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Abstract
Introduction
Mechanics
Cell mechanics (cell movements in time) in PhysiCell are produced through interactions among cells (cell-cell interactions)and basement membrane (if present). The impact of other cells and the BM (basement membrane) on the cell of interest is best expressed through adhesion and repulsion. The mechanics of adhesion and repulsion can be complicated, but they are modeled by the equation below. Adhesion is a cell’s tendency to "stick" to things, while repulsion is a cell’s tendency to be pushed away. The range and combination of these forces ultimately create a sweet spot for a cell at a certain distance away from its neighbors where it tends to rest, similar to the Leonard-Jones potential in atomic and particle Physics. The main equation in mechanics that we will be referencing is:
Where vi and xi are the velocity and position of the cell in question. xj is the position of another cell in the first neighborhood (this is what is meant by j is N(i)). Ccca represents the cell-to-cell adhesion (Cca) coefficient on the cell. This is NOT raised to power i or j. The other C constants are represented similarly and described in the Members/Parameters section. When the summation for all the cell components is said and done, then repulsion and adhesion are considered withthe basement matrix, and finally these correctional terms to the cell's velocity are added to its original velocity.
The functions φ and ψ are the adhesion and repulsion interaction functions (respectively), which is dependent upon the cellsand outside the scope of this lesson. The subscripts to those functionsRi, etc. are therelative maximum adhesion distance,a parameter mentioned later in this lesson. d(xi) is the distance from the Basement membrane to the cell in question, and n(xj) is the unit vector normal to the basement membrane.
Mechanics App-Parameters
Cell to Cell repulsion
"cell_cell_repulsion_strength" is the parameterCccrin the default PhysiCell mechanics model. It regulates the relative strengthof cell-cell "repulsive" forces (resistance to deformation and compression)..
Relative maximum adhesion distance
"relative_maximum_adhesion_distance" is the maximum distance of cell adhesion to other cells or a basement membrane, givenas a (dimensionless) multiple ofgeometry.radius.
use_function_to_set_relative_maximum_adhesion_distance
True, if you would like to use relative adhesion distance.
set_relative_maximum_adhesion_distance
Relative multiplier for maximum adhesion distance in fold of radius.
use_function_to_set_relative_maximum_adhesion_distance
True, if you would like to set relative equilibrium distance.
set_relative_equilibrium_distance
Relative multiplier for equilibrium distance in fold of radius. It is shown in Red Circle.
set_relative_equilibrium_distance
True, if you would like to set absolute equilibrium distance
set_absolute_equilibrium_distance
Absolute equilibrium distance in micron
Application
This app demonstrates "Mechanics" concept in PhysiCell.
Blue Circles: Cells
Gray Circles: Adhesion Distance
Red Circles: Equilibrium Distance
This model and cloud-hosted demo are part of a course on computational multicellular systems biology created and taught by Dr. Paul Macklin in the Department of Intelligent Systems Engineering at Indiana University. It is also part of the education and outreach for the IU Engineered nanoBIO Node and the NCI-funded cancer systems biology grant U01CA232137. The models are built using PhysiCell: a C++ framework for multicellular systems biology [1].
GUI Overview
- Config Basics tab: input parameters common to all models (e.g., domain grid, simulation time, choice/frequency of outputs)
- Microenvironment tab: microenvironment parameters that are model-specific
- User Params tab: user parameters that are model-specific
- Out: Cell Plots tab: output display of the cells
- Out: Substrate Plots tab: output display of the substrates
Clicking the 'Run' button will use the specified parameters and start a simulation. When clicked, it creates an "Output" widget that can be clicked/expanded to reveal the progress (text) of the simulation. When the simulation generates output file(s), they can be visualized in the appropriate output tabs. The "Max" count in each output tab will be dynamically updated as those output files are generated by the running simulation. When the "Run" button is clicked, it toggles to a "Cancel" button that will terminate (not pause) the simulation.
Basic instructions
Modify the parameters in the "Config Basics" and "User Params" tabs. Click the "Run" button once you are ready.
To view the behavior of the cells , click the "Cell Plots" tab, and slide the bar to advance through simulation frames. Note that as the simulation runs, the "Max" field (maximum frame number) will increase, so you can view more simulation frames.
To view the changing substrate fields, click the "Substrate Plots" tab, choose a substrate from the drop-down menu, and slide through the saved times. Note that as the simulation runs, the "max" field (maximum frame number) will increase, so you can view more simulation frames.
Note that you can download full simulation data for further exploration in your tools of choice.
Credits
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
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.
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/btv73
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