Adapting a Plant Tissue Model to Animal Development: Introducing Cell Sliding into VirtualLeaf

Henri B Wolff,Roeland M H Merks,Lance A Davidson

doi:10.1007/s11538-019-00599-9

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 cell rearrangement (T1) and cell extrusion (T2) transitions emerge naturally, allowing the 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.

Highlights

How cells form tissues, organs, and organisms remains one of the most intriguing and most central questions of biology
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
Cell sorting is due to the interplay of differential adhesion and random cell motility, which progressively replaces weaker intercellular adhesions for stronger adhesions

Summary

Introduction

How cells form tissues, organs, and organisms remains one of the most intriguing and most central questions of biology. Recent theoretical approaches to study collective cell behavior are taking a prominent role in addressing these questions. Theoretical approaches provide deeper intuition about processes that typically are unfamiliar to the researchers by testing the physical plausibility of speculative hypotheses or by making predictions that can be tested experimentally. To support theoretical analysis of tissue formation, a large range of mathematical methods have been proposed. These range from systems of partial differential equations models These range from systems of partial differential equations models (see, e.g,. Keller and Segel 1970, 1971; Painter et al 2015) to discrete methods that describe dense multicellular structures as interacting particle systems (see, e.g., Glazier and Graner 1993; Graner and Glazier 1992; Newman 2005; Sozinova et al 2006; Voss-Böhme and Deutsch 2010; Woods et al 2014; Smeets et al 2016; Barton et al 2017; Ghaffarizadeh et al 2018 and Liedekerke et al 2015 for review)

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Conclusion