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 -- such as symmetry breaking, folding and invagination -- concern surfaces with complex curved geometries. As yet, however, characterizing such complex behaviors in three dimensions has been frustrated due to the absence of proper image analysis methods; current state-of-the-art methods almost exclusively rely on two-dimensional (2D) 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 of tissue surfaces of arbitrary geometry, which we demonstrate in the context of in vitro multicellular aggregates, and in vivo zebrafish hearts. For the former, we correlate the number of topological defects with the aggregates surface area and verify theoretical predictions, whilst for the latter, we link biological properties to physical concepts (Laplace pressure) through spatio-temporal correlations of the heart geometry with fluorescence signals of intracellular proteins. Our analysis enables access to the hidden third dimension of conventional image acquisition via stacked 2D planes and highlights how such characterizations can deliver meaningful physical insight.