How high-resolution agent-based models can improve fundamental insights in tissue development and cell culturing methods

TL;DR

This work surveys high-resolution, physics-driven agent-based modeling for tissue development, focusing on Deformable Cell Models (DCMs) that represent cells as surface-traced shells with explicit cortex mechanics. By contrasting DCMs with SEMs, PFMs, CPMs, and Vertex Models, the authors highlight the trade-offs between geometric fidelity and computational cost, and they outline the force-balance framework that governs node dynamics in DCMs. The paper reviews DCM components, calibration/validation strategies, computational considerations, and software availability, and demonstrates applications to monolayers, spheroids, organoids, micro-carriers, and early embryonic morphogenesis, including lumen and canaliculi formation. The authors argue that DCMs can generate quantitative insights into how subcellular and cortical properties influence tissue-scale structure, with potential for hybrid models and digital-twin workflows, while also calling for standardization and broader access to DCM software to accelerate adoption in biology and biotechnology.

Abstract

The fundamental understanding of how cells physically interact with each other and their environment is key to understanding their organisation in living tissues. Over the past decades several computational methods have been developed to decipher emergent multi-cellular behaviors. In particular agent-based (or cell-based) models that consider the individual cell as basic modeling unit tracked in space and time enjoy increasing interest across scientific communities. In this article we explore a particular class of cell-based models, so-called Deformable Cell Models (DCMs), that allow to simulate the biophysics of the cell with high realism. After situating this model among other model types, We give an overview of past and recent DCM developments and discuss new simulation results of several applications covering in-vitro and in-vivo systems. Our goal is to demonstrate how such models can generate quantitative added value in biological and biotechnological problems.

Figures (10)

• Figure 1: 2D illustration of representations of frequently used cell-based models. In all cartoons the small black filled circles denote computational nodes for each model. A: center-based model (CBM). Cells are represented by spheres, B: Subcellular Element Model (SEM). Two cells are in contact. The lines between the nodes indicate the influence of an intracellular (blue) or intercellular (red) force potential, C: Phase-field model (PFM) for two 2D cells with phases given for 1D, D: Cellular Potts Model (CPM) for two cells, E: Vertex model (VM) for epithelial cells, F: Deformable Cell Model (DCM) for two cells.
• Figure 2: A: DCM with its cortex triangulation and nucleus. B-C Two different approaches to simulate cell division in DCM. B: Inside the mother cell envelope, two new cells are created that are separated by the division plane. These daughter cells inflate until they touch the mother envelope. The latter is finally removed. Re-meshing is not necessary. C: The cytokinesis process is simulated, with a furrow contraction of the cortex along the division plane. Two daughter cells emerge when the contractile ring is small enough. In this case, re-meshing is necessary (picture taken from Cuvelier2023).
• Figure 3: Single cell experiments to calibrate a DCM. (A) optical stretcher. (B) Optical tweezer. (C) Micro pipetting. (D) Cell-surface spreading experiment. Images are taken from Guyot2016VanLiedekerke2020Odenthal2013 and modified.
• Figure 4: (A) DCM simulation snapshot of a small growing spheroid with a cross section indicating the nuclei (right). (B) Simulations of an isotropic spheroid compression for two cell types with different cortex elastic properties, respectively with a normal (top) and stiff (higher $E_{cor}$) cortex (bottom). The color coding indicates the internal cell pressure. The right plot shows the appearance of a gradient in cell pressures along the spheroid radial distance in case of cells of the stiffer type, due to the fact that they bear a larger part of the applied pressure from outside, thus "protecting" the inner cells. The softer type cannot do this as much, and hence pressure is more equally distributed over the spheroid. Image taken from VanLiedekerke2019
• Figure 5: A: DCM monolayer simulation with respectively low (cell type 1, left) and high cell-substrate adhesion energy (cell type 2, right) at the same time point. Color coding is according to cell internal pressure, i.e. its state of being compressed. A vertical cross-section showing the cell shapes is given as well. Bottom: A zoom-in for the right case shows cells popping out of the monolayer and becoming apoptotic (brown color) due to substrate contact loss. B: Evolution of average cell pressure for type 1 and type2.