Figure - PMC

Skip to main content

An official website of the United States government

Here's how you know

Here's how you know

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.

View full-text article in PMC

. 2018 Jul 27;9:2960. doi: 10.1038/s41467-018-05376-1

Search in PMC
Search in PubMed
View in NLM Catalog
Add to search

© The Author(s) 2018

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

PMC Copyright notice

Fig. 6 — Graphic summary of 3D packing in epithelia. a The graph represents the curvature ratio (surface ratio) depending of the dimensionless values of ${\hat{R}}_{a}$ and ${\hat{R}}_{b}$ . The curvature ratio is defined by the ratio ${\hat{R}}_{a} ∕ {\hat{R}}_{b}$ in the case of basal reduction and ${\hat{R}}_{b} ∕ {\hat{R}}_{a}$ in the case of apical reduction. The bottom triangle (blue shaded region) covers the region where the epithelial bend generating a reduction of the apical surface ${\hat{R}}_{b} > {\hat{R}}_{a}$ . The top triangle (grey shaded region) shows the region where a reduction of the basal surface occurs ${\hat{R}}_{a} > {\hat{R}}_{b}$ . In all the geometrical solids and epithelial representations basal is at top (grey) and apical is at bottom (blue). The black dashed arrow in the main diagonal indicates the epithelium without curvature (ratio = 1). This planar epithelium is formed by prisms. The packing configuration space is compartmentalized into regions depending on the relative values of the curvature radii (or equivalently the aspect ratio) of epithelia. The curved arrows indicate the types of solids that are more favourable in the epithelia depending of the curvature: close to the diagonal the frusta shapes of the cells are preferred. On the contrary, in the top-right and bottom-left corners all the cells tend to be scutoids that take part in several apico-basal transitions. There is also an intermediate situation where the epithelium is packed using both scutoids and frusta shapes. b The model can be generalized to describe tissues with two main axes of curvature (h, transversal, and w, longitudinal), where R represents the Cauchy radius, e.g. $R_{b}^{h}$ accounts for the Cauchy radius along the h axis in the basal, b, surface. Here we assume that the apical surface lies in the inner part of the tissue. As a function of the Cauchy radii it is possible to assess the surface ratio anisotropy for different geometries as measured by the relative change of the aspect ratio from apical to basal (colour code): $(R_{b}^{h} ∕ R_{a}^{h}) ∕ (R_{b}^{w} ∕ R_{a}^{w}) - 1$ . The increment of the surface ratio anisotropy positively correlates with the percentage of scutoids