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Aboave-Weaire’s law in epithelia results from an angle constraint in contiguous polygonal lattices

View ORCID ProfileRoman Vetter, Marco Kokic, Harold Gómez, Leonie Hodel, Bruno Gjeta, Antonella Iannini, Gema Villa-Fombuena, Fernando Casares, View ORCID ProfileDagmar Iber
doi: https://doi.org/10.1101/591461
Roman Vetter
1Department of Biosystems, Science and Engineering (D-BSSE), ETH Zurich, Mattenstrasse 26, 4058 Basel, Switzerland
2Swiss Institute of Bioinformatics (SIB), Mattenstrasse 26, 4058 Basel, Switzerland
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Marco Kokic
1Department of Biosystems, Science and Engineering (D-BSSE), ETH Zurich, Mattenstrasse 26, 4058 Basel, Switzerland
2Swiss Institute of Bioinformatics (SIB), Mattenstrasse 26, 4058 Basel, Switzerland
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Harold Gómez
1Department of Biosystems, Science and Engineering (D-BSSE), ETH Zurich, Mattenstrasse 26, 4058 Basel, Switzerland
2Swiss Institute of Bioinformatics (SIB), Mattenstrasse 26, 4058 Basel, Switzerland
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Leonie Hodel
1Department of Biosystems, Science and Engineering (D-BSSE), ETH Zurich, Mattenstrasse 26, 4058 Basel, Switzerland
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Bruno Gjeta
1Department of Biosystems, Science and Engineering (D-BSSE), ETH Zurich, Mattenstrasse 26, 4058 Basel, Switzerland
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Antonella Iannini
3CABD, CSIC-Universidad Pablo de Olavide, Seville, Spain
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Gema Villa-Fombuena
3CABD, CSIC-Universidad Pablo de Olavide, Seville, Spain
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Fernando Casares
3CABD, CSIC-Universidad Pablo de Olavide, Seville, Spain
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Dagmar Iber
1Department of Biosystems, Science and Engineering (D-BSSE), ETH Zurich, Mattenstrasse 26, 4058 Basel, Switzerland
2Swiss Institute of Bioinformatics (SIB), Mattenstrasse 26, 4058 Basel, Switzerland
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  • ORCID record for Dagmar Iber
  • For correspondence: dagmar.iber@bsse.ethz.ch
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ABSTRACT

It has long been noted that the cell arrangements in epithelia, regardless of their origin, exhibit some striking regularities: first, the average number of cell neighbours at the apical side is (close to) six. Second, the average apical cell area is linearly related to the number of neighbours, such that cells with larger apical area have on average more neighbours, a relation termed Lewis’ law. Third, Aboav-Weaire’s (AW) law relates the number of neighbours that a cell has to that of its direct neighbours. While the first rule can be explained with topological constraints in contiguous polygonal lattices, and the second rule (Lewis’ law) with the minimisation of the lateral contact surface energy, the driving forces behind the AW law have remained elusive. We now show that also the AW law emerges to minimise the lateral contact surface energy in polygonal lattices by driving cells to the most regular polygonal shape, but while Lewis’ law regulates the side lengths, the AW law controls the angles. We conclude that global apical epithelial organization is the result of energy minimisation under topological constraints.

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The copyright holder for this preprint is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under a CC-BY-NC 4.0 International license.
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Posted March 27, 2019.
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Aboave-Weaire’s law in epithelia results from an angle constraint in contiguous polygonal lattices
Roman Vetter, Marco Kokic, Harold Gómez, Leonie Hodel, Bruno Gjeta, Antonella Iannini, Gema Villa-Fombuena, Fernando Casares, Dagmar Iber
bioRxiv 591461; doi: https://doi.org/10.1101/591461
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Aboave-Weaire’s law in epithelia results from an angle constraint in contiguous polygonal lattices
Roman Vetter, Marco Kokic, Harold Gómez, Leonie Hodel, Bruno Gjeta, Antonella Iannini, Gema Villa-Fombuena, Fernando Casares, Dagmar Iber
bioRxiv 591461; doi: https://doi.org/10.1101/591461

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