Quantification of nematic cell polarity in three-dimensional tissues

Abstract

How epithelial cells coordinate their polarity to form functional tissues is an open question in cell biology. Here, we characterize a unique type of polarity found in liver tissue, nematic cell polarity, which is different from vectorial cell polarity in simple, sheet-like epithelia. We propose a conceptual and algorithmic framework to characterize complex patterns of polarity proteins on the surface of a cell in terms of a multipole expansion. To rigorously quantify previously observed tissue-level patterns of nematic cell polarity (Morales-Navarrete et al., eLife 2019), we introduce the concept of co-orientational order parameters, which generalize the known biaxial order parameters of the theory of liquid crystals. Applying these concepts to three-dimensional reconstructions of single cells from high-resolution imaging data of mouse liver tissue, we show that the axes of nematic cell polarity of hepatocytes exhibit local coordination and are aligned with the biaxially anisotropic sinusoidal network for blood transport. Our study characterizes liver tissue as a biological example of a biaxial liquid crystal. The general methodology developed here could be applied to other tissues and in-vitro organoids.

Anisotropic expansion of hepatocyte lumina enforced by apical bulkheads

“…5 c ), suggesting that knock-down of Rab35 also did not lead to inversion of polarity as reported for MDCK cells ( Klinkert et al, 2016 ). Therefore, the depletion of Rab35 caused a change from biaxial to vectorial polarity ( Morales-Navarrete et al, 2019 ; Scholich et al, 2020 ). Interestingly, the lumina of the tubes and cysts were connected with the residual BC (orange arrowhead, Fig.…”

“…It contains two types of epithelial cells, bile duct cells (cholangiocytes) and hepatocytes, both derived from embryonic progenitors called hepatoblasts ( Müsch, 2018 ). Bile duct cells have the typical apico-basal polarity that can be described with one vector pointing to the apical surface ( Morales-Navarrete et al, 2019 ; Scholich et al, 2020 ). The apical surface expands isotropically to form 3D cysts in vitro ( Tanimizu et al, 2007 ; Prior et al, 2019 ), or generate tubes in vivo ( Antoniou et al, 2009 ; Tanimizu et al, 2016 ), which elongate under tissue-level forces ( Navis and Nelson, 2016 ).…”

“…In contrast, hepatocytes have a complex polarity, where the apical surface elongates anisotropically as a tubular belt surrounding the cells ( Morales-Navarrete et al, 2015 ). Such polarity can be described by biaxial nematic tensors, a mathematical description of the belt-like and multi-polar apical surface ( Morales-Navarrete et al, 2019 ; Scholich et al, 2020 ). Hepatocytes can initiate apical lumina with multiple neighboring hepatocytes concurrently in all directions, allowing them to form a complex 3D luminal network of highly branched ∼1-µm-thin bile canaliculi (BC; Morales-Navarrete et al, 2015 ).…”

Learning developmental mode dynamics from single-cell trajectories

“…The second index provides additional information about the orientation of the harmonic scalar function or vector field. The modes and are particularly useful for characterizing the symmetry of spatial patterns on a spherical surface ( Mietke et al, 2019 ; Scholich et al, 2020 ): Modes with indicate patterns with a global polar symmetry, whereas modes with represent spatial patterns with a global nematic symmetry. We now exploit these features for a detailed characterization of the symmetry breaking that takes place during cellular rearrangements and to study the properties of the cellular flux in more detail.…”

Network permeability changes according to a quadratic power law upon removal of a single edge

“…Here, a nematic axis of network alignment of the sinusoidal network [7,8,25] is oriented parallel to the x-axis. Analogous results hold for flow along the y-axis, i.e., perpendicular to the nematic axis of network alignment, see fig.…”