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Mathematical Modeling Can Limit Tumor Cell Growth

Limit Tumor Cell Growth

Cancers are identified as dynamic and complex systems because they consist of many interconnected parts and have the ability to transform over time and space. In this sense, cancer can be compared to weather because the latter is one of the most complex and dynamic systems known to man. Having seen the concealed parallels between the weather and cancer, researchers from the Moffitt Cancer Center have started to use mathematical methods in order to find new ways to understand and defeat cancer. Cancer Research May issue included the cover article from Moffitt Cancer Center’s team which showed how mathematical modeling can predict the response of tumor cells to the changing environment. They have identified that by using mathematical models it is possible to change the environment in order to influence the growth of less aggressive cancer cells, thus decreasing the number of aggressive and fast growing tumor cells.

Each tumor consists of numerous populations of cells. The combination of mathematical and experimental studies used by the Moffitt researchers recognized two cell populations that usually co-exist in tumors. The first type is the aggressive one which invades surrounding space creating metastases and the second type which consists of less aggressive and non-invasive cells that stay in one place. They have seen from their experiments that usual cancer that develops in mice consists more from invasive cells that have a strong survival advantage over less aggressive cells.

However, according to the evolutionary principals, actions and behaviors of any organism is it human, animal, plant, or a tumor cell have its pros and cons. Although aggressive tumor cells have their advantage which is invading surrounding space, they also have their drawbacks: amplified vulnerability to variations in resources and environment. The researchers were able to predict that minor changes in pH in the tumor could reduce invasive cells’ survival advantage giving more power to non-invasive cells.

Experiments on mice with prostate cancer confirmed the predictions of Moffitt researchers when they have changed pH of mice’s prostate tumor environment by adding sodium bicarbonate to their drinking water. As a result, non-invasive cells obtained the survival advantage over invasive ones which led to reducing of tumors in the prostate and fewer metastases. The analogous results were obtained during the experiments with breast cancer.

“Butterfly effect” inherent to all dynamic complex systems, suggests that butterfly flying in India can cause a tornado in Colorado. Such explanation of the butterfly effect is given to show that complex systems are too complicated and can’t be controlled. In contrast with this, Moffitt investigators have shown that complex systems also have the tendency to amplify some small trepidation (i.e. flight of the butterfly) in fact can be exploited. Moffitt team demonstrated that mathematical models combined with ample understanding of different factors that influence the eco-evolutionary dynamics can make complex systems more understandable. From that point, it is possible to influence them in the desired way.

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