Cell-based models

Last updated

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]

Contents

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.

NameModeldimsOpenly available source codeInstallation instructionsUsage documentationLanguageSpeedup
ACAM [20] Off-lattice, ODE solvers2D [21] YesYes Python
Agents.jl [22] Center/agent-based2D,3D [23] YesYes Julia Distributed.jl
Artistoo [24] Cellular Potts, Cellular Automaton2D, (3D) https://github.com/ingewortel/artistoo YesYes JavaScript
Biocellion [25] [26] Center/agent-basedNoYesYes C++
cellular_razaOff-lattice, Allows for Generic Implementations1D, 2D, 3D github.com/jonaspleyer/cellular_raza Yes Yes Rust
CBMOS [27] Center/agent-based [28] Python GPU
CellularPotts.jlCellular Potts, agent-based2D,3D https://github.com/RobertGregg/CellularPotts.jl not ready for usage Julia
Chaste [29] [30] Center/agent-based, on-/off-lattice, cellular automata, vertex-based, immersed boundary2D, 3D [31] YesYes C++
CompuCell3D [32] Cellular Potts, PDE solvers, cell type automata3D https://github.com/CompuCell3D/CompuCell3D YesYes C++, Python OpenMP
EdgeBased [33] Off-lattice, ODE solvers2D https://github.com/luckyphill/EdgeBased YesYes Matlab
EPISIM [34] Center/agent-based2D, 3D http://tigacenter.bioquant.uni-heidelberg.de/downloads.html Java
IAS (Interacting Active Surfaces) [35] FEM, ODE solvers3D https://github.com/torressancheza/ias YesNo C++ MPI, OpenMP
IBCellImmersed Boundary2D http://rejniak.net/RejniakLab/LabsTools.html YesYes Matlab
LBIBCell [36] Lattice-Boltzmann, Immersed Boundary2D https://tanakas.bitbucket.io/lbibcell/ YesYes C++ OpenMP
MecaGen [37] Center/agent-based3D https://github.com/juliendelile/MECAGEN YesYes C++ CUDA, GPU
Minimal Cell [38] ODE solvers, stochastic PDE solvers3D https://github.com/Luthey-Schulten-Lab/Lattice_Microbes https://github.com/Luthey-Schulten-Lab/Minimal_Cell YesYes Python CUDA, GPU
Morpheus [39] Cellular Potts, ODE solvers, PDE solvers2D, 3D https://morpheus.gitlab.io/ YesYes C++
NetLogo Lattice gas cellular automata2D, (3D) https://github.com/NetLogo/NetLogo Scala, Java
PhysiCell [40] Center/agent-based, ODE3D https://github.com/MathCancer/PhysiCell YesYes C++ OpenMP
TiSim (formerly CellSys)Center/agent-based, off-lattice, ODE solvers2D, 3Din preparation
Timothy [41] Center/agent-based3D http://timothy.icm.edu.pl/downloads.html NoNo C MPI, OpenMP
URDME - DLCM workflow [42] [43] FEM, FVM 2D,3D https://github.com/URDME/urdme YesYes Matlab, C
VirtualLeaf [44] (2021)Off-lattice2D https://github.com/rmerks/VirtualLeaf2021 YesYes C++
yalla [45] Center/agent-based3D https://github.com/germannp/yalla CUDA, GPU
VCell (Virtual Cell) ODE solvers, PDE solvers, stochastic PDE solvers3D https://github.com/virtualcell/vcell YesYes Java, C++, Perl
Tyssue [46] Vertex-based2D, 3D https://github.com/DamCB/tyssue YesYes Python
4DFUCCICenter/agent-based3D https://github.com/ProfMJSimpson/4DFUCCI YesYes Matlab, C, Python

Related Research Articles

<span class="mw-page-title-main">Bioinformatics</span> Computational analysis of large, complex sets of biological data

Bioinformatics is an interdisciplinary field of science that develops methods and software tools for understanding biological data, especially when the data sets are large and complex. Bioinformatics uses biology, chemistry, physics, computer science, computer programming, information engineering, mathematics and statistics to analyze and interpret biological data. The subsequent process of analyzing and interpreting data is referred to as computational biology.

<span class="mw-page-title-main">Computational biology</span> Branch of biology

Computational biology refers to the use of data analysis, mathematical modeling and computational simulations to understand biological systems and relationships. An intersection of computer science, biology, and big data, the field also has foundations in applied mathematics, chemistry, and genetics. It differs from biological computing, a subfield of computer science and engineering which uses bioengineering to build computers.

<span class="mw-page-title-main">Gene regulatory network</span> Collection of molecular regulators

A generegulatory network (GRN) is a collection of molecular regulators that interact with each other and with other substances in the cell to govern the gene expression levels of mRNA and proteins which, in turn, determine the function of the cell. GRN also play a central role in morphogenesis, the creation of body structures, which in turn is central to evolutionary developmental biology (evo-devo).

<span class="mw-page-title-main">Systems biology</span> Computational and mathematical modeling of complex biological systems

Systems biology is the computational and mathematical analysis and modeling of complex biological systems. It is a biology-based interdisciplinary field of study that focuses on complex interactions within biological systems, using a holistic approach to biological research.

In academia, computational immunology is a field of science that encompasses high-throughput genomic and bioinformatics approaches to immunology. The field's main aim is to convert immunological data into computational problems, solve these problems using mathematical and computational approaches and then convert these results into immunologically meaningful interpretations.

In computational biology, a Cellular Potts model is a computational model of cells and tissues. It is used to simulate individual and collective cell behavior, tissue morphogenesis and cancer development. CPM describes cells as deformable objects with a certain volume, that can adhere to each other and to the medium in which they live. The formalism can be extended to include cell behaviours such as cell migration, growth and division, and cell signalling. The first CPM was proposed for the simulation of cell sorting by François Graner and James Glazier as a modification of a large-Q Potts model. CPM was then popularized by Paulien Hogeweg for studying morphogenesis. Although the model was developed to describe biological cells, it can also be used to model individual parts of a biological cell, or even regions of fluid.

Paulien Hogeweg is a Dutch theoretical biologist and complex systems researcher studying biological systems as dynamic information processing systems at many interconnected levels. In 1970, together with Ben Hesper, she defined the term bioinformatics as "the study of informatic processes in biotic systems".

<span class="mw-page-title-main">Help Cure Muscular Dystrophy</span> BOINC based World Community Grid volunteer computing subproject

Help Cure Muscular Dystrophy is a volunteer computing project that runs on the BOINC platform.

Within biological systems, degeneracy occurs when structurally dissimilar components/pathways can perform similar functions under certain conditions, but perform distinct functions in other conditions. Degeneracy is thus a relational property that requires comparing the behavior of two or more components. In particular, if degeneracy is present in a pair of components, then there will exist conditions where the pair will appear functionally redundant but other conditions where they will appear functionally distinct.

Agent-based models have many applications in biology, primarily due to the characteristics of the modeling method. Agent-based modeling is a rule-based, computational modeling methodology that focuses on rules and interactions among the individual components or the agents of the matrix . The goal of this modeling method is to generate populations of the system components of interest and simulate their interactions in a virtual world. Agent-based models start with rules for behavior and seek to reconstruct, through computational instantiation of those behavioral rules, the observed patterns of behavior.

Trey Ideker is a professor of medicine and bioengineering at UC San Diego. He is the Director of the National Resource for Network Biology, the San Diego Center for Systems Biology, and the Cancer Cell Map Initiative. He uses genome-scale measurements to construct network models of cellular processes and disease.

Cellular noise is random variability in quantities arising in cellular biology. For example, cells which are genetically identical, even within the same tissue, are often observed to have different expression levels of proteins, different sizes and structures. These apparently random differences can have important biological and medical consequences.

Multi-state modeling of biomolecules refers to a series of techniques used to represent and compute the behaviour of biological molecules or complexes that can adopt a large number of possible functional states.

Nicolas Le Novère is a British and French biologist. His research focuses on modeling signaling pathways and developing tools to share mathematical models.

<span class="mw-page-title-main">Marta Filizola</span> Computational biophysicist

Marta Filizola is a computational biophysicist who studies membrane proteins. Filizola's research concerns drug discovery the application of methods of computational chemistry and theoretical chemistry to biochemical and biomedical problems.

<span class="mw-page-title-main">Cellular deconvolution</span> Set of computational techniques

Cellular deconvolution refers to computational techniques aiming at estimating the proportions of different cell types in samples collected from a tissue. For example, samples collected from the human brain are a mixture of various neuronal and glial cell types in different proportions, where each cell type has a diverse gene expression profile. Since most high-throughput technologies use bulk samples and measure the aggregated levels of molecular information for all cells in a sample, the measured values would be an aggregate of the values pertaining to the expression landscape of different cell types. Therefore, many downstream analyses such as differential gene expression might be confounded by the variations in cell type proportions when using the output of high-throughput technologies applied to bulk samples. The development of statistical methods to identify cell type proportions in large-scale bulk samples is an important step for better understanding of the relationship between cell type composition and diseases.

libRoadRunner is a C/C++ software library that supports simulation of SBML based models.. It uses LLVM to generate extremely high-performance code and is the fastest SBML-based simulator currently available. Its main purpose is for use as a reusable library that can be hosted by other applications, particularly on large compute clusters for doing parameter optimization where performance is critical. It also has a set of Python bindings that allow it to be easily used from Python as well as a set of bindings for Julia.

James Alexander Glazier is a biophysicist and bioengineer, author, and educator best known for his contributions to the field of multiscale modeling, pattern formation, and morphogenesis in biological systems. Glazier has published numerous articles in leading scientific journals, and his work has been widely recognized within the scientific community. He has also been influential in promoting the use of computational modeling and simulation in the study of complex biological phenomena.

Smoldyn is an open-source software application for cell-scale biochemical simulations. It uses particle-based simulation, meaning that it simulates each molecule of interest individually, in order to capture natural stochasticity and yield nanometer-scale spatial resolution. Simulated molecules diffuse, react, are confined by surfaces, and bind to membranes in similar manners as in real biochemical systems.

References

  1. 1 2 3 Metzcar J, Wang Y, Heiland R, Macklin P (February 2019). "A Review of Cell-Based Computational Modeling in Cancer Biology". JCO Clinical Cancer Informatics. 3 (3): 1–13. doi:10.1200/CCI.18.00069. PMC   6584763 . PMID   30715927.
  2. 1 2 Van Liedekerke P, Palm MM, Jagiella N, Drasdo D (1 December 2015). "Simulating tissue mechanics with agent-based models: concepts, perspectives and some novel results". Computational Particle Mechanics. 2 (4): 401–444. Bibcode:2015CPM.....2..401V. doi: 10.1007/s40571-015-0082-3 .
  3. ↑ Aslak Tveito; Kent-Andre Mardal; Marie E. Rognes, eds. (2021). Modeling Excitable Tissue. Simula SpringerBriefs on Computing. Vol. 7. Springer. doi:10.1007/978-3-030-61157-6. ISBN   978-3-030-61156-9. S2CID   228872673.
  4. ↑ Peirce SM, Van Gieson EJ, Skalak TC (April 2004). "Multicellular simulation predicts microvascular patterning and in silico tissue assembly". FASEB Journal. 18 (6): 731–733. doi: 10.1096/fj.03-0933fje . PMID   14766791. S2CID   11107214.
  5. ↑ Graner F, Glazier JA (September 1992). "Simulation of biological cell sorting using a two-dimensional extended Potts model". Physical Review Letters. 69 (13): 2013–2016. Bibcode:1992PhRvL..69.2013G. doi:10.1103/PhysRevLett.69.2013. PMID   10046374.
  6. ↑ Osborne JM, Fletcher AG, Pitt-Francis JM, Maini PK, Gavaghan DJ (February 2017). Nie Q (ed.). "Comparing individual-based approaches to modelling the self-organization of multicellular tissues". PLOS Computational Biology. 13 (2): e1005387. Bibcode:2017PLSCB..13E5387O. doi: 10.1371/journal.pcbi.1005387 . PMC   5330541 . PMID   28192427.
  7. ↑ Rejniak KA (July 2007). "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. Bibcode:2007JThBi.247..186R. doi:10.1016/j.jtbi.2007.02.019. PMID   17416390.
  8. ↑ Newman TJ (July 2005). "Modeling Multicellular Structures Using the Subcellular Element Model". Single-Cell-Based Models in Biology and Medicine. Mathematics and Biosciences in Interaction. Vol. 2. pp. 613–24. doi:10.1007/978-3-7643-8123-3_10. ISBN   978-3-7643-8101-1. PMID   20369943.{{cite book}}: |journal= ignored (help)
  9. ↑ Osborne JM, Fletcher AG, Pitt-Francis JM, Maini PK, Gavaghan DJ (February 2017). "Comparing individual-based approaches to modelling the self-organization of multicellular tissues". PLOS Computational Biology. 13 (2): e1005387. Bibcode:2017PLSCB..13E5387O. doi: 10.1371/journal.pcbi.1005387 . PMC   5330541 . PMID   28192427.
  10. ↑ Meineke FA, Potten CS, Loeffler M (August 2001). "Cell migration and organization in the intestinal crypt using a lattice-free model". Cell Proliferation. 34 (4): 253–266. doi:10.1046/j.0960-7722.2001.00216.x. PMC   6495866 . PMID   11529883.
  11. ↑ Drasdo D, Höhme S (July 2005). "A single-cell-based model of tumor growth in vitro: monolayers and spheroids". Physical Biology. 2 (3): 133–147. Bibcode:2005PhBio...2..133D. doi:10.1088/1478-3975/2/3/001. PMID   16224119. S2CID   24191020.
  12. ↑ Galle J, Aust G, Schaller G, Beyer T, Drasdo D (July 2006). "Individual cell-based models of the spatial-temporal organization of multicellular systems--achievements and limitations". Cytometry. Part A. 69 (7): 704–710. doi:10.1002/cyto.a.20287. PMID   16807896.
  13. ↑ Fletcher AG, Osterfield M, Baker RE, Shvartsman SY (June 2014). "Vertex models of epithelial morphogenesis". Biophysical Journal. 106 (11): 2291–2304. Bibcode:2014BpJ...106.2291F. doi:10.1016/j.bpj.2013.11.4498. PMC   4052277 . PMID   24896108.
  14. ↑ Fletcher AG, Osborne JM, Maini PK, Gavaghan DJ (November 2013). "Implementing vertex dynamics models of cell populations in biology within a consistent computational framework". Progress in Biophysics and Molecular Biology. 113 (2): 299–326. doi:10.1016/j.pbiomolbio.2013.09.003. PMID   24120733.
  15. ↑ Rodriguez EK, Hoger A, McCulloch AD (April 1994). "Stress-dependent finite growth in soft elastic tissues". Journal of Biomechanics. 27 (4): 455–467. doi:10.1016/0021-9290(94)90021-3. PMID   8188726.
  16. ↑ Tosenberger A, Gonze D, Bessonnard S, Cohen-Tannoudji M, Chazaud C, Dupont G (9 June 2017). "A multiscale model of early cell lineage specification including cell division". npj Systems Biology and Applications. 3 (1): 16. doi:10.1038/s41540-017-0017-0. PMC   5466652 . PMID   28649443.
  17. ↑ Fletcher AG, Cooper F, Baker RE (May 2017). "Mechanocellular models of epithelial morphogenesis". Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences. 372 (1720): 20150519. doi:10.1098/rstb.2015.0519. PMC   5379025 . PMID   28348253.
  18. ↑ Drasdo D, Dormann S, Hoehme S, Deutsch A (2004). "Cell-Based Models of Avascular Tumor Growth". In Deutsch A, Howard J, Falcke M, Zimmermann W (eds.). Function and Regulation of Cellular Systems. pp. 367–378. doi:10.1007/978-3-0348-7895-1_37. ISBN   978-3-0348-9614-6.
  19. ↑ De Matteis G, Graudenzi A, Antoniotti M (June 2013). "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. doi:10.1007/s00285-012-0539-4. PMID   22565629. S2CID   32661526.
  20. ↑ Nestor-Bergmann A, Blanchard GB, Hervieux N, Fletcher AG, Étienne J, Sanson B (January 2022). "Adhesion-regulated junction slippage controls cell intercalation dynamics in an Apposed-Cortex Adhesion Model". PLOS Computational Biology. 18 (1): e1009812. Bibcode:2022PLSCB..18E9812N. doi: 10.1371/journal.pcbi.1009812 . PMC   8887740 . PMID   35089922. S2CID   246387965.
  21. ↑ Nestor-Bergmann A, Blanchard GB, Hervieux N, Fletcher AG, Étienne J, Sanson B (2021). "ACAM - Apposed Cortex Adhesion Model". doi:10.1101/2021.04.11.439313. S2CID   233246026 – via Zenodo.{{cite journal}}: Cite journal requires |journal= (help)
  22. ↑ Datseris G, Vahdati AR, DuBois TC (2022-01-05). "Agents.jl: a performant and feature-full agent-based modeling software of minimal code complexity". Simulation: 003754972110688. arXiv: 2101.10072 . doi:10.1177/00375497211068820. ISSN   0037-5497. S2CID   231698977.
  23. ↑ "JuliaDynamics" – via GitHub.
  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. PMC   8143789 . PMID   33835022.
  25. ↑ Kang S, Kahan S, McDermott J, Flann N, Shmulevich I (November 2014). "Biocellion: accelerating computer simulation of multicellular biological system models". Bioinformatics. 30 (21): 3101–3108. doi:10.1093/bioinformatics/btu498. PMC   4609016 . PMID   25064572.
  26. ↑ "biocellion". biocellion. Retrieved 2022-04-05.
  27. ↑ Mathias S, Coulier A, Hellander A (January 2022). "CBMOS: a GPU-enabled Python framework for the numerical study of center-based models". BMC Bioinformatics. 23 (1): 55. doi: 10.1186/s12859-022-04575-4 . PMC   8805507 . PMID   35100968.
  28. ↑ "JuliaDynamics" – via GitHub.
  29. ↑ Pitt-Francis J, Bernabeu MO, Cooper J, Garny A, Momtahan L, Osborne J, et al. (September 2008). "Chaste: using agile programming techniques to develop computational biology software". Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences. 366 (1878): 3111–3136. doi:10.1016/j.cpc.2009.07.019. PMID   18565813 . Retrieved 2019-02-01.
  30. ↑ Mirams GR, Arthurs CJ, Bernabeu MO, Bordas R, Cooper J, Corrias A, et al. (14 March 2013). "Chaste: an open source C++ library for computational physiology and biology". PLOS Computational Biology. 9 (3): e1002970. Bibcode:2013PLSCB...9E2970M. doi: 10.1371/journal.pcbi.1002970 . PMC   3597547 . PMID   23516352.
  31. ↑ "Chaste" – via GitHub.
  32. ↑ Swat MH, Thomas GL, Belmonte JM, Shirinifard A, Hmeljak D, Glazier JA (1 January 2012). "Multi-Scale Modeling of Tissues Using CompuCell3D". Computational Methods in Cell Biology. Vol. 110. pp. 325–66. doi:10.1016/B978-0-12-388403-9.00013-8. ISBN   9780123884039. PMC   3612985 . PMID   22482955.
  33. ↑ Brown PJ, Green JE, Binder BJ, Osborne JM (November 2021). "A rigid body framework for multi-cellular modelling" (PDF). Nature Computational Science. 1 (11): 754–766. doi:10.1101/2021.02.10.430170. PMID   38217146. S2CID   231939320.
  34. ↑ Sütterlin T, Huber S, Dickhaus H, Grabe N (August 2009). "Modeling multi-cellular behavior in epidermal tissue homeostasis via finite state machines in multi-agent systems". Bioinformatics. 25 (16): 2057–2063. doi: 10.1093/bioinformatics/btp361 . PMID   19535533.
  35. ↑ Torres-Sánchez A, Winter MK, Salbreux G (2022-03-22). "Interacting active surfaces: a model for three-dimensional cell aggregates". bioRxiv. 18 (12): 2022.03.21.484343. doi:10.1101/2022.03.21.484343. PMC   9803321 . PMID   36525467. S2CID   247631653.
  36. ↑ Tanaka S, Sichau D, Iber D (July 2015). "LBIBCell: a cell-based simulation environment for morphogenetic problems". Bioinformatics. 31 (14): 2340–2347. arXiv: 1503.06726 . doi:10.1093/bioinformatics/btv147. PMID   25770313. S2CID   16749503.
  37. ↑ Delile J, Herrmann M, Peyriéras N, Doursat R (January 2017). "A cell-based computational model of early embryogenesis coupling mechanical behaviour and gene regulation". Nature Communications. 8: 13929. Bibcode:2017NatCo...813929D. doi:10.1038/ncomms13929. PMC   5264012 . PMID   28112150.
  38. ↑ Thornburg ZR, Bianchi DM, Brier TA, Gilbert BR, Earnest TM, Melo MC, et al. (January 2022). "Fundamental behaviors emerge from simulations of a living minimal cell". Cell. 185 (2): 345–360.e28. doi: 10.1016/j.cell.2021.12.025 . PMC   9985924 . PMID   35063075. S2CID   246065847.
  39. ↑ Starruß J, de Back W, Brusch L, Deutsch A (May 2014). "Morpheus: a user-friendly modeling environment for multiscale and multicellular systems biology". Bioinformatics. 30 (9): 1331–1332. doi:10.1093/bioinformatics/btt772. PMC   3998129 . PMID   24443380.
  40. ↑ Ghaffarizadeh A, Heiland R, Friedman SH, Mumenthaler SM, Macklin P (February 2018). "PhysiCell: An open source physics-based cell simulator for 3-D multicellular systems". PLOS Computational Biology. 14 (2): e1005991. Bibcode:2018PLSCB..14E5991G. doi: 10.1371/journal.pcbi.1005991 . PMC   5841829 . PMID   29474446.
  41. ↑ Cytowski M, Szymanska Z (September 2014). "Large-Scale Parallel Simulations of 3D Cell Colony Dynamics". Computing in Science & Engineering. 16 (5): 86–95. Bibcode:2014CSE....16e..86C. doi:10.1109/MCSE.2014.2. ISSN   1558-366X. S2CID   427712.
  42. ↑ Engblom S, Wilson DB, Baker RE (August 2018). "Scalable population-level modelling of biological cells incorporating mechanics and kinetics in continuous time". Royal Society Open Science. 5 (8): 180379. arXiv: 1706.03375 . Bibcode:2018RSOS....580379E. doi:10.1098/rsos.180379. PMC   6124129 . PMID   30225024.
  43. ↑ "URDME". URDME. Retrieved 2022-04-05.
  44. ↑ Antonovici CC, Peerdeman GY, Wolff HB, Merks RM (2022). "Modeling Plant Tissue Development Using VirtualLeaf". In Lucas M (ed.). Plant Systems Biology. Methods in Molecular Biology. Vol. 2395. New York, NY: Springer. pp. 165–198. doi:10.1007/978-1-0716-1816-5_9. hdl:1887/3479570. ISBN   978-1-0716-1816-5. PMID   34822154. S2CID   244668621.
  45. ↑ Germann P, Marin-Riera M, Sharpe J (March 2019). "ya||a: GPU-Powered Spheroid Models for Mesenchyme and Epithelium". Cell Systems. 8 (3): 261–266.e3. doi: 10.1016/j.cels.2019.02.007 . hdl: 10230/42284 . PMID   30904379. S2CID   85497718.
  46. ↑ Theis S, Suzanne M, Gay G (2021-06-07). "Tyssue: an epithelium simulation library". Journal of Open Source Software. 6 (62): 2973. Bibcode:2021JOSS....6.2973T. doi: 10.21105/joss.02973 . ISSN   2475-9066. S2CID   235965728.
This page is based on this Wikipedia article
Text is available under the CC BY-SA 4.0 license; additional terms may apply.
Images, videos and audio are available under their respective licenses.