Treating Cancer Through Math

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08/12/2021 August 2021 Perspectives

Our cells are constantly dividing. It happens billions of times every day, everywhere in our body. And every time a cell divides, it has to copy its genome — its complete set of genetic instructions with all the information needed to build and develop it. But when a cell divides and copies over the genetic information, it doesn’t always happen flawlessly. DNA replication isn’t perfect. Mistakes get made.

“Our cells are constantly becoming different from each other,” says Ivana Bozic, assistant professor of applied mathematics. “On average, each time a cell divides, one new mutation will occur.”

“The future of personalized therapy and precision oncology is to ask, ‘We have this cancer with this attribute: Can we predict how it will behave?’” says Ivana Bozic. “It’s a big question, but I think math can help answer it.”

Bozic studies this process using the tools of mathematics. “Ivana uses math as a creative enterprise and sees fundamental connections,” says Benjamin Kerr, professor of biology, who is collaborating with Bozic on a study of bacterial evolution. “She takes an abstract set of principles and applies that knowledge to biological processes, which can have deep impact on health.”


Mistakes are Made

Most mutations during cell division are harmless. Those are called “passenger” mutations; like a passenger, they’re passive, just along for the ride and accrue without producing a notable effect.  But then there are the “driver” mutations, which can become more problematic. If an error occurs in replication, that error then gets copied for the new cells created. As cells divide, their progeny collect more mutations.

“Typically, several driver mutations are needed for the development of solid cancers in adults,” says Bozic. “But some leukemias and childhood cancers can be caused by just a single mutation.”

These mutations are often stochastic, or randomly determined. They can be analyzed using probabilistic and statistical techniques, but they can’t be precisely predicted.


How can we measure a [cell mutation] process that can’t be observed in humans? ...We can use math, along with clinical observations, to infer what is happening.

Cancer, Bozic says, can be seen as an evolution within our body. And like evolution, it’s not something we can see happen at the moment it’s happening. She applies mathematical approaches to understand how cancer evolves.

“We have cells that are stochastically acquiring mutations. Some of them can be really bad. How can we measure a process that can’t be observed in humans? Math is a powerful tool to try and understand that process. We can use math, along with clinical observations, to infer what is happening,” she says.


Counting Rings — Biologically

Not only is Bozic interested in understanding the evolution of cancer as it’s occurring, but she’s also drawn to learning how we can harness this mathematical knowledge to influence how we treat cancer. Can math be used to design more effective treatments?

In recent years, medical research has brought a surge of DNA sequencing of all kinds, including cancer sequencing. This can reveal the types of genetic mutations present in a patient’s cancer. This, along with math, can indicate how long a cancer has been developing in the body, even if it was only recently diagnosed.

Ivana Bozic outside Lewis Hall, home to the UW Department of Applied Mathematics.

“When you use math to estimate how long a cancer has been present in the body, often you find that it’s been developing for decades,” she explains. “We can learn this by looking at the genetic mutations we find, account for the mathematical model of how they likely accumulate, and then calculate how long a tumor was actually present.”

This scientific version of counting rings on a tree to determine its age and history can provide clues about how to detect cancers earlier, before they become more complicated to treat or lethal.

Math can also help scientists develop more effective treatments, such as adjustments to targeted therapy, a type of cancer treatment specific to some mutations in cancer cells. Targeted therapies use drugs to target specific genes and proteins involved in the proliferation of cancer cells. At first, targeted therapy showed huge success for some, but then the shrunk or vanished tumor would reappear. This may have a mathematical basis, says Bozic.

“Most tumors bigger than a centimeter have pre-existing resistant cells,” she says. “Our calculations show this is because cells mutate to have resistance to certain treatments: A drug will kill some cells, but not the ones that are resistant. Then those cells will replicate.”

To treat cancer using targeted therapies, sometimes one drug will be given at a time and then another swapped in its place if it appears to stop working. But what may work better is giving a combination, all at the same time, to give a patient a stronger chance of conquering those pre-existing resistant cells, Bozic believes.


Optimizing Immunotherapy

Immunotherapy is a type of cancer treatment that harnesses the body’s immune system to fight cancer. Bozic is also studying how best to use math to optimize immunotherapy. She’s hoping to learn more about the dynamics of different kinds of immunotherapies, and how they work with the genetics of a patient’s cancer, for different kinds of cancer including melanoma, leukemia, and lymphoma.

Bozic recently published a paper on CAR-T cell therapy, in which a patient’s T-cells, part of the immune system, are taken out of their body during a blood draw, engineered to better fight cancer, and then put back in their body.

“Chemotherapy is usually given to patients prior to CAR-T therapy,” she explains. “But our initial investigations are showing that if you could give the same amount of chemotherapy over a longer period of time and shorten the timespan between the end of chemo and the start of this treatment, that might make a difference in how more patients respond.”

Another research project focuses on the genetic basis of colorectal cancer — work that has earned Bozic a CAREER grant from the National Science Foundation to quantify how colorectal cancer evolves. She studies how specific genes mutate at specific rates through a detailed mathematical model. This could inform efforts to detect colorectal cancer DNA in the blood — an exciting and relatively new technology called cell-free DNA — that could be used for early detection.

Bozic was also selected as the 2021 Mathematics recipient in the Johnson & Johnson Scholars Award Program, an international competition that awards and sponsors women in the science, technology, engineering, math, manufacturing, and design disciplines at critical points early in their careers. The award provides $150,000 over three years toward each recipient’s research.

All of Bozic’s grants and awards are contributing to her cancer-related research.

“The future of personalized therapy and precision oncology is to ask, ‘We have this cancer with this attribute: Can we predict how it will behave?’” says Bozic. “It’s a big question, but I think math can help answer it.”

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