Biology: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 a 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]

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

The simplest off-lattice model, the center-based model, depicts cells as spheres and models their mechanical interactions using pairwise potentials.[9][10] It is easily extended to a large number of cells in both 2D and 3D.[11]

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.[12] 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.[13]

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[14] 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[15] over epithelial morphogenesis[16] to tumour growth[17] and intestinal crypt dynamics[18]

Simulation frameworks

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

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. ↑ "Multicellular simulation predicts microvascular patterning and in silico tissue assembly". FASEB Journal 18 (6): 731–3. April 2004. doi:10.1096/fj.03-0933fje. PMID 14766791. http://www.fasebj.org/content/18/6/731.short. 
  4. ↑ "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. 
  5. ↑ "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. 
  6. ↑ "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. 
  7. ↑ Modeling multicellular systems using subcellular elements. 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. 
  8. ↑ "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. 
  9. ↑ "Cell migration and organization in the intestinal crypt using a lattice-free model". Cell Proliferation 34 (4): 253–66. August 2001. doi:10.1046/j.0960-7722.2001.00216.x. PMID 11529883. 
  10. ↑ "A single-cell-based model of tumor growth in vitro: monolayers and spheroids". Physical Biology 2 (3): 133–47. July 2005. doi:10.1088/1478-3975/2/3/001. PMID 16224119. Bibcode: 2005PhBio...2..133D. 
  11. ↑ "Individual cell-based models of the spatial-temporal organization of multicellular systems--achievements and limitations". Cytometry. Part A 69 (7): 704–10. July 2006. doi:10.1002/cyto.a.20287. PMID 16807896. 
  12. ↑ "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. 
  13. ↑ "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. 
  14. ↑ "Stress-dependent finite growth in soft elastic tissues". Journal of Biomechanics 27 (4): 455–67. April 1994. doi:10.1016/0021-9290(94)90021-3. PMID 8188726. 
  15. ↑ "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. 
  16. ↑ "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. 
  17. ↑ "Cell-Based Models of Avascular Tumor Growth". 2004. 367–378. doi:10.1007/978-3-0348-7895-1_37. ISBN 978-3-0348-9614-6. 
  18. ↑ "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. 
  19. ↑ "Chaste: using agile programming techniques to develop computational biology software". Philosophical Transactions of the Royal Society of London A: Mathematical, Physical and Engineering Sciences 366 (1878): 3111–36. September 2008. doi:10.1016/j.cpc.2009.07.019. PMID 18565813. http://eprints.maths.ox.ac.uk/846. Retrieved 2019-02-01. 
  20. ↑ "Chaste: an open source C++ library for computational physiology and biology". PLOS Computational Biology 9 (3): e1002970. 14 March 2013. doi:10.1371/journal.pcbi.1002970. PMID 23516352. Bibcode: 2013PLSCB...9E2970M. 
  21. ↑ "Multi-scale modeling of tissues using CompuCell3D". Computational Methods in Cell Biology. 110. 1 January 2012. 325–66. doi:10.1016/B978-0-12-388403-9.00013-8. ISBN 9780123884039. 
  22. ↑ "A cell-based simulation software for multi-cellular systems". Bioinformatics 26 (20): 2641–2. October 2010. doi:10.1093/bioinformatics/btq437. PMID 20709692. 
  23. ↑ "Morpheus: a user-friendly modeling environment for multiscale and multicellular systems biology". Bioinformatics 30 (9): 1331–2. May 2014. doi:10.1093/bioinformatics/btt772. PMID 24443380. 
  24. ↑ "VirtualLeaf: an open-source framework for cell-based modeling of plant tissue growth and development". Plant Physiology 155 (2): 656–66. February 2011. doi:10.1104/pp.110.167619. PMID 21148415. 
  25. ↑ "LBIBCell: a cell-based simulation environment for morphogenetic problems". Bioinformatics 31 (14): 2340–7. July 2015. doi:10.1093/bioinformatics/btv147. PMID 25770313. 
  26. ↑ "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. 
  27. ↑ "PhysiCell: an Open Source Physics-Based Cell Simulator for 3-D Multicellular Systems". PLOS Computational Biology 14 (2): e1005991. February 23, 2018. doi:10.1371/journal.pcbi.1005991. PMID 29474446. Bibcode: 2018PLSCB..14E5991G. 
  28. ↑ "Biocellion: accelerating computer simulation of multicellular biological system models". Bioinformatics 30 (21): 3101–3108. November 2014. doi:10.1093/bioinformatics/btu498. PMID 25064572. 
  29. ↑ "biocellion" (in en-US). https://biocellion.com/. 
  30. ↑ "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. 
  31. ↑ "URDME" (in en-US). http://urdme.github.io/urdme/. 



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