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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
Continuum-based models (PDE-based) models have also been developed – in particular, for cardiomyocytes and neurons. These represent the cells through explicit geometries and take into account spatial distributions of both intracellular and extracellular processes. They capture, depending on the research question and areas, ranges from a few to many thousand cells. In particular, the framework for electrophysiological models of cardiac cells is well-developed and made highly efficient using [[high-performance computing]].<ref>{{cite book | url=https://link.springer.com/book/10.1007/978-3-030-61157-6 | title=Modeling Excitable Tissue | series=Simula SpringerBriefs on Computing |editor=Aslak Tveito |editor2=Kent-Andre Mardal |editor3=Marie E. Rognes | year=2021 | volume=7 | publisher=Springer| doi=10.1007/978-3-030-61157-6 | isbn=978-3-030-61156-9 | s2cid=228872673 }}</ref>▼
▲'''Cell-based models''' are [[mathematical model]]s that represent biological [[cell (biology)|cells]] as a discrete entities. Within the field of [[computational biology]] they are often simply called [[Agent-based model|agent-based models]]<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>
▲Continuum-based models (PDE-based) models have also been developed – in particular, for cardiomyocytes and neurons. These represent the cells through explicit geometries and take into account spatial distributions of both intracellular and extracellular processes. They capture, depending on the research question and areas, ranges from a few to many thousand cells. In particular, the framework for electrophysiological models of cardiac cells is well-developed and made highly efficient using [[high-performance computing]].<ref>{{cite book | url=https://link.springer.com/book/10.1007/978-3-030-61157-6 | title=Modeling Excitable Tissue |editor=Aslak Tveito |editor2=Kent-Andre Mardal |editor3=Marie E. Rognes | year=2021 | publisher=Springer}}</ref>
== Model types ==
Cell-based models can be divided into on- and off-lattice models.
=== 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 =
=== 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 |
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 =
==== Vertex ====
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Since they account for individual behavior at the cell level such as [[cell proliferation]], [[cell migration]] or [[apoptosis]], cell-based models are a useful tool to study the influence of these behaviors on how tissues are organised in time and space.<ref name=Liederkerke2015 />
Due in part to the increase in computational power, they have arisen as an alternative to [[continuum mechanics]] models<ref>{{cite journal | vauthors = Rodriguez EK, Hoger A, McCulloch AD | title = Stress-dependent finite growth in soft elastic tissues | journal = Journal of Biomechanics | volume = 27 | issue = 4 | pages =
Cell-based mechanics models are often coupled to models describing intracellular dynamics, such as an [[ordinary differential equation|ODE]] representation of a relevant [[gene regulatory network]]. It is also common to connect them to a [[partial differential equation|PDE]] describing the diffusion of a chemical [[cell signaling|signaling molecule]] through the [[extracellular matrix]], in order to account for [[cellular communication|cell-cell communication]]. As such, cell-based models have been used to study processes ranging from [[embryogenesis]]<ref>{{cite journal | vauthors = Tosenberger A, Gonze D, Bessonnard S, Cohen-Tannoudji M, Chazaud C, Dupont G | title = A multiscale model of early cell lineage specification including cell division | journal =
== Simulation frameworks ==
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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>
|Agents.jl<ref>{{Cite journal |last=Datseris |first=George |last2=Vahdati |first2=Ali R. |last3=DuBois |first3=Timothy C. |date=2022-01-05 |title=Agents.jl: a performant and feature-full agent-based modeling software of minimal code complexity |url=http://journals.sagepub.com/doi/10.1177/00375497211068820 |journal=SIMULATION |language=en |pages=003754972110688 |doi=10.1177/00375497211068820 |issn=0037-5497}}</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
|[[Python (programming language)|Python]]
|
|-
▲|Agents.jl<ref>{{Cite journal |
|Center/agent-based
|2D,3D
|
| url = https://github.com/JuliaDynamics/Agents.jl | via = GitHub }}</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 |journal=eLife |volume=10 |pages=e61288 |doi=10.7554/eLife.61288 |issn=2050-084X |pmc=8143789 |pmid=33835022 |doi-access=free }}</ref>
|Biocellion<ref>{{cite journal |vauthors=Kang S, Kahan S, McDermott J, Flann N, Shmulevich I |date=November 2014 |title=Biocellion: accelerating computer simulation of multicellular biological system models |journal=Bioinformatics |volume=30 |issue=21 |pages=3101–3108 |doi=10.1093/bioinformatics/btu498 |pmc=4609016 |pmid=25064572}}</ref><ref>{{Cite web |title=biocellion |url=https://biocellion.com/ |access-date=2022-04-05 |website=biocellion |language=en-US}}</ref>▼
|Cellular Potts, Cellular Automaton
|2D, (3D)
|Yes
|Yes
|[[JavaScript]]
|
|-
▲|Biocellion<ref>{{cite journal | vauthors = Kang S, Kahan S, McDermott J, Flann N, Shmulevich I |
|Center/agent-based
|
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|-
| cellular_raza
|CBMOS<ref>{{Cite journal |last=Mathias |first=Sonja |last2=Coulier |first2=Adrien |last3=Hellander |first3=Andreas |date=2022-01-31 |title=CBMOS: a GPU-enabled Python framework for the numerical study of center-based models |url=https://doi.org/10.1186/s12859-022-04575-4 |journal=BMC Bioinformatics |volume=23 |issue=1 |pages=55 |doi=10.1186/s12859-022-04575-4 |issn=1471-2105 |pmc=PMC8805507 |pmid=35100968}}</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>{{
|Center/agent-based
|
|<ref>{{cite web | title = JuliaDynamics
▲|https://github.com/somathias/cbmos
| url = https://github.com/somathias/cbmos | via = GitHub }}</ref>
|
|
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|GPU
|-
|CellularPotts.jl
|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 |date=September 2008 |title=Chaste: using agile programming techniques to develop computational biology software |url=http://eprints.maths.ox.ac.uk/846 |journal=Philosophical Transactions of the Royal Society of London A: Mathematical, Physical and Engineering Sciences |volume=366 |issue=1878 |pages=3111–36 |doi=10.1016/j.cpc.2009.07.019 |pmid=18565813 |archive-url=https://web.archive.org/web/20151120234903/http://eprints.maths.ox.ac.uk/846/ |archive-date=2015-11-20 |access-date=2019-02-01 |author16-link=Sarah L. Waters}}</ref><ref>{{cite journal |vauthors=Mirams GR, Arthurs CJ, Bernabeu MO, Bordas R, Cooper J, Corrias A, Davit Y, Dunn SJ, Fletcher AG, Harvey DG, Marsh ME, Osborne JM, Pathmanathan P, Pitt-Francis J, Southern J, Zemzemi N, Gavaghan DJ |date=14 March 2013 |title=Chaste: an open source C++ library for computational physiology and biology |journal=PLOS Computational Biology |volume=9 |issue=3 |pages=e1002970 |bibcode=2013PLSCB...9E2970M |doi=10.1371/journal.pcbi.1002970 |pmc=3597547 |pmid=23516352}}</ref>▼
|Cellular Potts, agent-based
|2D,3D
|https://github.com/RobertGregg/CellularPotts.jl
|
|not ready for usage
|[[Julia (programming language)|Julia]]
|
|-
▲|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 |
|Center/agent-based, on-/off-lattice, cellular automata, vertex-based, immersed boundary
|2D, 3D
|[https://github.com/Chaste/Chaste https://github.com/Chaste/Chaste]
|Yes
|Yes
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|-
|[[CompuCell3D]]<ref>{{cite book
|Cellular Potts, PDE solvers, cell type automata
|3D
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|[[OpenMP]]
|-
|EdgeBased<ref>{{Cite journal |
|Off-lattice, ODE solvers
|2D
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|
|-
|EPISIM<ref>{{cite journal | vauthors = Sütterlin T, Huber S, Dickhaus H, Grabe N | title = Modeling multi-cellular behavior in epidermal tissue homeostasis via finite state machines in multi-agent systems | journal = Bioinformatics | volume = 25 | issue = 16 | pages = 2057–2063 | date = August 2009 | pmid = 19535533 | doi = 10.1093/bioinformatics/btp361 | doi-access = free }}</ref>
|Center/agent-based
|2D, 3D
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|
|-
|IAS (Interacting Active Surfaces)<ref>{{Cite journal |
|[[Finite element method|FEM]], ODE solvers
|3D
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|
|-
|LBIBCell<ref>{{cite journal | vauthors = Tanaka S, Sichau D, Iber D |
|Lattice-Boltzmann, Immersed Boundary
|2D
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|[[OpenMP]]
|-
|MecaGen<ref>{{cite journal | vauthors = Delile J, Herrmann M, Peyriéras N, Doursat R |
|Center/agent-based
|3D
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|[[CUDA]], [[Graphics processing unit|GPU]]
|-
|Minimal Cell<ref>{{
|ODE solvers, stochastic PDE solvers
|3D
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|[[CUDA]], [[Graphics processing unit|GPU]]
|-
|Morpheus<ref>{{cite journal | vauthors = Starruß J, de Back W, Brusch L, Deutsch A |
|Cellular Potts, ODE solvers, PDE solvers
|2D, 3D
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|
|-
|PhysiCell<ref>{{cite journal | vauthors = Ghaffarizadeh A, Heiland R, Friedman SH, Mumenthaler SM, Macklin P |
|Center/agent-based, ODE
|3D
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|
|-
|Timothy<ref>{{Cite journal |
|Center/agent-based
|3D
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|[[Message Passing Interface|MPI]], [[OpenMP]]
|-
|URDME - DLCM workflow<ref>{{cite journal | vauthors = Engblom S, Wilson DB, Baker RE |
|[[Finite element method|FEM]], [[Finite volume method|FVM]]
|2D,3D
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|-
|VirtualLeaf<ref>{{
|Off-lattice
|2D
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|-
|yalla<ref>{{
|Center/agent-based
|3D
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|-
|Tyssue<ref>{{Cite journal |
|Vertex-based
|2D, 3D
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|}
== References ==
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[[Category:Cells]]
[[Category:Simulation software]]
[[Category:Numerical analysis]]
[[Category:Biophysics]]
[[Category:Computational biology]]
[[Category:Tissues (biology)]]
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