June 2017 Features

Math in Action

With a toolkit that includes nonlinear dynamical systems, stochastic processes, and numerical simulation, Erica Graham ’04 
specializes in mathematical biology and mathematical modeling, with a general interest in cellular and molecular physiology and a particular focus on endocrinology.

Broadly construed, the field of mathematical biology uses the tools of math to shed light on biological processes. Put simply, “We apply mathematical descriptions to answer questions of biology and medicine,” as Erica Graham ’04 explains.

Although the field, had been around for decades, it became increasingly popular during the AIDS epidemic, says Graham, an assistant professor of mathematics at Bryn Mawr. “The idea of modeling epidemics and disease transmission through populations became a big focus of mathematical biology, and then other research areas emerged.” Today, the field has applications in biomedical and biotechnology research and has become another tool in developing treatments of disease.

I am an applied mathematician who focuses on biological problems. The goal of my work is to develop mathematical models motivated by biological phenomena.

Mathematical modeling offers a speculative platform that enables researchers to simulate processes and predict behaviors and outcomes: With math, researchers direct theoretical studies that would be too expensive to conduct in the lab or simply unethical to conduct on individual subjects. As Graham explains, “If we know enough about a particular system to describe it in mathematical terms—using computers and other tools—we can begin to understand that system and ask pertinent questions that insight into larger problems.”

In her work, Graham focuses on endocrinology, the branch of medicine focused on how hormones regulate body processes and, she says, “includes diabetes, infertility, among other conditions.”

Her current research is looking at reproductive hormone regulation. What happens when the ovulatory cycle doesn’t work as well as it should? Her particular focus is on a disorder called polycystic ovary syndrome—“a super-common cause of infertility in women that’s associated with hormone imbalances.”

A serious disease, PCOS can increase the likelihood of more serious health complications like cardiovascular disease and diabetes. But to date, no one has developed a cure. And that’s what Graham hopes her research can help bring about. “You have a population of women who want to have children but can’t, and I think it’s important to find a way to fix the underlying problem,” she says.

“To treat women with polycystic ovary syndrome, we’re trying to re-establish the ovulatory cycle so they can conceive. Even better would be the ability to identify the condition early on. That way, we could intervene from the teenage years and into adulthood.”

Diabetes, another focus of Graham’s research, can have more serious, even life-threatening, implications, especially when unregulated. “There are still so many things we don’t know about the progression of diabetes,” Graham explains. “As with PCOS, there are so many factors involved with diabetes that we just don’t know enough about the underlying causes.”

The promise of mathematical biology is that it may help biologists uncover those underlying causes and develop cures for conditions that we can now only mitigate. For Graham, that’s one of its attractions: “There are several things I care about currently—PCOS, diabetes—and maybe with this work, I can be one of the people who helps fix them.”

Math didn’t feel like work to me. It was just fun

Of her experience at Bryn Mawr, Graham says, “At Bryn Mawr, women don’t get the impression they’re not supposed to study math. You see people who look like you and your professors don’t tell you women aren’t good at STEM.”

In fact, she finds that Bryn Mawr students are especially passionate about math. “Teaching students who are extremely engaged,” she says, “means I have to be on top of my game and I have to keep it up for 16 weeks in the semester.”