Interacting active surfaces: A model for three-dimensional cell aggregates

Abstract

We introduce a modelling and simulation framework for cell aggregates in three dimensions based on interacting active surfaces. Cell mechanics is captured by a physical description of the acto-myosin cortex that includes cortical flows, viscous forces, active tensions, and bending moments. Cells interact with each other via short-range forces capturing the effect of adhesion molecules. We discretise the model equations using a finite element method, and provide a parallel implementation in C++. We discuss examples of application of this framework to small and medium-sized aggregates: we consider the shape and dynamics of a cell doublet, a planar cell sheet, and a growing cell aggregate. This framework opens the door to the systematic exploration of the cell to tissue-scale mechanics of cell aggregates, which plays a key role in the morphogenesis of embryos and organoids.

SimuCell3D: 3D Simulation of Tissue Mechanics with Cell Polarization

“…The total time complexity of such a simulation is , where Nc is the number of cells in the tissue, which is equivalent to the scaling observed in 2D simulations [51]. Under similar settings, we tested the performance of CellSim3D [36] and Interacting Active Surfaces (IAS) [34], two other cell-based 3D models offering low and high spatial resolution, respectively. CellSim3D generated a tissue of 75,000 cells in a day of computation time while IAS produced a tissue of 4 cells in the same amount of time.…”

“…), where Nc is the number of cells in the tissue, which is equivalent to the scaling observed in 2D simulations [51]. Under similar settings, we tested the performance of CellSim3D [36] and Interacting Active Surfaces (IAS) [34], two other cell-based CellSim3D generated a tissue of 75,000 cells in a day of computation time while IAS produced a tissue of 4 cells in the same amount of time. CellSim3D achieves comparable performance as our program by constraining the cell geometries to simple spherical shapes with a fixed number of nodes.…”

“…To address the limitations of vertex models, a family of cellbased models sometimes referred to as Deformable Cell Models (DCMs) has been developed. These models provide a more geometrically realistic representation of tissues by discretizing each cell membrane separately into a closed loop of connected points in 2D [27][28][29][30][31][32][33][34][35][36][37] or a closed triangulated surface in 3D [38][39][40][41][42][43]. The flexible representation of cells in DCMs qualifies them for the study of a wide range of morphogenetic processes arising from cellular behavior.…”

Organoids in high-throughput and high-content screenings

“…As epithelial cells change their neighbors along the apicalbasal axis (Gómez et al, 2021;Iber and Vetter, 2022), classical 3D vertex models have been extended to allow for an intermediate vertex along the apical-basal axis (Ioannou et al, 2020). Recently, high-resolution 3D simulation frameworks have become available that represent cells by individual, deformable meshes (Van Liedekerke et al, 2020;Torres-Sánchez et al, 2022). Given their high computational costs, these simulation frameworks are sometimes used in combination with spheroid models to permit the simulation of larger tissues and efficient parameter screens.…”

Predicting organoid morphology through a phase field model: insights into cell division and lumenal pressure

“…Although there are other models simulate the applicable assembly structure [39][40][41][42][43] and lumen-containing organoids [44], such as the cellular vertex and Potts models, considering the purpose of this study to determine the effect of mechanical factors including pressure, we adopted the phase field model, which can model the pressure of both the cells and lumens [43]. The cellular vertex model can clearly describe the forces generated by the cytoskeleton and applied to the vertex, but the shape of cells and lumens are limited to polygonal shapes.…”