Characterization of Appendage Formation in a Three-Dimensional Vertex Model of the Developing Drosophila Epithelium

Abstract

Developmental processes in which tube-like structures emerge from initially flat cell sheets are of great practical importance, as such processes are involved in formation of the human digestive, circulatory, and nervous systems. A relatively simple and genetically tractable model of tubulogensis is the formation of dorsal breathing appendages from the follicular epithelium of the developing Drosophila embryo. Although prior studies have produced detailed mapping of cell fates and an understanding of the morphogen pathways necessary for cell differentiation, mechanistic descriptions of appendage formation remain tentative. Computational modeling has emerged as a method to assess possible mechanisms in a simplified environment. The current work concerns a three-dimensional vertex model of appendage formation originally constructed by Osterfield et al. Although Osterfield et al. succeeded in constructing a simple, intuitive, and adaptable model representing the formation of appendage-like structures, they did not develop a detailed understanding of the essential elements necessary to produce a “correct” structure or the pathway through which the final structure is formed. In order to gain a greater mechanistic understanding, we reduced the complexity of the system by decreasing the size of the simulated tissue and by simplifying the implementation of T1 transitions, a crucial feature of the model that allows for cell rearrangements. We also performed a practical analysis of numerical integration methods, finding sensitivity to the threshold edge length of intercalation, a model parameter. Through a detailed exploration of parameter space, we found that different patterns of edge tensions produce two categories of “correct” structures, characterized by distinct geometric properties, topological arrangements of cell neighbors, and sequences of cell rearrangement.