Planar differential growth rates determine the position of folds in complex epithelia

Melda Tozluoğlu, Maria Duda, Natalie J Kirkland, Ricardo Barrientos, Jemima J Burden, José J Muñoz, Yanlan Mao

Preprint posted on 9 January 2019


Buckling of epithelium growing under spherical confinement

Anastasiya Trushko, Ilaria Di Meglio, Aziza Merzouki, Carles Blanch-Mercader, Shada Abuhattum, Jochen Guck, Kevin Alessandri, Pierre Nassoy, Karsten Kruse, Bastien Chopard, Aurelien Roux

Preprint posted on 7 January 2019

Article now published in Developmental Cell at

Grow under compressive forces and you will automatically fold

Selected by Sundar Naganathan


Folded epithelial sheets and tubes are observed across many organs in different phyla. How does a planar epithelial sheet fold into a complex 3D structure? Many different mechanisms such as apical constriction, basal relaxation and lateral constriction have been put forward to explain the mechanisms by which folding occurs during morphogenesis (see introduction of Tozluoglu et al. for an exhaustive list of mechanisms with references). All these processes involve active mechanical forces generated by the cytoskeleton intracellularly, which are communicated across cells in the tissue. Recent studies1-4, however, have demonstrated that passive forces that arise from mechanical instabilities between epithelial tissues and their surroundings can also lead to folding.

In most cases, epithelial tissues in embryos are not present in isolation. They are surrounded by an extracellular matrix (ECM) and/or other tissues that have different material properties. It turns out that if an epithelial tissue experiences compressive forces from its surroundings, the tissue tends to buckle and fold. The compressive forces can be either due to growth of the tissue by cell division confined by the ECM or due to differential growth of two connected tissues where one tissue grows faster than the other.

Irrespective of the mechanism, it is still unknown, how the initial position of the fold is determined. Tozluoglu et al. by investigating Drosophila wing imaginal disc, propose a novel mechanism where planar differential growth under the compression of ECM drives precise positioning of folds. In another preprint, Trushko et al. develop an in vitro model system to study folding of tissues growing under compression.

Key discoveries

Folding in Drosophila wing imaginal disc (Tozluoglu et al.):

The wing imaginal disc forms three folds between the hinge and pouch regions in the columnal layer between 80 and 96 hrs after egg laying. To understand fold formation, the authors first built a computational model where the epithelial tissue was represented as a non-homogeneous continuous material with temporally invariant material properties. When the tissue was allowed to proliferate spatially uniformly, no folds were observed to form in the absence of external resistance. Folds were observed with an introduction of external viscous resistance and correct number of folds (three) were obtained when apical stiffness was also increased concurrently. However, the shapes and positions of folds still could not be reproduced.

The authors then proceeded to experimentally test some of the assumptions in their model. Clonal analysis of the columnal layer revealed that growth is not uniform and that growth is relatively higher in the notum and pouch regions during early stages of folding. Moreover, an electron microscopy study revealed that the basement membrane (BM) gets thicker as folding proceeds. Implementing a differential planar growth rate as well as by considering the basement membrane as an elastic layer in the simulations, the authors show that the precise position, number and morphology of the folds can be predicted both in wild type as well as in wingless mutant scenarios.

Buckling of epithelium in vitro (Trushko et al.):

The authors encapsulated MDCK-II cells in spherical alginate capsules, whose inner surface had a few micrometres thick matrigel to which the cells adhered. The cells were allowed to proliferate thereby forming a monolayer. Incredibly, in this simple set up, after a few hrs of proliferation, folding of the monolayer was observed, where the monolayer detached from the alginate shell and bent inwards. As the monolayer proliferated, the thickness of the elastic alginate shell was observed to reduce suggesting that the cells were exerting pressure on the external environment. Knowing the thickness, Young’s modulus and stiffness of the capsule, monolayer folding was estimated to occur at a pressure of 100 Pa.

The authors then developed a continuum model of their system by considering the monolayer as an elastic ring that is confined in a circular domain. As the radius of the elastic ring increased, a first order buckling transition was observed similar to their experimental results. Furthermore, they performed simulations using a 2D vertex model and show that an effective friction of the monolayer to the matrigel and active cell mechanics are required to reproduce experimentally observed fold morphologies.

Why I chose these preprints

The preprints show through in vitro, in vivo and computational approaches that folding can occur through passive mechanical forces. Importantly, Tozluoglu et al. demonstrate that the position of folds can be explained by considering planar differential growth rate, which provides a crucial add-on for theoretical descriptions of folds. This is likely to motivate researchers investigating other instances of folding in diverse contexts to explore differential planar growth rates as a plausible mechanism. On the other hand, Trushko et al. bring out a much-needed in vitro model to study folding, where the mechanics of the folding process can be explored in depth.

Open questions

Wing imaginal disc:

  1. The authors experimentally measure differential growth rate in the columnal layer of the wing imaginal disc. What triggers this differential growth?
  2. The BM was assumed to be of uniform thickness in their model. Could the BM exhibit differential confinement on the columnar layer, which would bias the folding process to specific locations?
  3. Can the growth rate be changed in a spatiotemporal fashion in the columnal layer? According to their model, this should change the position of folds. Without this experiment it is hard to understand the extent to which planar differential growth rate determines fold positions.

In vitro system:

  1. Can the authors trigger differential growth in their monolayer similar to what has been observed in vivo in Tozluoglu et al. and quantify the extent to which fold position and morphology changes?
  2. Can the position of folds be biased by providing asymmetric confinement?
  3. Is the time-scale of folding comparable to what happens in vivo?


  1. Osborn, J. W., A model of growth restraints to explain the development and evolution of tooth shapes in mammals, J. Theor. Biol., 2008.
  2. Shyer, A. E., Tallinen, T., Nerurkar, N. L., Wei, Z., Gil, E. S., Kaplan, D. L., Tabin, C. J., and Mahadevan, L., Villification: How the gut gets its villi, Science, 2013.
  3. Savin, T., Kurpios, N. A., Shyer, A. E., Florescu, P., Liang, H., Mahadevan, L., and Tabin, C. J., On the growth and form of the gut, Nature, 2011.
  4. Varner, V. D., Gleghorn, J. P., Miller, E., Radisky, D. C., and Nelson, C. M., Mechanically patterning the embryonic airway epithelium, Proc. Natl. Acad. Sci., 2015.

Tags: buckling, confinement, fly, mechanics

Posted on: 23 February 2019 , updated on: 25 February 2019


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Author's response

Melda Tozluoğlu shared about Planar differential growth rates determine the position of folds in complex epithelia

We are delighted that our preprint was selected for preLights. We thank Sundar and are looking forward to feedback from the community. We think the highlight provides a clear summary of our work, and the significance in our point of view: Planar differential growth is a driver of precise fold positioning, and robust emergent tissue architecture in buckling epithelia. Some very key open questions are also highlighted, and we are happy to add our commentary on these.

The patterning of Drosophila wing imaginal disc has been subject to investigation over decades. We know the key morphogen gradients, such as Dpp and wingless, set the overall growth patterns and compartmentalisation of the disc. Regarding the fine details of growth patterns as we observe in our measurements, the simple comment is that what determines such fine-tuning of growth is indeed still an open question and a very interesting one. In our approach, we take the observed growth profiles as given, and investigate their downstream influences on tissue architecture.

The BM clearly has spatial and temporal heterogeneity; the younger discs seem to harbour thin and relatively uniform BM, whereas the BM of older discs (120hr AEL) is non-homogenous in both its thickness and the visible structure of the fibres. Although the intuitive argument is that a thicker BM would be stiffer, a thickness increase resulting from a sparser fibre network, or alteration of the composition of fibres, could result in reduction of BM stiffness. Clarification of these complexities of the BM structure requires extensive further research and indeed could influence the folding process. Our simulations demonstrate these fine details of the BM are not essential in precise positioning of the wing disc folds, as we can realise them with a homogenous BM definition. These complexities could in fact be functional in progression of the folds.

The strength of any computational model is demonstrated with its ability to provide testable, accurate predictions. With this philosophy in our work, beyond the definition of fold positioning, we predict perturbations to fold structure upon alterations of the growth rates. In the wing disc, global growth perturbations induce too severe deformations with excessive folding, hindering it impossible to judge perturbations on specific folds. The closest to a controllable, systematic growth perturbation we have in the experimental setup is mutations that naturally alter growth rates at specific regions of the tissue, such as the wingless spade mutant we tested in our study. Here, the mutant reduces growth specifically at the wing hinge, and by utilising only this reduction in growth; we can successfully predict the new emergent fold number and structure. We believe our model predictions and their experimental validation on emergent fold morphology upon perturbation of growth demonstrate the role of differential growth in definition of precise fold architecture.


Aurélien Roux shared about Buckling of epithelium growing under spherical confinement

a. It seems a priori difficult to modulate cell growth in a spatially controlled manner. However, we could use two epithelial cell types with different growth rates (and labelled differentially so that they can be traced) and co-encapsulate them. These cells will form islets with different growth rates that will merge into a confluent layer, reproducing the heterogeneity of growth rate. We then could correlate folds position and growth rate.

b. Indeed, if one look carefully at the picture, folding often occurs where the shell is the thinnest. We thus think that folding is coupled to the local stiffness of the surrounding substrate.

c. In our experiments, folding takes about 5 to 10 hours, which is fully compatible with the times observed in Tozluoglu et al. (8.5 hours in average), but also for other embryonic folding events like gastrulation or neurulation.

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