Vertex Model and Three-Dimensional Epithelial Morphogenesis

Abstract

Regulated deformations of epithelial sheets are frequently foreshadowed by patterning of their mechanical properties. The connection between patterns of cell properties and the emerging tissue deformations is studied in multiple experimental systems, but the general principles remain poorly understood. For instance, it is in general unclear what determines the direction in which the patterned sheet is going to bend and whether the resulting shape transformation will be discontinuous or smooth.

In chapter 2, these questions are explored computationally, using vertex models of epithelial shells assembled from prism-like cells. In response to rings and patches of apical cell contractility, model epithelia smoothly deform into invaginated or evaginated shapes similar to those observed in embryos and tissue organoids. Most of the observed effects can be captured by a simpler model with polygonal cells, modified to include the effects of the apicobasal polarity and natural curvature of epithelia. Our models can be readily extended to include the effects of multiple constraints and used to describe a wide range of morphogenetic processes.

In chapter 3, we employ the recently proposed modified vertex model to systematically explore the connection between the two-dimensional patterns of cell properties and the emerging three-dimensional structures. We illustrate it through the computational analysis of dorsal appendage morphogenesis in the developing Drosophila egg. We conclude this thesis by discussing possible future directions to extend this work.