Capturing nematic order on tissue surfaces of arbitrary geometry

A leading paradigm for understanding the large-scale behavior of tissues is via generalizations of liquid crystal physics; much like liquid crystals, tissues combine fluid-like, viscoelastic behaviors with local orientational order, such as nematic symmetry. Whilst aspects of quantitative agreement have been achieved for flat monolayers, the most striking features of tissue morphogenesis-including symmetry breaking, folding and invagination-concern surfaces with complex curved geometries in three dimensions. As yet, however, characterizing such behaviors has been frustrated due to the absence of proper image analysis methods; current state-of-the-art methods almost exclusively rely on two-dimensional intensity projections of multiple image planes, which superimpose data and lose geometric information that can be crucial. Here, we describe an analysis pipeline that properly captures the nematic order and topological defects associated with tissue surfaces of arbitrary geometry, which we demonstrate in the context of in vitro multicellular aggregates, and in vivo zebrafish hearts.