title: Vertex models of epithelial morphogenesis.
abstract: The dynamic behavior of epithelial cell sheets plays a central role during numerous developmental processes. Genetic and imaging studies of epithelial morphogenesis in a wide range of organisms have led to increasingly detailed mechanisms of cell sheet dynamics. Computational models offer a useful means by which to investigate and test these mechanisms, and have played a key role in the study of cell-cell interactions. A variety of modeling approaches can be used to simulate the balance of forces within an epithelial sheet. Vertex models are a class of such models that consider cells as individual objects, approximated by two-dimensional polygons representing cellular interfaces, in which each vertex moves in response to forces due to growth, interfacial tension, and pressure within each cell. Vertex models are used to study cellular processes within epithelia, including cell motility, adhesion, mitosis, and delamination. This review summarizes how vertex models have been used to provide insight into developmental processes and highlights current challenges in this area, including progressing these models from two to three dimensions and developing new tools for model validation.
authors.affiliation: Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Oxford, United Kingdom. Electronic address: alexander.fletcher@maths.ox.ac.uk.
authors.forename: Alexander G
authors.initials: AG
authors.lastname: Fletcher
authors.affiliation: Lewis-Sigler Institute for Integrative Genomics, Princeton, New Jersey.
authors.forename: Miriam
authors.initials: M
authors.lastname: Osterfield
authors.affiliation: Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Oxford, United Kingdom. Electronic address: ruth.baker@maths.ox.ac.uk.
authors.forename: Ruth E
authors.initials: RE
authors.lastname: Baker
authors.affiliation: Lewis-Sigler Institute for Integrative Genomics, Princeton, New Jersey; Department of Chemical and Biological Engineering, Princeton University, Princeton, New Jersey. Electronic address: stas@princeton.edu.
authors.forename: Stanislav Y
authors.initials: SY
authors.lastname: Shvartsman
mesh_terms: D000818:Animals; D002454:Cell Differentiation; D048430:Cell Shape; D000078404:Epidermal Cells; D004817:Epidermis / Q000254:growth & development*; D004847:Epithelial Cells / Q000166:cytology* / Q000502:physiology; D006801:Humans; D008954:Models, Biological; D009024:Morphogenesis