Adapting a plant tissue model to animal development: introducing cell
sliding into VirtualLeaf
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by
Henri B. Wolff, Lance A. Davidson, Roeland M.H. Merks
2019
Abstract
Cell-based, mathematical modeling of collective cell behavior has become a
prominent tool in developmental biology. Cell-based models represent individual
cells as single particles or as sets of interconnected particles, and predict
the collective cell behavior that follows from a set of interaction rules. In
particular, vertex-based models are a popular tool for studying the mechanics
of confluent, epithelial cell layers. They represent the junctions between
three (or sometimes more) cells in confluent tissues as point particles,
connected using structural elements that represent the cell boundaries. A
disadvantage of these models is that cell-cell interfaces are represented as
straight lines. This is a suitable simplification for epithelial tissues, where
the interfaces are typically under tension, but this simplification may not be
appropriate for mesenchymal tissues or tissues that are under compression, such
that the cell-cell boundaries can buckle. In this paper we introduce a variant
of VMs in which this and two other limitations of VMs have been resolved. The
new model can also be seen as on off-the-lattice generalization of the Cellular
Potts Model. It is an extension of the open-source package VirtualLeaf, which
was initially developed to simulate plant tissue morphogenesis where cells do
not move relative to one another. The present extension of VirtualLeaf
introduces a new rule for cell-cell shear or sliding, from which T1 and T2
transitions emerge naturally, allowing application of VirtualLeaf to problems
of animal development. We show that the updated VirtualLeaf yields different
results than the traditional vertex-based models for
differential-adhesion-driven cell sorting and for the neighborhood topology of
soft cellular networks.
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