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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.<\/jats:p>","DOI":"10.1371\/journal.pcbi.1008412","type":"journal-article","created":{"date-parts":[[2020,12,10]],"date-time":"2020-12-10T19:52:01Z","timestamp":1607629921000},"page":"e1008412","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":8,"title":["Quantification of nematic cell polarity in three-dimensional tissues"],"prefix":"10.1371","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9393-5459","authenticated-orcid":true,"given":"Andr\u00e9","family":"Scholich","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9955-9012","authenticated-orcid":true,"given":"Simon","family":"Syga","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9578-2556","authenticated-orcid":true,"given":"Hern\u00e1n","family":"Morales-Navarrete","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1546-0475","authenticated-orcid":true,"given":"Fabi\u00e1n","family":"Segovia-Miranda","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4705-7587","authenticated-orcid":true,"given":"Hidenori","family":"Nonaka","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2228-2550","authenticated-orcid":true,"given":"Kirstin","family":"Meyer","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4641-8472","authenticated-orcid":true,"given":"Walter","family":"de Back","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0137-5106","authenticated-orcid":true,"given":"Lutz","family":"Brusch","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6137-1193","authenticated-orcid":true,"given":"Yannis","family":"Kalaidzidis","sequence":"additional","affiliation":[]},{"given":"Marino","family":"Zerial","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4731-9185","authenticated-orcid":true,"given":"Frank","family":"J\u00fclicher","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9742-6555","authenticated-orcid":true,"given":"Benjamin M.","family":"Friedrich","sequence":"additional","affiliation":[]}],"member":"340","published-online":{"date-parts":[[2020,12,10]]},"reference":[{"issue":"11","key":"pcbi.1008412.ref001","doi-asserted-by":"crossref","first-page":"887","DOI":"10.1038\/nrm2523","article-title":"From cells to organs: Building polarized tissue","volume":"9","author":"DM Bryant","year":"2008","journal-title":"Nat Rev Mol Cell Biol"},{"issue":"4","key":"pcbi.1008412.ref002","doi-asserted-by":"crossref","first-page":"e1004190","DOI":"10.1371\/journal.pcbi.1004190","article-title":"Metrics for assessing cytoskeletal orientational correlations and consistency","volume":"11","author":"NK Drew","year":"2015","journal-title":"PLoS Comput Biol"},{"issue":"1","key":"pcbi.1008412.ref003","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1146\/annurev.cb.01.110185.001331","article-title":"Cell Surface Polarity in Epithelia","volume":"1","author":"K Simons","year":"1985","journal-title":"Annu Rev Cell Biol"},{"key":"pcbi.1008412.ref004","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1002\/cphy.c120009","article-title":"Hepatocyte polarity","volume":"3","author":"A Treyer","year":"2013","journal-title":"Compr Physiol"},{"issue":"6","key":"pcbi.1008412.ref005","doi-asserted-by":"crossref","first-page":"420","DOI":"10.1096\/fasebj.8.6.8168692","article-title":"Cell adhesion molecules in liver function and pattern formation","volume":"8","author":"SC Stamatoglou","year":"1994","journal-title":"FASEB J"},{"issue":"6","key":"pcbi.1008412.ref006","doi-asserted-by":"crossref","first-page":"1623","DOI":"10.1242\/jcs.109.6.1623","article-title":"Establishment of hepatic cell polarity in the rat hepatoma-human fibroblast hybrid WIF-B9. 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