Can Math Cure Cancer?

UArizona Undergraduate Applies Mathematics Background in Biology Lab

Many students find mathematics difficult, frustrating, and above all else, pointless. For UA undergraduate Zach Schlamowitz, however, the point is crystal clear: treating cancer.

Working in the Molecular and Cellular Biology lab of Andrew Paek, Ph.D. at the University of Arizona, Schlamowitz uses mathematical modeling techniques to explore strategies for killing cancer cells. 

Portrait of Zachary Schlamowitz
Zach Schlamowitz is an undergraduate math student in the Paek Lab.

Cancer cells frequently develop resistance to drugs, forcing scientists to devise more sophisticated approaches to combating them. Often, multiple drugs are used together, which requires precise timing to be effective. That’s where the math comes in.

“By modeling how cancer cells respond to treatment, especially with drug-resistance, we can choose treatment timing and doses to better exploit their weaknesses,” Schlamowitz said.

In particular, cells which cycle in and out of a resistant phase can only be killed effectively if the drugs reach them while they are vulnerable. Julie Huynh, An M.D./Ph.D. student in the Paek Lab, has uncovered this alternating behavior between vulnerability and resistance in a type of non-small cell lung cancer. Together, Huynh and Schlamowitz are exploring the use of a combination of two drugs to attack them.

First, the FDA-approved drug palbociclib is used to hold cells in the vulnerable phase for extended periods of time. This facilitates the use of a second FDA-approved drug, osimertinib, to kill them. 

“It’s like playing Whack-a-Mole,” Schlamowitz describes. “It’s really hard to hit the moles if you don’t know when they will pop up or how long they will stay up.” Using the first drug to prevent cells from leaving their vulnerable state is akin to holding the moles above ground after they have popped up, he explained.

“That is where the math really shines. Imagine I can now tell you exactly when a mole will pop up and how long it will stay up. It becomes much easier to whack it. That is essentially what the mathematical equations tell us about the cancer cells.”

Having created the mathematical model, Schlamowitz is now using it to identify an optimal treatment strategy that takes full advantage of the cancer cells’ cyclic vulnerability. For instance, a standard treatment regimen might have a patient take the same dose of each drug on a daily basis. However, it might prove better to take higher doses every other day, with days off in-between.

Schlamowitz went on to explain that there is an inherent risk in trying to time treatments to ever-changing cells.

 “Imagine you treat cells with the first drug too early, so that they all sync up in the vulnerable phase but have time to escape as the drug wears off. Then, when you try to kill them with the second drug, the whole population is now in the resistant phase–which is less effective than if you hadn’t used the first drug at all.” 

Without using math to get precise, numerical predictions of cell behavior, improving upon a standard treatment plan is next to impossible. “Mathematics is the language of optimization. When we translate biological problems into mathematical terms, we have a much better shot at finding optimal solutions,” Schlamowitz said. 

Picture of mathematical formulae.
A Mathematical Model of Cell Growth. Equations describe the change in resistant and vulnerable populations over time. Photo by Zachary Schlamowitz and Julie Huynh.

Schlamowitz comes to biology research in an unusual way. Entering college with no major declared but having always enjoyed the process of mathematics, he was curious to determine where exactly math gets used.

“It’s probably easier to list the tasks for which math cannot be used. Math is everywhere and can be applied to almost anything, from economics to astronomy to cell biology,” Schlamowitz said.

Now two years down the road, his interests in the life sciences led him to apply to the University of Arizona’s Undergraduate Biology Research Program (UBRP). Admitted as part of the inaugural Data Science Academy (DSA), the program’s new collaboration with the Department of Mathematics, Schlamowitz was given the opportunity to bring mathematical modeling skills to the table of cancer biology under the supervision of Andrew Paek. 

“The fusion of mathematical techniques and biological problems is a vibrant and growing field,” Paek said. “Many biology programs around the country are beginning to require students to receive computational training in some capacity. The future of biology is rich with quantitative opportunities.”

Having embraced the fusion of mathematics and biology, Schlamowitz is excited for this future. His hope is that the cancer solutions they’re working on today will eventually go on to significantly improve the daily lives of patients.