Quantitative Morphology of Epithelial Folds

Abstract

The shape of spatially modulated epithelial morphologies such as villi and crypts is usually associated with the epithelium-stroma area mismatch leading to buckling. We propose an alternative mechanical model based on intraepithelial stresses generated by differential tensions of apical, lateral, and basal sides of cells as well as on the elasticity of the basement membrane. We use it to theoretically study longitudinal folds in simple epithelia and we identify four types of corrugated morphologies: compact, invaginated, evaginated, and wavy. The obtained tissue contours and thickness profiles are compared to epithelial folds observed in invertebrates and vertebrates, and for most samples, the agreement is within the estimated experimental error. Our model establishes the groove-crest modulation of tissue thickness as a morphometric parameter that can, together with the curvature profile, be used to estimate the relative differential apicobasal tension in the epithelium.

Vertex models: from cell mechanics to tissue morphogenesis

“…( top left ) Simulation of neural tube formation in amphibians as a result of a ‘purse-string’ contraction of apical surfaces and cell volume conservation (from [35]). ( top right ) Phase diagram of epithelial buckling as a function of bending stiffness and differential tensions along the apical and basal surfaces of cells (from [40]). ( bottom left ) Simulation of ventral furrow formation in Drosophila (from [37]).…”

“…Alternatively, difference in apical and basal tension in the mesoderm can drive tissue invagination, depending on the passive elastic properties of the cells and on the stiffness of the surrounding material [38,39]. The effect of the basement membrane elasticity on folds in flat epithelia induced by apico-basal tension asymmetry has also been discussed [40] (figure 2 c ). 2D lateral vertex model simulations have also been used to study the folding of an epithelium into the optical cup in mouse embryonic stem cell cultures [36] (figure 2 c ).…”

Mathematical Modeling of Tissue Folding and Asymmetric Tissue Flow during Epithelial Morphogenesis

“…The individual cells can be viewed as polygons with four edges and vertices that correspond to the apical, basal, and two lateral sides, as shown in Figure 1. Using the framework of a vertex model, we build a theoretical model of the two-dimensional cross section of the cell sheet that recapitulates tissue-autonomous epithelial folding [7,29,[33][34][35][36]. The forces exerted on the vertices are determined from the derivatives of a potential function, which describes the mechanical properties of the entire sheet.…”

Nonlinear and nonlocal elasticity in coarse-grained differential-tension models of epithelia

“…While the differential-tension models can quantitatively reproduce the morphology of epithelial folds in many different living systems [11], it is likely that, in general multilayered epithelia, the formation of epithelial folds must be ascribed to a combination of these intra-epithelial stresses and differential growth of different parts of the tissue. Models based on the latter only have for example been invoked to describe, at the scale of the epithelium, the formation of cortical convolutions in the brain [15][16][17][18][19][20] and of the intestinal villi [21][22][23], the 'fication' of which lends itself to the pun that gave Ref.…”