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Scholich A, Syga S, Morales-Navarrete H, Segovia-Miranda F, Nonaka H, Meyer K, de Back W, Brusch L, Kalaidzidis Y, Zerial M, Jülicher F, Friedrich BM. Quantification of nematic cell polarity in three-dimensional tissues. PLoS Comput Biol 2020; 16:e1008412. [PMID: 33301446 PMCID: PMC7755288 DOI: 10.1371/journal.pcbi.1008412] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/22/2020] [Revised: 12/22/2020] [Accepted: 10/01/2020] [Indexed: 01/12/2023] Open
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.
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Affiliation(s)
- André Scholich
- Max Planck Institute for the Physics of Complex Systems, Dresden, Germany
| | - Simon Syga
- Max Planck Institute for the Physics of Complex Systems, Dresden, Germany
- Centre for Information Services and High Performance Computing, TU Dresden, Dresden, Germany
| | | | | | - Hidenori Nonaka
- Max Planck Institute of Molecular Cell Biology and Genetics, Dresden, Germany
| | - Kirstin Meyer
- Max Planck Institute of Molecular Cell Biology and Genetics, Dresden, Germany
| | - Walter de Back
- Centre for Information Services and High Performance Computing, TU Dresden, Dresden, Germany
- Institute for Medical Informatics and Biometry, Faculty of Medicine Carl Gustav Carus, TU Dresden, Dresden, Germany
| | - Lutz Brusch
- Centre for Information Services and High Performance Computing, TU Dresden, Dresden, Germany
| | - Yannis Kalaidzidis
- Max Planck Institute of Molecular Cell Biology and Genetics, Dresden, Germany
| | - Marino Zerial
- Max Planck Institute of Molecular Cell Biology and Genetics, Dresden, Germany
- Center for Advancing Electronics Dresden, TU Dresden, Germany
- Cluster of Excellence Physics of Life, TU Dresden, Germany
| | - Frank Jülicher
- Max Planck Institute for the Physics of Complex Systems, Dresden, Germany
- Center for Advancing Electronics Dresden, TU Dresden, Germany
- Cluster of Excellence Physics of Life, TU Dresden, Germany
| | - Benjamin M. Friedrich
- Center for Advancing Electronics Dresden, TU Dresden, Germany
- Cluster of Excellence Physics of Life, TU Dresden, Germany
- Institute for Theoretical Physics, TU Dresden, Germany
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Karschau J, Scholich A, Wise J, Morales-Navarrete H, Kalaidzidis Y, Zerial M, Friedrich BM. Resilience of three-dimensional sinusoidal networks in liver tissue. PLoS Comput Biol 2020; 16:e1007965. [PMID: 32598356 PMCID: PMC7351228 DOI: 10.1371/journal.pcbi.1007965] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/22/2019] [Revised: 07/10/2020] [Accepted: 05/19/2020] [Indexed: 12/19/2022] Open
Abstract
Can three-dimensional, microvasculature networks still ensure blood supply if individual links fail? We address this question in the sinusoidal network, a plexus-like microvasculature network, which transports nutrient-rich blood to every hepatocyte in liver tissue, by building on recent advances in high-resolution imaging and digital reconstruction of adult mice liver tissue. We find that the topology of the three-dimensional sinusoidal network reflects its two design requirements of a space-filling network that connects all hepatocytes, while using shortest transport routes: sinusoidal networks are sub-graphs of the Delaunay graph of their set of branching points, and also contain the corresponding minimum spanning tree, both to good approximation. To overcome the spatial limitations of experimental samples and generate arbitrarily-sized networks, we developed a network generation algorithm that reproduces the statistical features of 0.3-mm-sized samples of sinusoidal networks, using multi-objective optimization for node degree and edge length distribution. Nematic order in these simulated networks implies anisotropic transport properties, characterized by an empirical linear relation between a nematic order parameter and the anisotropy of the permeability tensor. Under the assumption that all sinusoid tubes have a constant and equal flow resistance, we predict that the distribution of currents in the network is very inhomogeneous, with a small number of edges carrying a substantial part of the flow-a feature known for hierarchical networks, but unexpected for plexus-like networks. We quantify network resilience in terms of a permeability-at-risk, i.e., permeability as function of the fraction of removed edges. We find that sinusoidal networks are resilient to random removal of edges, but vulnerable to the removal of high-current edges. Our findings suggest the existence of a mechanism counteracting flow inhomogeneity to balance metabolic load on the liver.
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Affiliation(s)
| | - André Scholich
- Max Planck Institute for the Physics of Complex Systems, Dresden, Germany
| | - Jonathan Wise
- cfaed, TU Dresden, Dresden, Germany
- Univ. Grenoble Alpes, CNRS, LPMMC, Grenoble, France
| | | | - Yannis Kalaidzidis
- Max Planck Institute of Molecular Cell Biology and Genetics, Dresden, Germany
| | - Marino Zerial
- Max Planck Institute of Molecular Cell Biology and Genetics, Dresden, Germany
- Cluster of Excellence ‘Physics of Life’, TU Dresden, Dresden, Germany
| | - Benjamin M. Friedrich
- cfaed, TU Dresden, Dresden, Germany
- Cluster of Excellence ‘Physics of Life’, TU Dresden, Dresden, Germany
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Morales-Navarrete H, Nonaka H, Scholich A, Segovia-Miranda F, de Back W, Meyer K, Bogorad RL, Koteliansky V, Brusch L, Kalaidzidis Y, Jülicher F, Friedrich BM, Zerial M. Liquid-crystal organization of liver tissue. eLife 2019; 8:e44860. [PMID: 31204997 PMCID: PMC6598764 DOI: 10.7554/elife.44860] [Citation(s) in RCA: 25] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/04/2019] [Accepted: 06/14/2019] [Indexed: 12/13/2022] Open
Abstract
Functional tissue architecture originates by self-assembly of distinct cell types, following tissue-specific rules of cell-cell interactions. In the liver, a structural model of the lobule was pioneered by Elias in 1949. This model, however, is in contrast with the apparent random 3D arrangement of hepatocytes. Since then, no significant progress has been made to derive the organizing principles of liver tissue. To solve this outstanding problem, we computationally reconstructed 3D tissue geometry from microscopy images of mouse liver tissue and analyzed it applying soft-condensed-matter-physics concepts. Surprisingly, analysis of the spatial organization of cell polarity revealed that hepatocytes are not randomly oriented but follow a long-range liquid-crystal order. This does not depend exclusively on hepatocytes receiving instructive signals by endothelial cells, since silencing Integrin-β1 disrupted both liquid-crystal order and organization of the sinusoidal network. Our results suggest that bi-directional communication between hepatocytes and sinusoids underlies the self-organization of liver tissue.
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Affiliation(s)
| | - Hidenori Nonaka
- Max Planck Institute of Molecular Cell Biology and GeneticsDresdenGermany
| | - André Scholich
- Max Planck Institute for the Physics of Complex SystemsDresdenGermany
| | | | - Walter de Back
- Institute for Medical Informatics and Biometry, Faculty of Medicine Carl Gustav CarusTechnische Universität DresdenDresdenGermany
- Centre for Information Services and High Performance ComputingTechnische Universität DresdenDresdenGermany
| | - Kirstin Meyer
- Max Planck Institute of Molecular Cell Biology and GeneticsDresdenGermany
| | - Roman L Bogorad
- David H. Koch Institute for Integrative Cancer ResearchMassachusetts Institute of TechnologyCambridgeUnited States
| | - Victor Koteliansky
- Skolkovo Institute of Science and TechnologySkolkovoRussia
- Department of ChemistryMV Lomonosov Moscow State UniversityMoscowRussia
| | - Lutz Brusch
- Centre for Information Services and High Performance ComputingTechnische Universität DresdenDresdenGermany
| | - Yannis Kalaidzidis
- Max Planck Institute of Molecular Cell Biology and GeneticsDresdenGermany
| | - Frank Jülicher
- Max Planck Institute for the Physics of Complex SystemsDresdenGermany
- Cluster of Excellence Physics of LifeTU DresdenDresdenGermany
| | - Benjamin M Friedrich
- Cluster of Excellence Physics of LifeTU DresdenDresdenGermany
- Center for Advancing Electronics DresdenTechnische Universität DresdenDresdenGermany
| | - Marino Zerial
- Max Planck Institute of Molecular Cell Biology and GeneticsDresdenGermany
- Cluster of Excellence Physics of LifeTU DresdenDresdenGermany
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