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{{Short description|Mathematical models representing biological cells}}
'''Cell-based models''' are [[mathematical model]]s that represent biological [[cell (biology)|cells]] as discrete entities. Within the field of [[computational biology]] they are often simply called [[agent-based model]]s<ref name=":0" /> of which they are a specific application and they are used for simulating the [[biomechanics]] of multicellular structures such as [[Tissue (biology)|tissue]]s. to study the influence of these behaviors on how tissues are organised in time and space. Their main advantage is the easy integration of cell level processes such as [[cell division]], intracellular processes and [[single-cell variability]] within a cell population.<ref name=Liederkerke2015>{{cite journal | vauthors = Van Liedekerke P, Palm MM, Jagiella N, Drasdo D | title=Simulating tissue mechanics with agent-based models: concepts, perspectives and some novel results|journal=Computational Particle Mechanics|date=1 December 2015|volume=2|issue=4|pages=401–444|doi=10.1007/s40571-015-0082-3 | bibcode=2015CPM.....2..401V|doi-access=free}}</ref>
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=== On-lattice ===
On-lattice models such as [[Cellular automaton|cellular automata]] or [[Cellular Potts model|cellular potts]] restrict the spatial arrangement of the cells to a fixed grid. The mechanical interactions are then carried out according to literature-based rules (cellular automata)<ref>{{cite journal | vauthors = Peirce SM, Van Gieson EJ, Skalak TC | title = Multicellular simulation predicts microvascular patterning and in silico tissue assembly | journal = FASEB Journal | volume = 18 | issue = 6 | pages = 731–733 | date = April 2004 | pmid = 14766791 | doi = 10.1096/fj.03-0933fje | doi-access = free | s2cid = 11107214 }}</ref> or by minimizing the total energy of the system (cellular potts),<ref>{{cite journal | vauthors = Graner F, Glazier JA | title = Simulation of biological cell sorting using a two-dimensional extended Potts model | journal = Physical Review Letters | volume = 69 | issue = 13 | pages = 2013–2016 | date = September 1992 | pmid = 10046374 | doi = 10.1103/PhysRevLett.69.2013 | bibcode = 1992PhRvL..69.2013G }}</ref> resulting in cells being displaced from one grid point to another.
=== Off-lattice ===
Off-lattice models allow for continuous movement of cells in space and evolve the system in time according to [[force]] laws governing the mechanical interactions between the individual cells. Examples of off-lattice models are center-based models,<ref>{{cite journal | vauthors = Osborne JM, Fletcher AG, Pitt-Francis JM, Maini PK, Gavaghan DJ | title = Comparing individual-based approaches to modelling the self-organization of multicellular tissues | journal = PLOS Computational Biology | volume = 13 | issue = 2 | pages = e1005387 | date = February 2017 | pmid = 28192427 | pmc = 5330541 | doi = 10.1371/journal.pcbi.1005387 | veditors = Nie Q | bibcode = 2017PLSCB..13E5387O | doi-access = free }}</ref> vertex-based models,<ref name=":0" /> models
based on the [[immersed boundary method]]<ref>{{cite journal | vauthors = Rejniak KA | title = An immersed boundary framework for modelling the growth of individual cells: an application to the early tumour development | journal = Journal of Theoretical Biology | volume = 247 | issue = 1 | pages = 186–204 | date = July 2007 | pmid = 17416390 | doi = 10.1016/j.jtbi.2007.02.019 | bibcode = 2007JThBi.247..186R }}</ref> and the subcellular element
method.<ref>{{cite book | vauthors = Newman TJ | title = Single-Cell-Based Models in Biology and Medicine | chapter = Modeling
cell shape. As a consequence they vary in their ability to capture different biological mechanisms, the effort needed to extend them from two- to three-dimensional models and also in their computational cost.<ref>{{cite journal | vauthors = Osborne JM, Fletcher AG, Pitt-Francis JM, Maini PK, Gavaghan DJ | title = Comparing individual-based approaches to modelling the self-organization of multicellular tissues | journal = PLOS Computational Biology | volume = 13 | issue = 2 | pages = e1005387 | date = February 2017 | pmid = 28192427 | pmc = 5330541 | doi = 10.1371/journal.pcbi.1005387 | bibcode = 2017PLSCB..13E5387O | doi-access = free }}</ref>
The simplest off-lattice model, the center-based model, depicts cells as spheres and models their mechanical interactions using pairwise potentials.<ref>{{cite journal | vauthors = Meineke FA, Potten CS, Loeffler M | title = Cell migration and organization in the intestinal crypt using a lattice-free model | journal = Cell Proliferation | volume = 34 | issue = 4 | pages = 253–266 | date = August 2001 | pmid = 11529883 | pmc = 6495866 | doi = 10.1046/j.0960-7722.2001.00216.x }}</ref><ref>{{cite journal | vauthors = Drasdo D, Höhme S | title = A single-cell-based model of tumor growth in vitro: monolayers and spheroids | journal = Physical Biology | volume = 2 | issue = 3 | pages = 133–147 | date = July 2005 | pmid = 16224119 | doi = 10.1088/1478-3975/2/3/001 | bibcode = 2005PhBio...2..133D | s2cid = 24191020 }}</ref> It is easily extended to a large number of cells in both 2D and 3D.<ref>{{cite journal | vauthors = Galle J, Aust G, Schaller G, Beyer T, Drasdo D | title = Individual cell-based models of the spatial-temporal organization of multicellular systems--achievements and limitations | journal = Cytometry. Part A | volume = 69 | issue = 7 | pages = 704–710 | date = July 2006 | pmid = 16807896 | doi = 10.1002/cyto.a.20287 | doi-access =
==== Vertex ====
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!Speedup
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|ACAM<ref>{{cite journal | vauthors = Nestor-Bergmann A, Blanchard GB, Hervieux N, Fletcher AG, Étienne J, Sanson B | title = Adhesion-regulated junction slippage controls cell intercalation dynamics in an Apposed-Cortex Adhesion Model | journal = PLOS Computational Biology | volume = 18 | issue = 1 | pages = e1009812 | date = January 2022 | pmid = 35089922 | doi = 10.1371/journal.pcbi.1009812 | pmc = 8887740 | s2cid = 246387965 | doi-access = free | bibcode = 2022PLSCB..18E9812N }}</ref>
|Off-lattice, ODE solvers
|2D
|<ref>{{cite journal | vauthors = Nestor-Bergmann A, Blanchard GB, Hervieux N, Fletcher AG, Étienne J, Sanson B | title = ACAM - Apposed Cortex Adhesion Model | year = 2021 | doi = 10.1101/2021.04.11.439313
| s2cid = 233246026 | url = https://zenodo.org/record/5838249 | via = Zenodo | doi-access = free }}</ref>
|Yes
|Yes
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|[https://docs.julialang.org/en/v1/stdlib/Distributed/ Distributed.jl]
|-
|Artistoo<ref>{{Cite journal |last1=Wortel |first1=Inge MN |last2=Textor |first2=Johannes |date=2021-04-09 |editor-last=Walczak |editor-first=Aleksandra M |editor2-last=Buttenschoen |editor2-first=Andreas |editor3-last=Macklin |editor3-first=Paul |title=Artistoo, a library to build, share, and explore simulations of cells and tissues in the web browser
|Cellular Potts, Cellular Automaton
|2D, (3D)
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|
|-
| cellular_raza
|CBMOS<ref>{{cite journal | vauthors = Mathias S, Coulier A, Hellander A | title = CBMOS: a GPU-enabled Python framework for the numerical study of center-based models | journal = BMC Bioinformatics | volume = 23 | issue = 1 | pages = 55 | date = January 2022 | pmid = 35100968 | pmc = 8805507 | doi = 10.1186/s12859-022-04575-4 }}</ref>▼
|Off-lattice, Allows for Generic Implementations
| 1D, 2D, 3D
| [https://github.com/jonaspleyer/cellular_raza github.com/jonaspleyer/cellular_raza]
| Yes
| [https://docs.rs/cellular_raza Yes]
| [[Rust_(programming_language)|Rust]]
|
|-
▲|CBMOS<ref>{{cite journal | vauthors = Mathias S, Coulier A, Hellander A | title = CBMOS: a GPU-enabled Python framework for the numerical study of center-based models | journal = BMC Bioinformatics | volume = 23 | issue = 1 | pages = 55 | date = January 2022 | pmid = 35100968 | pmc = 8805507 | doi = 10.1186/s12859-022-04575-4 | doi-access = free }}</ref>
|Center/agent-based
|
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|
|-
|Chaste<ref>{{cite journal | vauthors = Pitt-Francis J, Bernabeu MO, Cooper J, Garny A, Momtahan L, Osborne J, Pathmanathan P, Rodriguez B, Whiteley JP, Gavaghan DJ | display-authors = 6 | title = Chaste: using agile programming techniques to develop computational biology software | journal = Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences | volume = 366 | issue = 1878 | pages = 3111–3136 | date = September 2008 | pmid = 18565813 | doi = 10.1016/j.cpc.2009.07.019 | url =
|Center/agent-based, on-/off-lattice, cellular automata, vertex-based, immersed boundary
|2D, 3D
▲| url = https://github.com/Chaste/Chaste | via = GitHub }}</ref>
|Yes
|Yes
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|-
|[[CompuCell3D]]<ref>{{cite book |vauthors=Swat MH, Thomas GL, Belmonte JM, Shirinifard A, Hmeljak D, Glazier JA |title=Computational Methods in Cell Biology |chapter=Multi-Scale Modeling of Tissues Using CompuCell3D
|Cellular Potts, PDE solvers, cell type automata
|3D
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|[[OpenMP]]
|-
|EdgeBased<ref>{{Cite journal | vauthors = Brown PJ, Green JE, Binder BJ, Osborne JM |title=A rigid body framework for multi-cellular modelling | journal = Nature Computational Science | date = November 2021 | volume = 1 | issue = 11 | pages = 754–766 |doi=
|Off-lattice, ODE solvers
|2D
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|
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|PhysiCell<ref>{{cite journal | vauthors = Ghaffarizadeh A, Heiland R, Friedman SH, Mumenthaler SM, Macklin P | title = PhysiCell: An open source physics-based cell simulator for 3-D multicellular systems | journal = PLOS Computational Biology | volume = 14 | issue = 2 | pages = e1005991 | date = February 2018 | pmid = 29474446 | pmc = 5841829 | doi = 10.1371/journal.pcbi.1005991 | bibcode = 2018PLSCB..14E5991G | doi-access = free }}</ref>
|Center/agent-based, ODE
|3D
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|-
|yalla<ref>{{cite journal | vauthors = Germann P, Marin-Riera M, Sharpe J | title = ya||a: GPU-Powered Spheroid Models for Mesenchyme and Epithelium | language = English | journal = Cell Systems | volume = 8 | issue = 3 | pages = 261–266.e3 | date = March 2019 | pmid = 30904379 | doi = 10.1016/j.cels.2019.02.007 | s2cid = 85497718 | doi-access = free | hdl = 10230/42284 | hdl-access = free }}</ref>
|Center/agent-based
|3D
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