Faculty Lecture: Solving biological problems with math

James Murray

These days when a biologist, a medical researcher or even a psychologist wants to set up an experiment, the chances are they will contact a mathematician. Such interest in what was once a little-understood discipline, says the UW's James Murray, indicates how mathematics is now seen as an engine of change.

Instead of mathematics pursuing only the arcane, it is increasingly being applied to "real problems," such as cancer, AIDS, wound healing and the spread of rabies. "From a mathematical modeling point of view," says Murray, "nothing is sacrosanct."

Murray, who is the Boeing professor of applied mathematics at the UW, will present the 22^nd annual Faculty Lecture, Probing the Mysteries of Nature's Patterns: Sex and the Single Alligator, and Other Vignettes from the World of Interdisciplinary Science. The lecture will be at 7:30 p.m. Tuesday, Feb. 24, in 130 Kane. Admission is free.

A member of the UW faculty since 1988, Murray over the past 20 years has been largely responsible for the international creation of the new field of mathematical biology, the application of mathematics to biomedical sciences. A native of Scotland, he was the first professor of mathematical biology at the University of Oxford. In the 1980s he was the founding director of Oxford's prestigious Centre for Mathematical Biology. He has written three books on the subject, co-edited three others and written about 200 journal articles.

At the heart of Murray's work is the mathematical model, a series of equations that predict how fundamental biological systems will act on one another. In medical sciences, that could involve cells, chemicals and tissue. In the case of cancer cells, the equations might picture reaction diffusion, in which cancer cells grow, then diffuse out. Using such a model can enable a doctor to predict how a tumor will respond to surgery or therapy.

Biologists and medical researchers are encouraged to use such formulas, says Murray, because "the equations can be written down in words, not just figures." This, he says, immediately brings a degree of trust from non-mathematicians who see that the models actually reflect reality.

As a result, "more and more biologists, particularly in America, are being trained to think mathematically," says Murray. At the same time, applied mathematicians are taking crash courses in biological and medical subjects and "are becoming so astonishingly well informed that biologists and doctors are listening to them."

Murray has applied his modeling to many unusual subjects over the years, including a study of wolf packs. His mathematical model showed that packs establish boundaries across which each pack will not cross, and between which their prey—deer and moose—can exist in safety. He then applied this model to 18^th century Chippewa and Sioux Indian tribes and found that they, too, had established boundaries, through treaties, between which their animal food reserves went unhindered. It was, he says, the threat of intertribal war that kept the tribes from starvation.

He also applied his modeling to alligators, after discovering that the temperature at which the eggs are incubated determines the animals' sex. Thus, in a colder environment, females would be hatched. He believes this is an evolutionary survival technique, because, he calculates, a female alligator has to produce only slightly more than one female surviving offspring in a lifetime to ensure the survival of the species.

But, says Murray, the most "exciting" application of his work has been in the field of marital relations, working with UW psychology professor John Gottman. The two researchers have developed a mathematical model that can predict, "with astonishing accuracy," whether a marriage will last or end in divorce. However, Murray is quick to add, Gottman could still have reached such conclusions even without mathematics.

Indeed, so involved does Murray become in his various subjects it is easy to forget that he was trained as a mathematician. He well remembers a compliment from an eminent Yale biologist who asked him, "how did you find time to learn all that math?" ¶

David Brand, News and Information