Quantification of Nematic Cell Polarity in Three-dimensional Tissues

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-Navarette et al., eLife 8:e44860, 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 or in-vitro organoids.Comment: 27 pages, 9 color figure

A Dynamically Diluted Alignment Model Reveals the Impact of Cell Turnover on the Plasticity of Tissue Polarity Patterns

The polarisation of cells and tissues is fundamental for tissue morphogenesis during biological development and regeneration. A deeper understanding of biological polarity pattern formation can be gained from the consideration of pattern reorganisation in response to an opposing instructive cue, which we here consider by example of experimentally inducible body axis inversions in planarian flatworms. Our dynamically diluted alignment model represents three processes: entrainment of cell polarity by a global signal, local cell-cell coupling aligning polarity among neighbours and cell turnover inserting initially unpolarised cells. We show that a persistent global orienting signal determines the final mean polarity orientation in this stochastic model. Combining numerical and analytical approaches, we find that neighbour coupling retards polarity pattern reorganisation, whereas cell turnover accelerates it. We derive a formula for an effective neighbour coupling strength integrating both effects and find that the time of polarity reorganisation depends linearly on this effective parameter and no abrupt transitions are observed. This allows to determine neighbour coupling strengths from experimental observations. Our model is related to a dynamic $8$-Potts model with annealed site-dilution and makes testable predictions regarding the polarisation of dynamic systems, such as the planarian epithelium.Comment: Preprint as prior to first submission to Journal of the Royal Society Interface. 25 pages, 6 figures, plus supplement (18 pages, contains 1 table and 7 figures). A supplementary movie is available from https://dx.doi.org/10.6084/m9.figshare.c388781

Stochastic model for cell polarity

Cell polarity refers to the spatial asymmetry of molecules on the cell membrane. Altschuler, Angenent, Wang and Wu have proposed a stochastic model for studying the emergence of polarity in the presence of feedback between molecules. We analyze their model further by representing it as a model of an evolving population with interacting individuals. Under a suitable scaling of parameters, we show that in the infinite population limit we get a Fleming--Viot process. Using well-known results for such processes, we establish that cell polarity is exhibited by the model and also study its dependence on the biological parameters of the model.Comment: Published in at http://dx.doi.org/10.1214/11-AAP788 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Tyrosine-Based Signals Regulate the Assembly of Daple⋅PARD3 Complex at Cell-Cell Junctions.

Polarized distribution of organelles and molecules inside a cell is vital for a range of cellular processes and its loss is frequently encountered in disease. Polarization during planar cell migration is a special condition in which cellular orientation is triggered by cell-cell contact. We demonstrate that the protein Daple (CCDC88C) is a component of cell junctions in epithelial cells which serves like a cellular "compass" for establishing and maintaining contact-triggered planar polarity. Furthermore, these processes may be mediated through interaction with the polarity regulator PARD3. This interaction, mediated by Daple's PDZ-binding motif (PBM) and the third PDZ domain of PARD3, is fine-tuned by tyrosine phosphorylation on Daple's PBM by receptor and non-receptor tyrosine kinases, such as Src. Hypophosphorylation strengthens the interaction, whereas hyperphosphorylation disrupts it, thereby revealing an unexpected role of Daple as a platform for signal integration and gradient sensing for tyrosine-based signals within the planar cell polarity pathway

Complex polarity: building multicellular tissues through apical membrane traffic

The formation of distinct subdomains of the cell surface is crucial for multicellular organism development. The most striking example of this is apical-basal polarization. What is much less appreciated is that underpinning an asymmetric cell surface is an equally dramatic intracellular endosome rearrangement. Here, we review the interplay between classical cell polarity proteins and membrane trafficking pathways, and discuss how this marriage gives rise to cell polarization. We focus on those mechanisms that regulate apical polarization, as this is providing a number of insights into how membrane traffic and polarity are regulated at the tissue level

Cadherin-26 (CDH26) regulates airway epithelial cell cytoskeletal structure and polarity.

Polarization of the airway epithelial cells (AECs) in the airway lumen is critical to the proper function of the mucociliary escalator and maintenance of lung health, but the cellular requirements for polarization of AECs are poorly understood. Using human AECs and cell lines, we demonstrate that cadherin-26 (CDH26) is abundantly expressed in differentiated AECs, localizes to the cell apices near ciliary membranes, and has functional cadherin domains with homotypic binding. We find a unique and non-redundant role for CDH26, previously uncharacterized in AECs, in regulation of cell-cell contact and cell integrity through maintaining cytoskeletal structures. Overexpression of CDH26 in cells with a fibroblastoid phenotype increases contact inhibition and promotes monolayer formation and cortical actin structures. CDH26 expression is also important for localization of planar cell polarity proteins. Knockdown of CDH26 in AECs results in loss of cortical actin and disruption of CRB3 and other proteins associated with apical polarity. Together, our findings uncover previously unrecognized functions for CDH26 in the maintenance of actin cytoskeleton and apicobasal polarity of AECs

Memristive excitable cellular automata

The memristor is a device whose resistance changes depending on the polarity and magnitude of a voltage applied to the device's terminals. We design a minimalistic model of a regular network of memristors using structurally-dynamic cellular automata. Each cell gets info about states of its closest neighbours via incoming links. A link can be one 'conductive' or 'non-conductive' states. States of every link are updated depending on states of cells the link connects. Every cell of a memristive automaton takes three states: resting, excited (analog of positive polarity) and refractory (analog of negative polarity). A cell updates its state depending on states of its closest neighbours which are connected to the cell via 'conductive' links. We study behaviour of memristive automata in response to point-wise and spatially extended perturbations, structure of localised excitations coupled with topological defects, interfacial mobile excitations and growth of information pathways.Comment: Accepted to Int J Bifurcation and Chaos (2011

The coordination of cell growth during fission yeast mating requires Ras1-GTP hydrolysis

The spatial and temporal control of polarity is fundamental to the survival of all organisms. Cells define their polarity using highly conserved mechanisms that frequently rely upon the action of small GTPases, such as Ras and Cdc42. Schizosaccharomyces pombe is an ideal system with which to study the control of cell polarity since it grows from defined tips using Cdc42-mediated actin remodeling. Here we have investigated the importance of Ras1-GTPase activity for the coordination of polarized cell growth during fission yeast mating. Following pheromone stimulation, Ras1 regulates both a MAPK cascade and the activity of Cdc42 to enable uni-directional cell growth towards a potential mating partner. Like all GTPases, when bound to GTP, Ras1 adopts an active conformation returning to an inactive state upon GTP-hydrolysis, a process accelerated through interaction with negative regulators such as GAPs. Here we show that, at low levels of pheromone stimulation, loss of negative regulation of Ras1 increases signal transduction via the MAPK cascade. However, at the higher concentrations observed during mating, hyperactive Ras1 mutations promote cell death. We demonstrate that these cells die due to their failure to coordinate active Cdc42 into a single growth zone resulting in disorganized actin deposition and unsustainable elongation from multiple tips. These results provide a striking demonstration that the deactivation stage of Ras signaling is fundamentally important in modulating cell polarity