On folding morphogenesis, a mechanical problem

Abstract

Tissue folding is a fundamental process that sculpts a simple flat epithelium into a complex three-dimensional organ structure. Whether it is the folding of the brain, or the looping of the gut, it has become clear that to generate an invagination or a fold of any form, mechanical asymmetries must exist in the epithelium. These mechanical asymmetries can be generated locally, involving just the invaginating cells and their immediate neighbours, or on a more global tissue-wide scale. Here, we review the different mechanical mechanisms that epithelia have adopted to generate folds, and how the use of precisely defined mathematical models has helped decipher which mechanisms are the key driving forces in different epithelia. This article is part of a discussion meeting issue 'Contemporary morphogenesis'.

Keywords: folding; mathematical models; mechanics; morphogenesis.

Figure 1.

Local active mechanisms driving fold formation. (a) A combination of apical constriction, lateral shortening and basal relaxation, together with cell volume conservation, drives folds, in tissues such as the Drosophila embryo, during ventral furrow formation. Similar mechanisms also occur in generating some of the folds of the wing disc. (b) Apical constriction and apoptosis drive fold formation in the Drosophila leg disc. (c) Apical junction shifting followed by cell shortening drives folding in the dorsal folds of Drosophila embryos.

Figure 2.

Neighbouring active mechanisms driving fold formation. (a) In Drosophila salivary gland formation, the folding force primarily comes from the surrounding actomyosin cable that compresses the invaginating cells. Apical constriction of the invaginating cells is not essential. (b) During lung branching morphogenesis, smooth muscle wraps around the growing buds to constrict and fold the epithelia into shape. Without smooth muscle, the lung epithelium folds randomly as it grows against the mesenchyme.

Figure 3.

Differential growth as a global mechanism that drives tissue folding. (a) In simple one dimension, differential expansion of two connected layers will cause bending. (b) In two dimensions, differential growth between different regions or layers of connected material will cause wrinkling or doming. (c–e) Real examples of differential growth in different layers of the tissue causing folding include the looping of the gut (c), the formation of villi in the gut (d) and the folds in the brain (e).

Figure 4.

Differential growth in the plane of the tissue drives the position of folds in the Drosophila wing disc. A computational model (a), has shown that uniform growth gives uniform ripples in the wing (b), whereas heterogeneous growth, as measured in the real wing disc, gives the non-uniform fold topology that matches experiments (c).