Abstract
Tissue folding is a frequently observed phenomenon, from the cerebral cortex gyrification, to the gut villi formation and even the crocodile head scales development. Although its causes are not yet well understood, some hypotheses suggest that it is related to the physical properties of the tissue and its growth under mechanical constraints. In order to study the underlying mechanisms affecting tissue folding, experimental models are developed where epithelium monolayers are cultured inside hydrogel microcapsules. In this work, we use a 2D vertex model of circular cross-sections of cell monolayers to investigate how cell mechanical properties and proliferation affect the shape of in-silico growing tissues. We observe that increasing the cells’ contractility and the intercellular adhesion reduces tissue buckling. This is found to coincide with smaller and thicker cross-sections that are characterized by shorter relaxation times following cell division. Finally, we show that the smooth or folded morphology of the simulated monolayers also depends on the combination of the cell proliferation rate and the tissue size.
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Notes
\(A^0\) of a cell \(\alpha\) is increased each 3000 iterations by \(\Delta {A^0} = {0.1\cdot A_{\alpha }\text {(before mitosis)}}\), which is enough time for a cell to reach equilibrium between each \(A^0\) increment in our simulations, with a time step \(\delta t\) and a damping \(\eta\) parameters equal to \(10^{-1}\) sec and 1 sec\(^{-1}\). The choice of the cell growth rate corresponds to the implementation of a multi-scale simulation technique (combining the relaxation time scale in the order of minutes and the proliferation time scale in the order of 10–20 h), and does not correspond to biologically realistic growth times. We artificially accelerate the cell growth to speed up the execution of our simulations. However, the quasi-static growth of cells insures that we get the same results as those we would have obtained with a slower and more biologically realistic cell growth.
As long as the tissue does not have the time to return to its equilibrium state between two cell divisions.
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We thank the SystemsX.ch initiative who supported this work (project EpiPhysX).
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Merzouki, A., Malaspinas, O., Trushko, A. et al. Influence of cell mechanics and proliferation on the buckling of simulated tissues using a vertex model. Nat Comput 17, 511–519 (2018). https://doi.org/10.1007/s11047-017-9629-y
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DOI: https://doi.org/10.1007/s11047-017-9629-y