at various stages of embryonic development. The 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 early gastrulation process reveals a multilayer interaction network
between dominant dynamical modes that enables the symmetry breaking transition
from a homogeneous animal pole to an increasingly structured cell assembly. Due
to its generic conceptual foundation, we expect this approach to be broadly
applicable to obtain a quantitative biophysical understanding of a wide range
of developmental structure formation processes.
