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Mathematicians Propose New Model for Cancer Growth

  • Adriana Salerno

What do zebras, bacteria, and cancer have in common? They all can evolve in response to pressures in their environment. This simple biological fact inspired researchers from the University of California, Irvine, to study cancer in a new light. They used the tools of mathematics (rather than biology) to test a theory that that tumors change their mutation rate "intentionally" throughout their development, in order to grow as quickly as possible. This research was published in the Royal Society's journal Interface.

For some time now, laboratory scientists have known that cancer cells behave very differently from normal cells, constantly changing their genetic makeup. As Natalia Komarova explains, a normal human cell has 23 pairs of chromosomes, "but if you look at the cancer cell it's a complete mess: some chromosomes are present only in one copy, some are missing, some are present in five or six or ten copies." This phenomenon of losing and gaining genetic material as cells divide is called genetic instability.

Komarova notes that everyone who studies cancer knows that genetic instability (and the mutations it causes) are important for cancer cells: cancer couldn't spread without it. It's not so clear why this mutation rate slows down in later stages of the tumor. She says that this has been observed experimentally, but researchers can't decide whether it's important for cancer growth or if it's just a side-effect of cancer.

To try to understand the process, Komarova and her colleagues turned to optimal control theory, a branch of mathematics used to determine the most efficient pathways, and they applied it to the mystery of cancer growth.

Their results showed that it was indeed advantageous for cancer to be highly genetically unstable in its earlier stages and to become more stable later on. "So it kind of pays off to change all the time," says the mathematician, "to lose chromosomes, to gain chromosomes, at the beginning; and then stop doing this and remain at the same level for the rest of the natural history of a tumor."

Natalia Komarova is a mathematician, not a medical researcher. But Dr. Andrew Pierce, of the University of Kentucky College of Medicine, says her results make sense because they parallel what many living organisms do to thrive in their environment. He points to the way bacteria develop resistance against an antibiotic, "and so the idea is 'OK, my current genetic solution isn't a very good solution anymore, so let's mix it up and try a bunch of random stuff and see if something can be come up with randomly that just happens to work better.'"

Dr. Pierce explains that this fits with the current theories on evolution. He says that the stress from the environment is reduced once the right genetic mutation has been found. "It perfectly fits with their result", he concludes, "that now that a new solution has been acquired what you don't want to do is keep on messing with it, you know? If it's not broken, don't fix it."

Knowing the reason for a tumor's genetic instability, mathematician Komarova says, might affect the development of cancer treatment strategies. She explains that some treatments are mutogenic, that is, they make cells mutate. Chemotherapy, she says, is very mutogenic, and small molecule inhibitors are not.

Although her research is not at that point yet, Komarova says she would like to incorporate treatments and their mutogenic properties into her model.

She says mathematical tools can enhance medical research. Their work is not experimental notes Komarova, they don't work in a lab, but they believe that their work could help create theories for laboratory researchers. "We kind of provide ideas or explanations to the medical community", she adds.

Dr. Neal Meropol, from the Fox-Chase Cancer Center in Philadelphia, agrees that a multidisciplinary effort might help find the best alternatives. He says it's good that researchers from other disciplines, like mathematicians, are coming up with new ideas. "We are certainly learning the hard way," he says, "to some extent, through our failures, that a team approach to solving the cancer problem is required if we're going to achieve our holy grail of eliminating death from cancer in the future."

University of California mathematician Natalia Komarova hopes that her research will give the medical community food for thought during their quest for new approaches to fighting cancer.

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