Cell-based models

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Short description: Mathematical models representing biological cells


Cell-based models are mathematical models that represent biological cells as discrete entities. Within the field of computational biology they are often simply called agent-based models[1] of which they are a specific application and they are used for simulating the biomechanics of multicellular structures such as tissues. 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.[2]

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.[3]

Model types

Cell-based models can be divided into on- and off-lattice models.

On-lattice

On-lattice models such as cellular automata or 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)[4] or by minimizing the total energy of the system (cellular potts),[5] 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,[6] vertex-based models,[1] models based on the immersed boundary method[7] and the subcellular element method.[8] 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.[9]

The simplest off-lattice model, the center-based model, depicts cells as spheres and models their mechanical interactions using pairwise potentials.[10][11] It is easily extended to a large number of cells in both 2D and 3D.[12]

Vertex

Vertex-based models are a subset of off-lattice models.[1] 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.[13] 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.[14]

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.[2] Due in part to the increase in computational power, they have arisen as an alternative to continuum mechanics models[15] 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 ODE representation of a relevant gene regulatory network. It is also common to connect them to a PDE describing the diffusion of a chemical signaling molecule through the extracellular matrix, in order to account for cell-cell communication. As such, cell-based models have been used to study processes ranging from embryogenesis[16] over epithelial morphogenesis[17] to tumour growth[18] and intestinal crypt dynamics[19]

Simulation frameworks

There exist several software packages implementing cell-based models, e.g.

Name Model dims Openly available source code Installation instructions Usage documentation Language Speedup
ACAM[20] Off-lattice, ODE solvers 2D [21] Yes Yes Python
Agents.jl[22] Center/agent-based 2D,3D [23] Yes Yes Julia Distributed.jl
Artistoo[24] Cellular Potts, Cellular Automaton 2D, (3D) https://github.com/ingewortel/artistoo Yes Yes JavaScript
Biocellion[25][26] Center/agent-based No Yes Yes C++
cellular_raza Off-lattice, Allows for Generic Implementations 1D, 2D, 3D github.com/jonaspleyer/cellular_raza Yes Yes Rust
CBMOS[27] Center/agent-based [28] Python GPU
CellularPotts.jl Cellular Potts, agent-based 2D,3D https://github.com/RobertGregg/CellularPotts.jl not ready for usage Julia
Center/agent-based, on-/off-lattice, cellular automata, vertex-based, immersed boundary 2D, 3D [29] Yes Yes C++
CompuCell3D[30] Cellular Potts, PDE solvers, cell type automata 3D https://github.com/CompuCell3D/CompuCell3D Yes Yes C++, Python OpenMP
EdgeBased[31] Off-lattice, ODE solvers 2D https://github.com/luckyphill/EdgeBased Yes Yes Matlab
EPISIM[32] Center/agent-based 2D, 3D http://tigacenter.bioquant.uni-heidelberg.de/downloads.html Java
IAS (Interacting Active Surfaces)[33] FEM, ODE solvers 3D https://github.com/torressancheza/ias Yes No C++ MPI, OpenMP
IBCell Immersed Boundary 2D http://rejniak.net/RejniakLab/LabsTools.html Yes Yes Matlab
LBIBCell[34] Lattice-Boltzmann, Immersed Boundary 2D https://tanakas.bitbucket.io/lbibcell/ Yes Yes C++ OpenMP
MecaGen[35] Center/agent-based 3D https://github.com/juliendelile/MECAGEN Yes Yes C++ CUDA, GPU
Minimal Cell[36] ODE solvers, stochastic PDE solvers 3D https://github.com/Luthey-Schulten-Lab/Lattice_Microbeshttps://github.com/Luthey-Schulten-Lab/Minimal_Cell Yes Yes Python CUDA, GPU
Morpheus[37] Cellular Potts, ODE solvers, PDE solvers 2D, 3D https://morpheus.gitlab.io/ Yes Yes C++
NetLogo Lattice gas cellular automata 2D, (3D) https://github.com/NetLogo/NetLogo Scala, Java
PhysiCell[38] Center/agent-based, ODE 3D https://github.com/MathCancer/PhysiCell Yes Yes C++ OpenMP
TiSim (formerly CellSys) Center/agent-based, off-lattice, ODE solvers 2D, 3D in preparation
Timothy[39] Center/agent-based 3D http://timothy.icm.edu.pl/downloads.html No No C MPI, OpenMP
URDME - DLCM workflow[40][41] FEM, FVM 2D,3D https://github.com/URDME/urdme Yes Yes Matlab, C
VirtualLeaf[42] (2021) Off-lattice 2D https://github.com/rmerks/VirtualLeaf2021 Yes Yes C++
yalla[43] Center/agent-based 3D https://github.com/germannp/yalla CUDA, GPU
VCell (Virtual Cell) ODE solvers, PDE solvers, stochastic PDE solvers 3D https://github.com/virtualcell/vcell Yes Yes Java, C++, Perl
Tyssue[44] Vertex-based 2D, 3D https://github.com/DamCB/tyssue Yes Yes Python
4DFUCCI Center/agent-based 3D https://github.com/ProfMJSimpson/4DFUCCI Yes Yes Matlab, C, Python

References

  1. ↑ 1.0 1.1 1.2 "A Review of Cell-Based Computational Modeling in Cancer Biology". JCO Clinical Cancer Informatics 3 (3): 1–13. February 2019. doi:10.1200/CCI.18.00069. PMID 30715927. 
  2. ↑ 2.0 2.1 "Simulating tissue mechanics with agent-based models: concepts, perspectives and some novel results". Computational Particle Mechanics 2 (4): 401–444. 1 December 2015. doi:10.1007/s40571-015-0082-3. Bibcode: 2015CPM.....2..401V. 
  3. ↑ Aslak Tveito, ed (2021). Modeling Excitable Tissue. Simula SpringerBriefs on Computing. 7. Springer. doi:10.1007/978-3-030-61157-6. ISBN 978-3-030-61156-9. https://link.springer.com/book/10.1007/978-3-030-61157-6. 
  4. ↑ "Multicellular simulation predicts microvascular patterning and in silico tissue assembly". FASEB Journal 18 (6): 731–733. April 2004. doi:10.1096/fj.03-0933fje. PMID 14766791. 
  5. ↑ "Simulation of biological cell sorting using a two-dimensional extended Potts model". Physical Review Letters 69 (13): 2013–2016. September 1992. doi:10.1103/PhysRevLett.69.2013. PMID 10046374. Bibcode: 1992PhRvL..69.2013G. 
  6. ↑ "Comparing individual-based approaches to modelling the self-organization of multicellular tissues". PLOS Computational Biology 13 (2): e1005387. February 2017. doi:10.1371/journal.pcbi.1005387. PMID 28192427. Bibcode: 2017PLSCB..13E5387O. 
  7. ↑ "An immersed boundary framework for modelling the growth of individual cells: an application to the early tumour development". Journal of Theoretical Biology 247 (1): 186–204. July 2007. doi:10.1016/j.jtbi.2007.02.019. PMID 17416390. Bibcode: 2007JThBi.247..186R. 
  8. ↑ "Modeling Multicellular Structures Using the Subcellular Element Model". Single-Cell-Based Models in Biology and Medicine. Mathematics and Biosciences in Interaction. 2. July 2005. 613–24. doi:10.1007/978-3-7643-8123-3_10. ISBN 978-3-7643-8101-1. 
  9. ↑ "Comparing individual-based approaches to modelling the self-organization of multicellular tissues". PLOS Computational Biology 13 (2): e1005387. February 2017. doi:10.1371/journal.pcbi.1005387. PMID 28192427. Bibcode: 2017PLSCB..13E5387O. 
  10. ↑ "Cell migration and organization in the intestinal crypt using a lattice-free model". Cell Proliferation 34 (4): 253–266. August 2001. doi:10.1046/j.0960-7722.2001.00216.x. PMID 11529883. 
  11. ↑ "A single-cell-based model of tumor growth in vitro: monolayers and spheroids". Physical Biology 2 (3): 133–147. July 2005. doi:10.1088/1478-3975/2/3/001. PMID 16224119. Bibcode: 2005PhBio...2..133D. 
  12. ↑ "Individual cell-based models of the spatial-temporal organization of multicellular systems--achievements and limitations". Cytometry. Part A 69 (7): 704–710. July 2006. doi:10.1002/cyto.a.20287. PMID 16807896. 
  13. ↑ "Vertex models of epithelial morphogenesis". Biophysical Journal 106 (11): 2291–2304. June 2014. doi:10.1016/j.bpj.2013.11.4498. PMID 24896108. Bibcode: 2014BpJ...106.2291F. 
  14. ↑ "Implementing vertex dynamics models of cell populations in biology within a consistent computational framework". Progress in Biophysics and Molecular Biology 113 (2): 299–326. November 2013. doi:10.1016/j.pbiomolbio.2013.09.003. PMID 24120733. https://ora.ox.ac.uk/objects/uuid:ff94a74e-ef93-4ac2-ab61-1e08795e67b8. 
  15. ↑ "Stress-dependent finite growth in soft elastic tissues". Journal of Biomechanics 27 (4): 455–467. April 1994. doi:10.1016/0021-9290(94)90021-3. PMID 8188726. 
  16. ↑ "A multiscale model of early cell lineage specification including cell division". npj Systems Biology and Applications 3 (1): 16. 9 June 2017. doi:10.1038/s41540-017-0017-0. PMID 28649443. 
  17. ↑ "Mechanocellular models of epithelial morphogenesis". Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences 372 (1720): 20150519. May 2017. doi:10.1098/rstb.2015.0519. PMID 28348253. 
  18. ↑ "Cell-Based Models of Avascular Tumor Growth". Function and Regulation of Cellular Systems. 2004. pp. 367–378. doi:10.1007/978-3-0348-7895-1_37. ISBN 978-3-0348-9614-6. 
  19. ↑ "A review of spatial computational models for multi-cellular systems, with regard to intestinal crypts and colorectal cancer development". Journal of Mathematical Biology 66 (7): 1409–1462. June 2013. doi:10.1007/s00285-012-0539-4. PMID 22565629. 
  20. ↑ "Adhesion-regulated junction slippage controls cell intercalation dynamics in an Apposed-Cortex Adhesion Model". PLOS Computational Biology 18 (1): e1009812. January 2022. doi:10.1371/journal.pcbi.1009812. PMID 35089922. 
  21. ↑ ACAM - Apposed Cortex Adhesion Model. 2021. doi:10.1101/2021.04.11.439313. https://zenodo.org/record/5838249. 
  22. ↑ "Agents.jl: a performant and feature-full agent-based modeling software of minimal code complexity" (in en). Simulation: 003754972110688. 2022-01-05. doi:10.1177/00375497211068820. ISSN 0037-5497. http://journals.sagepub.com/doi/10.1177/00375497211068820. 
  23. ↑ "JuliaDynamics". https://github.com/JuliaDynamics/Agents.jl. 
  24. ↑ Wortel, Inge MN; Textor, Johannes (2021-04-09). Walczak, Aleksandra M; Buttenschoen, Andreas; Macklin, Paul. eds. "Artistoo, a library to build, share, and explore simulations of cells and tissues in the web browser". eLife 10: e61288. doi:10.7554/eLife.61288. ISSN 2050-084X. PMID 33835022. 
  25. ↑ "Biocellion: accelerating computer simulation of multicellular biological system models". Bioinformatics 30 (21): 3101–3108. November 2014. doi:10.1093/bioinformatics/btu498. PMID 25064572. 
  26. ↑ "biocellion" (in en-US). https://biocellion.com/. 
  27. ↑ "CBMOS: a GPU-enabled Python framework for the numerical study of center-based models". BMC Bioinformatics 23 (1): 55. January 2022. doi:10.1186/s12859-022-04575-4. PMID 35100968. 
  28. ↑ "JuliaDynamics". https://github.com/somathias/cbmos. 
  29. ↑ "Chaste". https://github.com/Chaste/Chaste. 
  30. ↑ "Multi-Scale Modeling of Tissues Using CompuCell3D". Computational Methods in Cell Biology. 110. 1 January 2012. pp. 325–66. doi:10.1016/B978-0-12-388403-9.00013-8. ISBN 9780123884039. 
  31. ↑ "A rigid body framework for multi-cellular modelling". Nature Computational Science 1 (11): 754–766. November 2021. doi:10.1101/2021.02.10.430170. https://www.biorxiv.org/content/biorxiv/early/2021/02/10/2021.02.10.430170.full.pdf. 
  32. ↑ "Modeling multi-cellular behavior in epidermal tissue homeostasis via finite state machines in multi-agent systems". Bioinformatics 25 (16): 2057–2063. August 2009. doi:10.1093/bioinformatics/btp361. PMID 19535533. 
  33. ↑ "Interacting active surfaces: a model for three-dimensional cell aggregates". bioRxiv 18 (12): 2022.03.21.484343. 2022-03-22. doi:10.1101/2022.03.21.484343. PMID 36525467. 
  34. ↑ "LBIBCell: a cell-based simulation environment for morphogenetic problems". Bioinformatics 31 (14): 2340–2347. July 2015. doi:10.1093/bioinformatics/btv147. PMID 25770313. 
  35. ↑ "A cell-based computational model of early embryogenesis coupling mechanical behaviour and gene regulation". Nature Communications 8: 13929. January 2017. doi:10.1038/ncomms13929. PMID 28112150. Bibcode: 2017NatCo...813929D. 
  36. ↑ "Fundamental behaviors emerge from simulations of a living minimal cell" (in English). Cell 185 (2): 345–360.e28. January 2022. doi:10.1016/j.cell.2021.12.025. PMID 35063075. 
  37. ↑ "Morpheus: a user-friendly modeling environment for multiscale and multicellular systems biology". Bioinformatics 30 (9): 1331–1332. May 2014. doi:10.1093/bioinformatics/btt772. PMID 24443380. 
  38. ↑ "PhysiCell: An open source physics-based cell simulator for 3-D multicellular systems". PLOS Computational Biology 14 (2): e1005991. February 2018. doi:10.1371/journal.pcbi.1005991. PMID 29474446. Bibcode: 2018PLSCB..14E5991G. 
  39. ↑ "Large-Scale Parallel Simulations of 3D Cell Colony Dynamics". Computing in Science & Engineering 16 (5): 86–95. September 2014. doi:10.1109/MCSE.2014.2. ISSN 1558-366X. Bibcode: 2014CSE....16e..86C. 
  40. ↑ "Scalable population-level modelling of biological cells incorporating mechanics and kinetics in continuous time". Royal Society Open Science 5 (8): 180379. August 2018. doi:10.1098/rsos.180379. PMID 30225024. Bibcode: 2018RSOS....580379E. 
  41. ↑ "URDME" (in en-US). http://urdme.github.io/urdme/. 
  42. ↑ "Modeling Plant Tissue Development Using VirtualLeaf". Plant Systems Biology. Methods in Molecular Biology. 2395. New York, NY: Springer. 2022. pp. 165–198. doi:10.1007/978-1-0716-1816-5_9. ISBN 978-1-0716-1816-5. 
  43. ↑ "ya||a: GPU-Powered Spheroid Models for Mesenchyme and Epithelium" (in English). Cell Systems 8 (3): 261–266.e3. March 2019. doi:10.1016/j.cels.2019.02.007. PMID 30904379. 
  44. ↑ "Tyssue: an epithelium simulation library" (in en). Journal of Open Source Software 6 (62): 2973. 2021-06-07. doi:10.21105/joss.02973. ISSN 2475-9066. Bibcode: 2021JOSS....6.2973T. 



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