Mechanical Model of Geometric Cell and Topological Algorithm for Cell Dynamics from Single-Cell to Formation of Monolayered Tissues with Pattern

Abstract

Geometric and mechanical properties of individual cells and interactions among neighboring cells are the basis of formation of tissue patterns. Understanding the complex interplay of cells is essential for gaining insight into embryogenesis, tissue development, and other emerging behavior. Here we describe a cell model and an efficient geometric algorithm for studying the dynamic process of tissue formation in 2D (e.g. epithelial tissues). Our approach improves upon previous methods by incorporating properties of individual cells as well as detailed description of the dynamic growth process, with all topological changes accounted for. Cell size, shape, and division plane orientation are modeled realistically. In addition, cell birth, cell growth, cell shrinkage, cell death, cell division, cell collision, and cell rearrangements are now fully accounted for. Different models of cell-cell interactions, such as lateral inhibition during the process of growth, can be studied in detail. Cellular pattern formation for monolayered tissues from arbitrary initial conditions, including that of a single cell, can also be studied in detail. Computational efficiency is achieved through the employment of a special data structure that ensures access to neighboring cells in constant time, without additional space requirement. We have successfully generated tissues consisting of more than 20,000 cells starting from 2 cells within 1 hour. We show that our model can be used to study embryogenesis, tissue fusion, and cell apoptosis. We give detailed study of the classical developmental process of bristle formation on the epidermis of D. melanogaster and the fundamental problem of homeostatic size control in epithelial tissues. Simulation results reveal significant roles of solubility of secreted factors in both the bristle formation and the homeostatic control of tissue size. Our method can be used to study broad problems in monolayered tissue formation. Our software is publicly available.

Multiscale Modeling of Cellular Epigenetic States: Stochasticity in Molecular Networks, Chromatin Folding in Cell Nuclei, and Tissue Pattern Formation of Cells

“…(b) Each cell is tiled by a triangular mesh generated using the farthest point sampling method based on Delaunay triangulation. [107] (c) Cell grows incrementally, with volume change attributed to individual boundary element that sum to Δ V (adapted from references [81,104] ).…”

“…These include the cellular Potts model, center-based model, finite element models and vertex models. Below we briefly summarize these methods (see Sëma et al [81] for a detailed comparison).…”

“…We have recently developed a physical model of cell and a simulation algorithm that incorporates cell size, shape, lineage, growth rate, death rate, and different cell-cell interactions (Fig 9 [81] ). Our method can model monolayered tissue formation by following the growth process of either a single cell, or a group of cells with arbitrarily pre-arranged spatial relationship, unlike previous studies that must start with a specific pre-existing cellular pattern.…”

“…We have used our dynamic vertex model [81,98] to examine the mechanisms regulating topological changes in tissue formation. Specifically, we studied the effects of orientation of division plane, differential proliferation, and mechanical forces on animal epithelial cells.…”

Cell–substrate mechanics guide collective cell migration through intercellular adhesion: a dynamic finite element cellular model

“…Recently, computational models have become increasingly useful to complement experimental observations towards understanding the mechanisms of collective cell migration. A number of computational cell models have been developed to study the mechanical interactions between cells or between cell and ECM (Albert and Schwarz, 2016;Basan et al, 2013;Checa et al, 2015;Drasdo and Hoehme, 2012;Hoehme and Drasdo, 2010;Hutson et al, 2009;Kabla, 2012;Kachalo et al, 2015;Kim et al, 2018Kim et al, , 2015Lee and Wolgemuth, 2011;Lee et al, 2017;Marée et al, 2007;Merchant et al, 2018;Nagai and Honda, 2009;Nematbakhsh et al, 2017;Sandersius et al, 2011;Van Liedekerke et al, 2019;Vermolen and Gefen, 2015;Vitorino et al, 2011;Zhao et al, 2013). However, these models have limitations.…”