Making a Mark

A UMBC mathematician finds the right equation for biologists

Kathleen Hoffman, a professor of mathematics and statistics at UMBC, works in math biology, but she often felt that her biology colleagues didn’t really understand what she was doing.

“The work I did was very foundational in mathematics and it didn’t really help them design an experiment or impact their way of thinking,” Hoffman says. So after she got tenure, Hoffman did something most mathematicians wouldn’t think of doing: she took a sabbatical, got funding from the National Science Foundation and joined a biology lab.

“I called it an immersion program,” says Hoffman, “because what I wanted to do was like learning a new language, where you just go to the country and live there, and that’s what I did.”

Hoffman had done her homework. She knew she wanted to work with Avis Cohen, a professor of biology at the University of Maryland, College Park who researches lampreys – a kind of a jawless fish that sucks the blood out of other fish – and how they swim. Scientists study lamprey locomotion because these fish possess neurons similar to those that power human locomotion, but thousands and thousands of orders of magnitude fewer in number – and thus much easier to study.

Joining Cohen’s lab brought about a fundamental change in Hoffman’s research, introducing her to an interdisciplinary group of mathematicians, biologists, and engineers all working on lampreys. “We had the best meetings,” says Hoffman, “because we were such an interdisciplinary group and it was predominantly women, which is very unusual in mathematics.”

Hoffman’s task was to mathematically model neurons. “The model pushes you in the right direction experimentally,” she explains. In developing the equations for the model, however, Hoffman had to grapple with lamprey biology.

“You don’t know what you’re trying to model if you don’t understand the biology,” she says. “But I wouldn’t say I sit down and understand the biology and then start writing math. It’s a process. I understand a little bit of the biology, and then I do a little bit of the math, and then I go back.”

One colleague says that Hoffman’s work modeling work is critical for the biologists and other researchers on the team to understand locomotion and design their experiments. “The problem of locomotion is difficult to understand without mathematics,” says Tim Kiemel, a research assistant professor in the department kinesiology at the University of Maryland, College Park.

Hoffman eventually needs the power of computing to actually “do” the modeling. But before she dives into programming, she starts out using a pencil and paper to define the problem and pose the right questions.

“Sometimes you just have to sit there and stare at it,” Hoffman says. “Sometimes you have to do a lot of calculation, or sometimes you just have to let it stew.”