Computing whole embryo strain maps during gastrulation

Gastrulation is a critical process during embryonic development that transforms a single-layered blastula into a multilayered embryo with distinct germ layers, which eventually give rise to all the tissues and organs of the organism. Studies across species have uncovered the mechanisms underlying the building blocks of gastrulation movements, such as localized in-plane and out-of-plane epithelial deformations. The next challenge is to understand dynamics on the scale of the embryo: this requires quantifying strain tensors, which rigorously describe the differences between the deformed configurations taken on by local clusters of cells at time instants of observation and their reference configuration at an initial time. We present a systematic strategy for computing such tensors from the local dynamics of cell clusters, which are chosen across the embryo from several regions whose morphogenetic fate is central to viable gastrulation. As an application of our approach, we demonstrate a strategy of identifying distinct Drosophila morphological domains using strain tensors.