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Abstract
For more information and detailed explanations see the PowerPoint presentation in the supporting documents
The model is set up with a steering panel that allows you to change the settings and function without editing the model
The simulation will pause until you select an option under “Select Simulation to Run”
Hit “Tile” in the “Window” Pulldown Menu to configure the display
This example has a few simulation types for Evolution in Tumors. Namely neutral variation and simple somatic simulation. The user can also select different cancer treatments to be used against the tumor and explore their results in the cancer's progression (growth, death, and evolution). The simulated tumor may evolve resistance to treatments.
What Story Would We Tell if We Were Thinking About Cancer for the First Time?
Cancer is a group of diseases involving abnormal cell growth with the potential to invade or spread to other parts of the body
•For a cell to become cancerous it needs to respond inappropriately to the signals that normally regulate cell proliferation. Specifically, it must proliferate in situations when a normal cell would not. Such proliferation, by itself, results in disorganization of tissue and may create a tumor, but not a cancer
•In order to be cancerous the cell must also not respond appropriately to cell death signals, which would normally recognize the inappropriate proliferation and cause the cell to arrest or die
•Cancer is a process, the nature of the cells and tumor change continually during the progression of the disease
•To become invasive, the cell must also alter its interactions with neighboring cells and increase its motility allowing it to move from its original location and create new tumors (we won’t discuss much today)
•In order to be cancerous the cell must also not respond appropriately to cell death signals, which would normally recognize the inappropriate proliferation and cause the cell to arrest or die
•Cancer is a process, the nature of the cells and tumor change continually during the progression of the disease
•To become invasive, the cell must also alter its interactions with neighboring cells and increase its motility allowing it to move from its original location and create new tumors (we won’t discuss much today)
Space Competition Model
A very simplified model where the cells compete for a single limiting resource, space to survive and grow (in reality competition is more complicated)
Loosely based on papers by Heiko Enderling and collaborators (original version of the model written many years ago with Heiko)
Enderling, Heiko, et al. "A mathematical model of breast cancer development, local treatment and recurrence." Journal of theoretical biology 246 (2007): 245-259.
Enderling, Heiko, et al. "Paradoxical dependencies of tumor dormancy and progression on basic cell kinetics." Cancer research 69 (2009): 8814-8821.
Gao, Xuefeng, et al. "Cell-cell interactions in solid tumors—the role of cancer stem cells." New Challenges for Cancer Systems Biomedicine. Springer, Milano, 2012. 191-204.
Enderling, Heiko, and Philip Hahnfeldt. "Cancer stem cells in solid tumors: Is ‘evading apoptosis a hallmark of cancer?" Progress in biophysics and molecular biology 106 (2011): 391-399.
Three Cell types:
Stem cells (which can divide an unlimited number of times) Somatic cells (which die after a given number of divisions)
Necrotic cells (dying cells which rapidly disappear)
Two evolvable parameters:
Frequency with which stem cell division gives rise to extra or missing stem cells “Stemness”
Number of Generations before somatic cells die from senescence
Heritable Mutations May Occur at any Division
Neutral Variation
In our simulation we want all of the changes in our evolving parameters P, the number of stem-cell offspring of a stem cell division and Rho, the number of generations a somatic cell can divide before it dies of senescence to change ONLY because of selection not because of bias in the variation algorithm
Getting variation to be neutral is tricky, so the simulation has a demonstration in which these parameters mutate but have no effect on cell survival
If the variation is neutral, then these parameters should change only a small amount and the direction of change should be random run to run
Select “killing_type” “Constant Killing Somatic Only”
Set the Killing_efficacy to “1”
Set the growth_type to “Exponential”
Then select simulation_type “Neutral Variation” to run the simulation
You will see cells grow, divide and dies and the plots will show the histogram of the stemness and the number of somatic generations
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Credits
Juliano Ferrari Gianlupi, James A. Glazier
References
Shirinifard, Abbas, J. Scott Gens, Benjamin L. Zaitlen, Nikodem J. Popławski, Maciej Swat, and James A. Glazier. "3D multi-cell simulation of tumor growth and angiogenesis." PLoS ONE 4 (2009): e7190.
Enderling, Heiko, et al. "A mathematical model of breast cancer development, local treatment and recurrence." Journal of theoretical biology 246 (2007): 245-259.
Enderling, Heiko, et al. "Paradoxical dependencies of tumor dormancy and progression on basic cell kinetics." Cancer research 69 (2009): 8814-8821.
Gao, Xuefeng, et al. "Cell-cell interactions in solid tumors—the role of cancer stem cells." New Challenges for Cancer Systems Biomedicine. Springer, Milano, 2012. 191-204.
Enderling, Heiko, and Philip Hahnfeldt. "Cancer stem cells in solid tumors: Is ‘evading apoptosis a hallmark of cancer?" Progress in biophysics and molecular biology 106 (2011): 391-399.
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