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Abstract
The 3-Type Problem
Inspired by the 3-body problem in physics, this virtual cell laboratory explores a tunable multicellular system with 3 interacting cell types. Similarly to the 3-body problem, simple cell-cell interactions can lead to complex emergent dynamics, including cooperativity, competition, oscillations, and chaotic phenomena.
This virtual cell lab lets you broadly explore the effects of your assumptions of how cells affect one another to drive the emergent multicellular dynamics.
Each cell's behavior can be influenced by a combination of environmental signals:
- Resource (R): All cells consume a resource R that diffuses from the boundary. The resource is necessary for cell proliferation and survival. (0 ≤ R ≤ 1)
- Signal A (α): Type A cells () secrete this chemical factor, which can influence the behavior of any cell type. (0 ≤ α ≤ 1)
- Signal B (β): Type B cells () secrete this chemical factor, which can influence the behavior of any cell type. (0 ≤ β ≤ 1)
- Signal C (γ): Type C cells () secrete this chemical factor, which can influence the behavior of any cell type. (0 ≤ γ ≤ 1)
- Pressure (p): When cells are pressed by other cells, it generates a pressure that can affect proliferation and death. (0 ≤ p. p ∼ 0.5 for a cell in uncompressed confluent 2D tissue without further forces)
Cell Types
- Type A cells secrete a diffusing factor α that can influence the behavior of any other cell.
- Type B cells secrete a diffusing factor β that can influence the behavior of any other cell.
- Type C cells secrete a diffusing factor γ that can influence the behavior of any other cell.
In the visualization, each live cell fluoresces proportionally to its expression (secretion) of its signal.
Key cell behaviors
Each cell can individually modulate several key behaviors, under the influence of R, α, β, γ, and p.
Proliferation
The cell division rate increases as R increases. The signals α, β, and γ can individually inhibit, promote, or be neutral towards division. High pressure can inhibit proliferation. (These are set in the User Params tab.
Apoptotic death
The signals α, β, γ, and R can individually inhibit, promote, or be neutral towards death. High pressure can promote apoptotic death. These are set in the User Params tab.
Necrotic death
Necrotic death can occur when the resource R falls below a threshold, increasing towards a maximum rate. The maximum necrotic death rate is set in the Cell Types tab, and the resource threshold is in the User Params tab.
Secretion
Cells secrete their respective signaling factor. The signals α, β, γ, and R can individually inhibit, promote, or be neutral towards this secretion. This is set in the User Params tab.
Motility
Cells can perform a biased random migration (with varying bias, speed, persistence time, and direction. (See the interactive tutorial at trmotility.) In this framework, cell motility can be purely Brownian (no migration bias direction), or biased up or down the gradient of R, α, β, or γ. The base motility parameters are set in the Cell Types tab.
Adhesion
Cells adhere to one another based on the parameters in the Cell Types tab.
Repulsion
Cells resist deformation by imposing a ``repulsive'' force against other cells. Summing up these forces gives the (dimensionless) pressure p Set parameters in the Cell Types tab.
Powered by
This software is powered by PhysiCell [1-2], a powerful simulation tool that combines multi-substrate diffusive transport and off-lattice cell models. PhysiCell is BSD-licensed, and available at:
- GitHub releases: https://github.com/MathCancer/PhysiCell/releases
- SourceForge downloads: https://sourceforge.net/projects/physicell/
It is a C++, cross-platform code with minimal software dependencies. It has been tested and deployed in Linux, BSD, OSX, Windows, and other environments, using the standard g++ compiler.
See http://PhysiCell.MathCancer.org.
The Jupyter-based GUI was auto-generated by xml2jupyter [3], a technique to create graphical user interfaces for command-line scientific applications.
Sponsored by
- NSF EEC-1720625. Network for Computational Nanotechnology - Engineered nanoBIO Node
- NSF MCB-1818187. Integrative Mathematical and Experimental Approaches to
- Breast Cancer Research Foundation
- Jayne Koskinas Ted Giovanis Foundation for Health and Policy
- NIH U01CA232137. Multiscale systems biology modeling to exploit tumor-stromal metabolic crosstalk in colorectal cancer.
References
[1] Ghaffarizadeh A, Heiland R, Friedman SH, Mumenthaler SM, Macklin P (2018) PhysiCell: An open source physics-based cell simulator for 3-D multicellular systems. PLoS Comput Biol 14(2): e1005991. https://doi.org/10.1371/journal.pcbi.1005991
[2] Ghaffarizadeh A, Friedman SH, Macklin P (2016) BioFVM: an efficient, parallelized diffusive transport solver for 3-D biological simulations. Bioinformatics 32(8):1256-8. https://doi.org/10.1093/bioinformatics/btv730
[3] Heiland R, Mishler D, Zhang T, Bower E, Macklin P (2019, in preparation) Xml2jupyter: Mapping parameters between XML and Jupyter widgets. J Open Source Software.
Publications
This tool is still in preparation for submission. For now, please cite:
Ghaffarizadeh A, Heiland R, Friedman SH, Mumenthaler SM, Macklin P (2018) PhysiCell: An open source physics-based cell simulator for 3-D multicellular systems. PLoS Comput Biol 14(2): e1005991. https://doi.org/10.1371/journal.pcbi.1005991
Cite this work
Researchers should cite this work as follows:
-
[1] Ghaffarizadeh A, Heiland R, Friedman SH, Mumenthaler SM, Macklin P (2018) PhysiCell: An open source physics-based cell simulator for 3-D multicellular systems. PLoS Comput Biol 14(2): e1005991. https://doi.org/10.1371/journal.pcbi.1005991
[2] Ghaffarizadeh A, Friedman SH, Macklin P (2016) BioFVM: an efficient, parallelized diffusive transport solver for 3-D biological simulations. Bioinformatics 32(8):1256-8. https://doi.org/10.1093/bioinformatics/btv730
[3] Heiland R, Mishler D, Zhang T, Bower E, Macklin P (2019, in preparation) Xml2jupyter: Mapping parameters between XML and Jupyter widgets. J Open Source Software.