Modeling the mechanics of growing epithelia with a bilayer plate theory

Abstract

Epithelia, which consists of cell sheets lying on a substrate, are prevalent structures of multicellular organisms. The physical basis of epithelial morphogenesis has been intensely investigated in recent years. However, as 2D mechanics focused most attention, we still lack a rigorous description of how the mechanical interactions between the cell layer and its substrate can lead to 3D distortions. This work provides a complete description of epithelial mechanics using the most straightforward model of an epithelium: a thin elastic bilayer. We first provide experimental evidence in Drosophila tissues that localized alterations of the cell substrate (the extracellular matrix) can lead to profound 3D shape changes in epithelia. We then develop an analytical model modifying the Föppl-von Kármán equation with growth for bilayers. We provide a complete description of all contributions from biophysical characteristics of epithelia. We show how any localized inhomogeneity of stiffness or thickness drastically changes the bending process when the two layers grow differently. Comparison with finite element simulations and experiments performed on Drosophila wing imaginal discs validates this approach for thin epithelia Joseph Ackermann and Paul-Qiuyang Qu equally Contributed.

A mechanical transition from tension to buckling underlies the jigsaw puzzle shape morphogenesis of histoblasts in the Drosophila epidermis

“…The precise numbers for each experiment are listed hereafter. WT: 69 (11,14,11,26,7 respectively at ¡ 90h AEL, 90-95 h AEL, 95-100 h AEL, wandering stage, white pupa), sqh:GFP : 18, Af:GFP : 12, src:GFP : 10, Rab11-DN: 12, stg: 11 Statistical analysis and plotting were done using built-in functions in Matlab and R. First, All measured variables (area, perimeter, circularity) were tested for normality using Lillifors test. Then, normally distributed variables were compared by t-test, while non-normally distributed variables were evaluated by Mann-Whitney non parametric test.…”

“…Other than tensile forces, compressive forces are also important shape generators. For example, an elastic body under compressive forces can go through buckling instability [19][20][21] , a process at play in gut vilification 22,23 , in gastrulating embryos 24 , in the formation of brain cortical lobules by differential growth of apposed cortical cell layers 25 or in some cell-ECM systems 26 . While these examples are taken from elasticity operating at large scale, in this work we find evidences that similar effects exist at the level of individual cells.…”

Variational methods and deep Ritz method for active elastic solids

“…These calculations can be further extended to study the dynamics of tissue morphogenesis by considering dissipative processes and multilayered composite plates that mimic tissue structure. 68 (ii) Taking into account of the elasto-active feedback. In this work, we have only considered active stresses with frozen, given distributions.…”

“…These calculations can be further extended to study the dynamics of tissue morphogenesis by considering dissipative processes and multilayered composite plates that mimic tissue structure. 68…”

Epithelial folding through local degradation of an elastic basement membrane plate

“…Here, we propose a continuum-mechanical model to rationalize the observation of basal epithelial folding upon local degradation of the basement membrane. While already previous studies have used plate theory to account for folding upon local plate degradation in epithelia 22,23 , these models were relying on epithelial growth as a key mechanism for a) Electronic mail: Corresponding author: elisabeth.fischer-friedrich@tu-dresden.de folding. However, it was shown experimentally that formation of the H/H fold in the fruit fly larval tissue takes place in a timely manner in the absence of cell division 21 suggesting that fold formation is independent of tissue growth.…”