|
=== 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 = 731–3731–733 | date = April 2004 | pmid = 14766791 | doi = 10.1096/fj.03-0933fje | s2cid = 11107214 | url = http://www.fasebj.org/content/18/6/731.short }}</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 = PLOSPLoS Computational Biology | volume = 13 | issue = 2 | pages = e1005387 | date = February 2017 | pmid = 28192427 | pmc = 5330541 | doi = 10.1371/journal.pcbi.1005387 | bibcodeveditors = 2017PLSCB..13E5387ONie Q | veditorsbibcode = Nie Q2017PLSCB..13E5387O }}</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 = Modeling multicellular systems using subcellular elements | journal = Mathematical Biosciences and Engineering | volume = 2 | issue = 3 | pages = 613–24 | date = July 2005 | pmid = 20369943 | doi = 10.1007/978-3-7643-8123-3_10 | series = Mathematics and Biosciences in Interaction | isbn = 978-3-7643-8101-1 }}</ref> They differ mainly in the level of detail with which they represent the
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 = PLOSPLoS Computational Biology | volume = 13 | issue = 2 | pages = e1005387 | date = February 2017 | pmid = 28192427 | pmc = 5330541 | doi = 10.1371/journal.pcbi.1005387 | bibcode = 2017PLSCB..13E5387O }}</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 = 253–66253–266 | date = August 2001 | pmid = 11529883 | pmc = 6495866 | doi = 10.1046/j.0960-7722.2001.00216.x | pmc = 6495866 }}</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 = 133–47133–147 | date = July 2005 | pmid = 16224119 | doi = 10.1088/1478-3975/2/3/001 | bibcode = 2005PhBio...2..133D }}</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 = 704–10704–710 | date = July 2006 | pmid = 16807896 | doi = 10.1002/cyto.a.20287 | doi-access = free }}</ref>
==== Vertex ====
Vertex-based models are a subset of off-lattice models.<ref name=":0">{{cite journal | vauthors = Metzcar J, Wang Y, Heiland R, Macklin P | title = A Review of Cell-Based Computational Modeling in Cancer Biology | journal = JCO Clinical Cancer Informatics | volume = 3 | issue = 3 | pages = 1–13 | date = February 2019 | pmid = 30715927 | pmc = 6584763 | doi = 10.1200/CCI.18.00069 }}</ref> They track the cell membrane as a set of polygonal points and update the position of each vertex according to tensions in the cell membrane resulting from cell-cell adhesion forces and cell elasticity.<ref>{{cite journal | vauthors = Fletcher AG, Osterfield M, Baker RE, Shvartsman SY | title = Vertex models of epithelial morphogenesis | journal = Biophysical Journal | volume = 106 | issue = 11 | pages = 2291–2304 | date = June 2014 | pmid = 24896108 | pmc = 4052277 | doi = 10.1016/j.bpj.2013.11.4498 | bibcode = 2014BpJ...106.2291F }}</ref> They are more difficult to implement and also more costly to run.
As cells move past one another during a simulation, regular updates of the polygonal edge connections are necessary.<ref>{{cite journal | vauthors = Fletcher AG, Osborne JM, Maini PK, Gavaghan DJ | title = Implementing vertex dynamics models of cell populations in biology within a consistent computational framework | journal = Progress in Biophysics and Molecular Biology | volume = 113 | issue = 2 | pages = 299–326 | date = November 2013 | pmid = 24120733 | doi = 10.1016/j.pbiomolbio.2013.09.003 | url = https://ora.ox.ac.uk/objects/uuid:ff94a74e-ef93-4ac2-ab61-1e08795e67b8 }}</ref>
== Applications ==
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 = 455–67455–467 | date = April 1994 | pmid = 8188726 | doi = 10.1016/0021-9290(94)90021-3 }}</ref> which treat tissues as viscoelastic materials by averaging over single cells.
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 = NPJ Systems Biology and Applications | volume = 3 | issue = 1 | pages = 16 | date = 9 June 2017 | pmid = 28649443 | pmc = 5466652 | doi = 10.1038/s41540-017-0017-0 }}</ref> over [[Epithelium|epithelial]] [[morphogenesis]]<ref>{{cite journal | vauthors = Fletcher AG, Cooper F, Baker RE | title = Mechanocellular models of epithelial morphogenesis | journal = Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences | volume = 372 | issue = 1720 | pages = 20150519 | date = May 2017 | pmid = 28348253 | pmc = 5379025 | doi = 10.1098/rstb.2015.0519 }}</ref> to tumour growth<ref>{{cite book | vauthors = Drasdo D, Dormann S, Hoehme S, Deutsch A |chapter=Cell-Based Models of Avascular Tumor Growth |veditors=Deutsch A, Howard J, Falcke M, Zimmermann W|title=Function and Regulation of Cellular Systems|date=2004|pages=367–378|doi=10.1007/978-3-0348-7895-1_37|isbn=978-3-0348-9614-6 }}</ref> and intestinal crypt dynamics<ref>{{cite journal | vauthors = De Matteis G, Graudenzi A, Antoniotti M | title = A review of spatial computational models for multi-cellular systems, with regard to intestinal crypts and colorectal cancer development | journal = Journal of Mathematical Biology | volume = 66 | issue = 7 | pages = 1409–1462 | date = June 2013 | pmid = 22565629 | doi = 10.1007/s00285-012-0539-4 | s2cid = 32661526 }}</ref>
!Speedup
|-
|Agents.jl<ref>{{Cite journal |last vauthors = Datseris |first=GeorgeG, |last2=Vahdati |first2=AliAR, R. |last3=DuBois |first3=Timothy C.TC |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>
|Center/agent-based
|2D,3D
|[https://docs.julialang.org/en/v1/stdlib/Distributed/ Distributed.jl]
|-
|Biocellion<ref>{{cite journal | vauthors = Kang S, Kahan S, McDermott J, Flann N, Shmulevich I |date=November 2014title |title= Biocellion: accelerating computer simulation of multicellular biological system models | journal = Bioinformatics | volume = 30 | issue = 21 | pages = 3101–3108 | date = November 2014 | pmid = 25064572 | pmc = 4609016 | 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>
|Center/agent-based
|
|
|-
|CBMOS<ref>{{Citecite journal |last vauthors = Mathias |first=SonjaS, |last2=Coulier |first2=AdrienA, |last3=Hellander |first3=AndreasA |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 | date = January 2022 | pmid = 35100968 | pmc = 8805507 | doi = 10.1186/s12859-022-04575-4 |issn=1471-2105 |pmc=8805507 |pmid=35100968}}</ref>
|Center/agent-based
|
|GPU
|-
|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 display-authors =September 20086 | 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 LondonSeries A:, Mathematical, Physical, and Engineering Sciences | volume = 366 | issue = 1878 | pages =3111–36 3111–3136 | date = September 2008 | pmid = 18565813 | doi = 10.1016/j.cpc.2009.07.019 |pmid url =18565813 http://eprints.maths.ox.ac.uk/846 | access-date = 2019-02-01 | author16-link = Sarah L. Waters | 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 Marchdisplay-authors 2013= 6 | title = Chaste: an open source C++ library for computational physiology and biology | journal =PLOS PLoS Computational Biology | volume = 9 | issue = 3 | pages = e1002970 |bibcode date =2013PLSCB...9E2970M 14 March 2013 | pmid = 23516352 | pmc = 3597547 | doi = 10.1371/journal.pcbi.1002970 |pmc=3597547 |pmidbibcode =23516352 2013PLSCB...9E2970M }}</ref>
|Center/agent-based, on-/off-lattice, cellular automata, vertex-based, immersed boundary
|2D, 3D
|[[OpenMP]]
|-
|EdgeBased<ref>{{Cite journal |last=Brown |first=Phillipvauthors J. |last2=Green |first2=J.Brown EdwardPJ, F.Green JE, |last3=Binder |first3=BenjaminBJ, J. |last4=Osborne |first4=JamesJM M. |date=2021-02-10 |title=A rigid body framework for multi-cellular modelling |url journal =https://www.biorxiv.org/content/10.1101/ Nature Computational Science | date = November 2021.02.10.430170v1 |language volume =en 1 | issue = 11 | pages =2021.02.10.430170 754-766 |doi= 10.1101/2021.02.10.430170v1.full}}</ref>
|Off-lattice, ODE solvers
|2D
|
|-
|EPISIM<ref>{{Citecite webjournal |first1 vauthors =Thomas |last1=Sütterlin |first2=SimoneT, |last2=Huber |first3=HartmutS, |last3=Dickhaus |first4=NielsH, |last4=Grabe N | title = Modeling multi-cellular behavior in epidermal tissue homeostasis via finite state machines in multi-agent systems|url=https://academic.oup.com/bioinformatics/article-lookup/doi/10.1093/bioinformatics/btp361 |access-date=2022-11-08 |journal = Bioinformatics | volume = 25 | issue = 16 | pages = 2057–2063 | date =15 August 2009 | pmid = 19535533 | doi = 10.1093/bioinformatics/btp361 }}</ref>
|Center/agent-based
|2D, 3D
|
|-
|IAS (Interacting Active Surfaces)<ref>{{Cite journal |last vauthors = Torres-Sánchez |first=AlejandroA, |last2=Winter |first2=MaxMK, Kerr |last3=Salbreux |first3=GuillaumeG |date=2022-03-22 |title=Interacting active surfaces: a model for three-dimensional cell aggregates |url journal =https://www.biorxiv.org/content/10.1101/2022.03.21.484343v1 |language=enbioRxiv |pages=2022.03.21.484343 |doi=10.1101/2022.03.21.484343}}</ref>
|[[Finite element method|FEM]], ODE solvers
|3D
|
|-
|LBIBCell<ref>{{cite journal | vauthors = Tanaka S, Sichau D, Iber D |date=July 2015 |title = LBIBCell: a cell-based simulation environment for morphogenetic problems | journal = Bioinformatics | volume = 31 | issue = 14 | pages =2340–7 2340–2347 |arxiv date =1503.06726 July 2015 | pmid = 25770313 | doi = 10.1093/bioinformatics/btv147 |pmid arxiv =25770313 1503.06726 | s2cid = 16749503 }}</ref>
|Lattice-Boltzmann, Immersed Boundary
|2D
|[[OpenMP]]
|-
|MecaGen<ref>{{cite journal | vauthors = Delile J, Herrmann M, Peyriéras N, Doursat R |date=January 2017title |title= A cell-based computational model of early embryogenesis coupling mechanical behaviour and gene regulation | journal = Nature Communications | volume = 8 | pages = 13929 |bibcode date =2017NatCo...813929D January 2017 | pmid = 28112150 | pmc = 5264012 | doi = 10.1038/ncomms13929 |pmc=5264012 |pmidbibcode =28112150 2017NatCo...813929D }}</ref>
|Center/agent-based
|3D
|[[CUDA]], [[Graphics processing unit|GPU]]
|-
|Minimal Cell<ref>{{Citecite journal |last vauthors = Thornburg |first=ZaneZR, R. |last2=Bianchi |first2=DavidDM, M. |last3=Brier |first3=TroyTA, A. |last4=Gilbert |first4=BenjaminBR, R. |last5=Earnest |first5=TylerTM, M. |last6=Melo |first6=MarceloMC, C. R. |last7=Safronova |first7=NataliyaN, |last8=Sáenz |first8=JamesJP, P. |last9=Cook |first9=AndrásAT, T. |last10=Wise |first10=KimKS, S. |last11=Hutchison |first11=ClydeCA, A. |last12=Smith |first12=HamiltonHO, O. |last13=Glass |first13=JohnJI, I. |last14=Luthey-Schulten Z |first14 display-authors =Zaida 6 |date=2022-01-20 |title = Fundamental behaviors emerge from simulations of a living minimal cell |url language =https://www.cell.com/cell/abstract/S0092-8674(21)01488-4 English | journal = Cell |language=English |volume = 185 | issue = 2 | pages = 345–360.e28 | date = January 2022 | pmid = 35063075 | doi = 10.1016/j.cell.2021.12.025 |issn=0092-8674 |pmid=35063075}}</ref>
|ODE solvers, stochastic PDE solvers
|3D
|[[CUDA]], [[Graphics processing unit|GPU]]
|-
|Morpheus<ref>{{cite journal | vauthors = Starruß J, de Back W, Brusch L, Deutsch A |date=May 2014title |title= Morpheus: a user-friendly modeling environment for multiscale and multicellular systems biology | journal = Bioinformatics | volume = 30 | issue = 9 | pages =1331–2 1331–1332 | date = May 2014 | pmid = 24443380 | pmc = 3998129 | doi = 10.1093/bioinformatics/btt772 |pmc=3998129 |pmid=24443380}}</ref>
|Cellular Potts, ODE solvers, PDE solvers
|2D, 3D
|
|-
|PhysiCell<ref>{{cite journal | vauthors = Ghaffarizadeh A, Heiland R, Friedman SH, Mumenthaler SM, Macklin P |date=February 23,title 2018= |title=PhysiCell: anAn Openopen Sourcesource Physicsphysics-Basedbased Cellcell Simulatorsimulator for 3-D Multicellularmulticellular Systemssystems | journal =PLOS PLoS Computational Biology | volume = 14 | issue = 2 | pages = e1005991 |bibcode date =2018PLSCB..14E5991G February 2018 | pmid = 29474446 | pmc = 5841829 | doi = 10.1371/journal.pcbi.1005991 |pmc=5841829 |pmidbibcode =29474446 2018PLSCB..14E5991G }}</ref>
|Center/agent-based, ODE
|3D
|
|-
|Timothy<ref>{{Cite journal |last vauthors = Cytowski |first=MaciejM, |last2=Szymanska |first2=ZuzannaZ |date=September 2014 |title=Large-Scale Parallel Simulations of 3D Cell Colony Dynamics |url=https://ieeexplore.ieee.org/document/6728930 |journal=Computing in Science & Engineering |volume=16 |issue=5 |pages=86–95 |doi=10.1109/MCSE.2014.2 |issn=1558-366X}}</ref>
|Center/agent-based
|3D
|[[Message Passing Interface|MPI]], [[OpenMP]]
|-
|URDME - DLCM workflow<ref>{{cite journal | vauthors = Engblom S, Wilson DB, Baker RE |date=August 2018title |title= Scalable population-level modelling of biological cells incorporating mechanics and kinetics in continuous time | journal = Royal Society Open Science | volume = 5 | issue = 8 | pages = 180379 |arxiv date =1706.03375 August 2018 |bibcode pmid =2018RSOS....580379E 30225024 | pmc = 6124129 | doi = 10.1098/rsos.180379 |pmc bibcode =6124129 2018RSOS....580379E |pmid arxiv =30225024 1706.03375 }}</ref><ref>{{Cite web |title=URDME |url=http://urdme.github.io/urdme/ |access-date=2022-04-05 |website=URDME |language=en-US}}</ref>
|[[Finite element method|FEM]], [[Finite volume method|FVM]]
|2D,3D
|
|-
|VirtualLeaf<ref>{{Citationcite journal |last vauthors = Antonovici CC, Peerdeman GY, Wolff HB, Merks RM |first=Claudiu-Cristi |title = Modeling Plant Tissue Development Using VirtualLeaf |date=2022 |url=https://doi.org/10.1007/978-1-0716-1816-5_9journal |work=Plant SystemsMethods in Molecular Biology: Methods| andvolume Protocols= 2395 | pages = 165–198 |editor-last=Lucas |editor-firstdate =Mikaël 2022 |place=New York,pmid NY |publisher=Springer 34822154 |language=en |doi = 10.1007/978-1-0716-1816-5_9 | publisher = Springer | isbn = 978-1-0716-1816-5 |access-date=2022-11-08 |last2=Peerdemanseries |first2=Guacimo Y.Plant Systems Biology: Methods and Protocols |last3=Wolff |first3place =Harold B.New |last4=MerksYork, NY |first4 veditors =Roeland Lucas M. H.}}</ref> (2021)
|Off-lattice
|2D
|
|-
|yalla<ref>{{Citecite journal |last vauthors = Germann |first=PhilippP, |last2=Marin-Riera |first2=MiquelM, |last3=Sharpe |first3=JamesJ |date=2019-03-27 |title = ya{{!}}{{!}}||a: GPU-Powered Spheroid Models for Mesenchyme and Epithelium |url language =https://www.cell.com/cell-systems/abstract/S2405-4712(19)30068-7 English | journal = Cell Systems |language=English |volume = 8 | issue = 3 | pages = 261–266.e3 | date = March 2019 | pmid = 30904379 | doi = 10.1016/j.cels.2019.02.007 |issn=2405-4712 |pmid=30904379}}</ref>
|Center/agent-based
|3D
|
|-
|Tyssue<ref>{{Cite journal |last vauthors = Theis |first=SophieS, |last2=Suzanne |first2=MagaliM, |last3=Gay |first3=GuillaumeG |date=2021-06-07 |title=Tyssue: an epithelium simulation library |url=https://joss.theoj.org/papers/10.21105/joss.02973 |journal=Journal of Open Source Software |language=en |volume=6 |issue=62 |pages=2973 |doi=10.21105/joss.02973 |issn=2475-9066}}</ref>
|Vertex-based
|2D, 3D
|
|}
== References ==
|
