Mathematician takes a turn in the laboratory

Despite growing up in a medical family whose dinner table talk often revolved around strange diseases and interesting bodily quirks, Julie Simons’ first love wasn’t biology. In high school, the UW–Madison mathematics graduate student became captivated by geometry. As an undergraduate at the University of California, Berkeley, she majored in math and minored in statistics. And upon graduating, she did an internship in cryptography and code breaking.

Biology always interested her, though, and after joining BACTER, a UW–Madison training program in computational biology, in 2005, Simons finally got a chance to try it out. On the first day of three months of study in the laboratory of Oxford University biochemistry professor, Judy Armitage, things changed. “Judy turned to me and said, ‘Would you fancy doing a bit of lab work?’ and I said, ‘Sure,’” recalls Simons. “I’d been hoping to get into the lab, but I didn’t know if it would be possible, since I had (very little) experience.

“I was just fortunate that people wanted me to get into the lab, break some things and do my best,” she laughs.

All joking aside, Simons is now wielding a powerful combination of mathematical and experimental techniques to understand one of microbiology’s most enduring questions: What controls the growth patterns that arise as bacteria sense and swim toward needed substrates in the environment, and away from harmful ones? This process, called chemotaxis, has been studied extensively in E. coli; in fact, the dense rings of cells that E. coli produces as it swarms toward sugars, amino acids and other attractants are considered the model for microbes generally.

Armitage is questioning, however, whether E. coli’s behavior really is so typical. Chemotaxis in the bacterium she studies, Rhodobacter sphaeroides, creates a very different pattern of cells — much more diffuse, and often lacking in distinct rings or bands. Why this puzzling disparity exists is the problem that Simons and her adviser, mathematics professor Paul Milewski, are now helping untangle with math.

Why mathematics? Simons explains that while the Armitage lab has thoroughly described the chemotactic pathways in Rhodobacter’s cells, the behavior of populations has proven much harder to grasp experimentally.

“At the population level, they can take pictures to record how far bacteria swarm and swim in different environments, but without any other sort of tool, this doesn’t tell you much about the biology,” says Simons. “So that’s where we thought the math could come in.”

How to model the collective response of a population without describing the complexity of each individual’s behavior is a classic mathematical problem. But the work has practical implications, as well. Because Rhodobacter can convert cadmium, uranium and other heavy metals into less toxic forms, bioengineers are eyeing it as a possible bioremediation tool.

Before this can happen, however, a better understanding of Rhodobacter’s natural chemotactic behavior is needed, says Simons. For instance, does its lack of distinct chemotactic rings signal that Rhodobacter doesn’t sense its environment as effectively as E. coli? Or is its response somehow more evolved, given its more complex suite of chemoreceptors? And which environments produce optimal growth and spreading in Rhodobacter anyway? While the questions sound basic, “these are things biologists just don’t know right now,” says Simons.

To get at the answers, Simons employs partial differential equations, known as Keller-Segel equations, which model the average behavior of a certain density of cells. Included in the models are terms for describing the diffusion of a chemoattractant, the cells’ motion toward the attractant (chemotaxis), and their consumption and growth on it — all derived from Simons’ experiments in the lab.

Growth, consumption and chemotaxis terms have been included in these models before, but what sets Simons’ approach apart is how it probes their interplay. As bacteria consume an attractant such as glucose, for example, they constantly alter its local concentration — a change that, in turn, affects their chemotactic response. Thus, by quantifying these interactions, Simons can describe the precise environment that bacteria experience at any spatial location in an agar plate, and gain a more realistic picture of the optimal conditions for spreading and growth.

Although she’s still refining the models, preliminary results suggest that growth and bacterial movement reach their optima at the very same attractant concentration in both E. coli and Rhodobacter — despite the different chemotactic patterns these microbes display.

“This makes sense from an evolutionary standpoint,” says Simons, “because if you assume organisms are optimally evolved to take advantage of resources, it wouldn’t make sense for them to move past their place of maximal growth — that would be a waste of energy.” She adds that you wouldn’t expect them to stop swimming before reaching this point, either.

Before she stands firm behind her results, though, Simons may return to the lab to strengthen her models with more experimental data. So, does this mean she’ll be making lab work a habit?

“I’m glad I’ve gotten the chance to work in the lab,” she says. “It has given me a real appreciation for experimental biology, how hard it is, and how much patience it takes.” But in the future, she laughs, “I’m happy to let the biologists do their jobs.”