Explicit calculation method for cell alignment in non-circular geometries
The alignment of spindle-shaped cells in two-dimensional geometries induces singular points called topological defects, at which the alignment angle of the cell cannot be defined. To control defects related to biological roles such as cell apoptosis, calculation methods for predicting the defect pos...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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The Royal Society
2022-01-01
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| Series: | Royal Society Open Science |
| Subjects: | |
| Online Access: | https://royalsocietypublishing.org/doi/10.1098/rsos.211663 |
| _version_ | 1797837630865408000 |
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| author | Hiroki Miyazako Takaaki Nara |
| author_facet | Hiroki Miyazako Takaaki Nara |
| author_sort | Hiroki Miyazako |
| collection | DOAJ |
| description | The alignment of spindle-shaped cells in two-dimensional geometries induces singular points called topological defects, at which the alignment angle of the cell cannot be defined. To control defects related to biological roles such as cell apoptosis, calculation methods for predicting the defect positions are required. This study proposes an explicit calculation method for predicting cell alignment and defect positions in non-circular geometries. First, a complex potential is introduced to describe the alignment angles of cells, which is used to derive an explicit formula for cell alignment in a unit disc. Then, the derived formula for the unit disc is extended to the case for non-circular geometries using a numerical conformal mapping. Finally, the complex potential allows a calculation of the Frank elastic energy, which can be minimized with respect to the defect positions to predict their equilibrium state in the geometry. The proposed calculation method is used to demonstrate a numerical prediction of multiple defects in circular and non-circular geometries, which are consistent with previous experimental results. |
| first_indexed | 2024-04-09T15:27:47Z |
| format | Article |
| id | doaj.art-4916be4862534465ba42a075a1eec51c |
| institution | Directory Open Access Journal |
| issn | 2054-5703 |
| language | English |
| last_indexed | 2024-04-09T15:27:47Z |
| publishDate | 2022-01-01 |
| publisher | The Royal Society |
| record_format | Article |
| series | Royal Society Open Science |
| spelling | doaj.art-4916be4862534465ba42a075a1eec51c2023-04-28T11:04:05ZengThe Royal SocietyRoyal Society Open Science2054-57032022-01-019110.1098/rsos.211663Explicit calculation method for cell alignment in non-circular geometriesHiroki Miyazako0Takaaki Nara1Department of Information Physics and Computing, Graduate School of Information Science and Technology, The University of Tokyo, 7-3-1, Hongo, Bunkyo-ku, Tokyo, JapanDepartment of Information Physics and Computing, Graduate School of Information Science and Technology, The University of Tokyo, 7-3-1, Hongo, Bunkyo-ku, Tokyo, JapanThe alignment of spindle-shaped cells in two-dimensional geometries induces singular points called topological defects, at which the alignment angle of the cell cannot be defined. To control defects related to biological roles such as cell apoptosis, calculation methods for predicting the defect positions are required. This study proposes an explicit calculation method for predicting cell alignment and defect positions in non-circular geometries. First, a complex potential is introduced to describe the alignment angles of cells, which is used to derive an explicit formula for cell alignment in a unit disc. Then, the derived formula for the unit disc is extended to the case for non-circular geometries using a numerical conformal mapping. Finally, the complex potential allows a calculation of the Frank elastic energy, which can be minimized with respect to the defect positions to predict their equilibrium state in the geometry. The proposed calculation method is used to demonstrate a numerical prediction of multiple defects in circular and non-circular geometries, which are consistent with previous experimental results.https://royalsocietypublishing.org/doi/10.1098/rsos.211663cell alignmentnematic liquid crystalscomplex analysisconformal mapping |
| spellingShingle | Hiroki Miyazako Takaaki Nara Explicit calculation method for cell alignment in non-circular geometries Royal Society Open Science cell alignment nematic liquid crystals complex analysis conformal mapping |
| title | Explicit calculation method for cell alignment in non-circular geometries |
| title_full | Explicit calculation method for cell alignment in non-circular geometries |
| title_fullStr | Explicit calculation method for cell alignment in non-circular geometries |
| title_full_unstemmed | Explicit calculation method for cell alignment in non-circular geometries |
| title_short | Explicit calculation method for cell alignment in non-circular geometries |
| title_sort | explicit calculation method for cell alignment in non circular geometries |
| topic | cell alignment nematic liquid crystals complex analysis conformal mapping |
| url | https://royalsocietypublishing.org/doi/10.1098/rsos.211663 |
| work_keys_str_mv | AT hirokimiyazako explicitcalculationmethodforcellalignmentinnoncirculargeometries AT takaakinara explicitcalculationmethodforcellalignmentinnoncirculargeometries |