Network-forming collagen, e.g., type IV |  Sheet-like ECM forms from fibers. |  Basement membrane
Elastin |  Provides tissue with elasticity and load-bearing capabilities. |  Interstitial ECM
Glycoproteins |  |
Fibronectin |  Cross-links with ECM proteins, influences cell adhesion and migration. |  Interstitial ECM (also found concentrated near basement membrane)
Laminin |  Forms a mesh-like network to aid in cell adhesion and migration. |  Basement membrane
Nidogen |  Promotes BM structural integrity by facilitating laminin and collagen type IV cross-linking. |  Basement membrane
Proteoglycans |  Regulate ECM structure, e.g., perlecan, performing a similar role to nidogen, and supports cellular functions by storing growth factors and other signaling molecules. |  Interstitial ECM and Basement membrane
Enzymes |  |
Lysyl oxidase (LOX) |  Mediates ECM structure, facilitating ECM protein cross-linking. |  Interstitial ECM
Matrix metalloproteinases (MMPs) |  Degrades ECM proteins such as collagens, fibronectin and laminin. |  Interstitial ECM and Basement membrane
Table 1:  Table describing some of the major ECM components alongside their functions and locations. Term |  Definition
---|---
ABM |  A mathematical and computational model comprised solely of multiple interacting individual elements.
Apical surface |  Surface of an epithelial cell that faces the lumen, or inside of a tubular structure, such as vessels or intestine.
Basal surface |  Surface of an epithelial cell that adjacent to the basement membrane and underlying tissue.
Cell tractoring |  A process in which the cell cortex creates a track around the cell to move the cell relative to its neighbors.
Chemotaxis |  The movement of cells in response to some chemical stimulus, for example, chemoattractants.
Durotaxis |  The movement of cells in response to a gradient of extracellular stiffness.
Haptotaxis |  The movement of cells in response to a gradient of adhesive substrates, for example, integrins.
Intercalation |  A process in which neighboring cells exchange places.
Invagination |  The process in which a surface folds back on itself, forming a cavity or pouch.
ODE |  A differential equation in one variable, for example, time.
Parameterization |  A mathematical process used to express a system through a function of parameters.
PDE |  A differential equation in more than one variable, for example, time and space.
Septa |  A dividing wall or membrane between tissues.
Table 2:  Glossary of important terms. Abbreviation | Definition
---|---
ABM | Agent-based model
BM | Basement membrane
CPM | Cellular Potts model
ECM | Extracellular matrix
EMT | Epithelial-to-mesenchymal transition
FEM | Finite element method
LOX | Lysyl oxidase
MDE | Matrix-degrading enzyme
MMP | Matrix metalloproteinases
NCC | Neural crest cell
ODE | Ordinary differential equation
PDE | Partial differential equation
VEGF | Vascular endothelial growth factor
Table 3:  Table of abbreviations and their definitions. Resource |  Description |  Publications
---|---|---
CompuCell3D https://compucell3d.org/ |  A C++ and Python-based software environment coupling ABMs for cellular processes to reaction-diffusion PDE models for chemicals in the cellular microenvironment. |  Swat et al. (2012); Izaguirre et al. (2004)
Chaste
https://www.cs.ox.ac.uk/chaste/index.html |  A C++ based open-source environment for the simulation of multi-scale models of cellular processes coupling discrete lattice-based and lattice-free models for cell populations to continuum models for chemical transport. |  Pitt-Francis et al. (2009); Mirams et al. (2013); Cooper et al. (2020)
CellSys
https://bio.tools/cellsys |  A C++ based modular software tool for off-lattice simulations of 2D and 3D growth and morphogenesis processes, permitting real-time 3D visualization of simulations. |  Hoehme and Drasdo (2010)
PhysiCell
http://physicell.org/ |  A C++ based open-source framework for 3D physics-based simulations of multicellular systems. An agent-based framework for cell movement and interactions is coupled to a PDE solver for chemicals secreted by cells. |  Ghaffarizadeh et al. (2018)
PhysiBoss
https://github.com/PhysiBoSS |  A PhysiCell-based framework that allows for the simulation of signaling and regulatory networks in individual cells. |  Letort et al. (2019); Ponce-de Leon et al. (2023)
Morpheus
https://morpheus.gitlab.io |  An open-source multi-scale modeling environment for the simulation of cell-based models coupling 2D and 3D cellular Potts models, ODEs, and PDEs. |  Starruß et al. (2014)
VirtualLeaf
https://code.google.com/archive/p/virtualleaf/ |  An open source C++ based ABM software to model plant cells and tissues. |  Merks et al. (2011); Merks and Guravage (2012)
Tissue Forge
https://compucell3d.org/TissueForge |  A C, C++, and Python-based interactive environment for the simulation of biological and biophysical systems from sub-cellular to tissue-level scales. |  Sego et al. (2023)
COMSOL
https://www.comsol.com |  An FEM-based numerical PDE solver environment for the simulation of complex biological and biophysical systems. |  Multiphysics (1998)
FEniCS
https://fenicsproject.org |  An open-source platform for solving complex PDEs with an FEM, offering C++ and Python interfacing. |  Alnaes et al. (2015)
VCell
https://vcell.org |  A Java, C++, and Perl-based open-source platform for the simulation of biochemical and electrophysiological systems through deterministic and stochastic ODE- and PDE-based models with data-integration capabilities. |  Schaff et al. (1997); Cowan et al. (2012)
Table 4:  A list of computational resources for modeling cell-ECM interactions
in cell migration and tissue morphogenesis.

## Conflict of Interest Statement

Author MBe is employed by Optics11 Life Inc. The remaining authors declare
that the research was conducted in the absence of any commercial or financial
relationships that could be construed as a potential conflict of interest.

## Author Contributions

RMC, SJ and ET share first authorship of the manuscript.

RMC: Conceptualization, Investigation, Writing - original draft and review &
editing; SJ: Conceptualization, Investigation, Visualization, Writing -
original draft and review & editing; ET: Conceptualization, Investigation,
Writing - original draft and review & editing; ZB: Investigation, Writing -
original draft; MBe: Investigation, Visualization, Writing - original draft;
MBo: Investigation, Writing - original draft; QJSB: Writing - original draft
and review & editing; JM: Conceptualization, Writing - original draft and
review & editing; MR: Investigation, Writing - original draft and review &
editing; YY: Investigation, Writing - original draft and review & editing; RS:
Conceptualization, Investigation, Visualization, Writing - original draft and
review & editing, Supervision.

## Funding

RMC is supported by funding from the Engineering and Physical Sciences
Research Council (EP/T517811/1) and the Oxford-Wolfson-Marriott scholarship at
Wolfson College, University of Oxford. SJ receives funding from the
Biotechnology and Biological Sciences Research Council (BBSRC) (BB/T008784/1).
ET is funded by the Dutch Research Council (NWO) grant number VI.Veni.222.323.
ZB is supported by funding from the Engineering and Physical Sciences Research
Council (EP/T517914/1). MBo acknowledges the University of Birmingham. QJSB is
funded by Dutch Research Council (NWO) by the ENW-XL program ’Active Matter
Physics of Collective Metastasis’ (OCENW.GROOT.2019.022). JM was supported in
part by NSF Grant 1735095 - NRT: Interdisciplinary Training in Complex
Networks and Systems, the Jayne Koskinas Ted Giovanis Foundation for Health
and Policy, and the Breast Cancer Research Foundation. MR is funded by
PerMedCoE. YY is funded by the Engineering and Physical Sciences Research
Council (EP/W524311/1) and supported by the Travel for Research & Study Grant
at St Hilda’s College, University of Oxford.

## Acknowledgments

Authors would like to acknowledge Cicely Macnamara and Robyn Shuttleworth,
alongside Centre Européen de Calcul Atomique et Moléculaire (CECAM) and the
Lorentz Centre for hosting the workshop "The Extracellular Matrix: How to
model structure complexity" in which this collaborative group was formed.

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