Leon Glass, pioneer in nonlinear mathematics earns McGill Medal

Leon Glass, Professor Emeritus of Physiology and the Isadore Rosenfeld Chair in Cardiology, is one of this year’s three winners of the McGill Medal for Exceptional Academic Achievement
Emeritus Professor Leon Glass is considered a pioneer of applying nonlinear mathematics to biological systemsOwen Egan

For many of us, the stereotypical mathematician is a lonely figure, a solitary thinker who mulls over theorems and differential equations. Leon Glass turns that stereotype on its head.

Speaking fondly of his career at McGill, he lists the many fruitful collaborations he has forged with his colleagues from other disciplines. “One of the reasons I came to McGill was that I was interested in sitting next to people who were actually doing experiments. I felt it was essential not to just do mathematics but to try to relate that to experimental work,” says Glass, one of this year’s three winners of the McGill Medal for Exceptional Academic Achievement. The Professor Emeritus of Physiology holds the Isadore Rosenfeld Chair in Cardiology.

Glass is considered a pioneer, one of the early researchers to apply nonlinear mathematics to biological systems. He is renowned for his seminal work applying nonlinear dynamics to physiological systems, most notably to the understanding, prediction and control of cardiac arrhythmias.

“You can think of the heartbeat from the perspective of a medical doctor going over an electrocardiogram looking for abnormalities and relating that to different anatomical or biochemical changes that are taking place in the body,” says Glass.

“But you can also study the rhythms from the perspective of mathematics to try to understand how they are generated and how they can change from a normal rhythm to an abnormal rhythm.”

Roots in chemistry

A native New Yorker, Glass went to Brooklyn’s Erasmus Hall High School, a school with a long list of famous alumni that includes actress Mae West, singer Barbra Streisand, and Nobel Prize laureates Eric Kandel and Barbara McClintock.

Glass obtained a BSc in chemistry at Brooklyn College in 1963, and a PhD in physical chemistry at the University of Chicago in 1968. Despite the focus on chemistry, however, Glass made a bold move and changed fields.

“I was a chemistry major in college. And then I did graduate work in chemistry, which was very theoretical chemistry. But I was always interested in biology,” says Glass. “Immediately after my PhD, I switched from chemistry and started doing research on biological topics. Chemistry, particularly the branch of chemistry I was interested in – statistical mechanics – gave me some technical knowledge of mathematics and a perspective that has served me well.”

Glass focused on applying mathematics to vision and genetic networks as a postdoctoral fellow and research associate at the University of Edinburgh, University of Chicago, and University of Rochester.

“In 1975, I got a job in [McGill’s] Department of Physiology – even though I had never taken a course in physiology,” says Glass with a chuckle.

Long and fruitful history of collaboration

Soon after his arrival at McGill, Glass began collaborating with colleagues. One his most impactful partnerships was with Michael Mackey, now the Joseph Morley Drake Emeritus Chair in Physiology, whose research interests include the mathematical modeling of physiological processes at the molecular, cellular and tissue level.

In 1977, Glass and Mackey published their groundbreaking paper “Oscillation and chaos in physiological control systems.”

“In this study, we talked about the problems related to the applications of mathematics to biology, and the physiology of disease,” says Glass. “We introduced the concept of dynamical disease in this paper but the thing that was most popular was the development of a mathematical model that shows chaos. That was one of the important early papers for me, which in some sense, really defined a lot of the future work that I was going to do.”

Classified as a citation classic in bibliometrics, the paper has been cited more than 4,400 times, and, more than 40 years after publication, is still being cited more than 200 times a year.

Glass said that he was also fortunate to find colleagues doing experiments with a laboratory down the hall. Alvin Shrier, who came to McGill shortly after Glass and is now the Hosmer Chair in Physiology, has been a collaborator for 40 years. “Shrier’s curiosity about mechanisms of cardiac dynamics, openness to new ideas, enthusiasm and friendship have been central to my McGill experience.” Their 1981 landmark paper “Phase locking, period-doubling bifurcations, and irregular dynamics in periodically stimulated cardiac cells,” written with former graduate student and current McGill Professor Michael Guevara, was the first experimental demonstration of chaos in biology.

Lighting a spark in students

While Glass is still conducting research (“Academics are fortunate because we do something we love and we can keep on doing it”), he has retired from the classroom – a place where he had built a reputation as an outstanding teacher and mentor.

Glass taught Mathematical Models in Biology, a class he taught to several generations of undergraduate students. The course introduced the idea that one can make mathematical models, not only of physical systems, but also of biology biological ones.

In another collaboration, Glass and Professor Danny Kaplan wrote the introductory textbook Understanding Nonlinear Dynamics. The book has been cited in the primary scientific literature over 1,300 times.

“I’ve always enjoyed the teaching because I like teaching the material,” says Glass, while admitting he found evaluations “burdensome.”

“One of the most enjoyable moments is when students become really interested in what you’re saying and you light a spark in them.”

Moving from niche field to more mainstream

Glass says that in those early pioneering days, the area of applied mathematics to biology “was something of a niche interdisciplinary area. That made it difficult in a number of ways.”

Biologists sniffed that it wasn’t really biology and mathematicians maintained it wasn’t really mathematics.

However, in recent years, scientists have begun to turn more and more to the field – especially during the COVID-19 pandemic.

“Applying mathematics to biology has become more widely accepted over the last decade or two,” says Glass. “In part, that was due to the development of genomics where it’s clear that you need people who are experts not just in biology but also in computers and mathematics. There are a lot of people in neuroscience who use it. When people talk about artificial neural networks and deep learning, this is all mathematics.”

“At the moment, with the COVID-19 epidemic, we see all of these predictions that people are making. That’s applied mathematics, to take data and make predictions for the future. I think the COVID-19 epidemic has also led to the recognition of potential relevance of mathematics to study problems in biology.”

Asked to look back at his career, Glass talks about the scientific endeavour as a collaborative continuum in which each successive generation builds upon the work of their predecessors.

“There are a few people who invent something new, right from the beginning, but I think that a lot of things that we have done is furthering the efforts of the people who were thinking and going in similar directions before us.”

“I think that scientists are in some sense an extended family,” says Glass. “While some are a little competitive, most are very cooperative.”

“One of the things about McGill that has been fantastic for me, is that it was very accepting and encouraging of interdisciplinary work. And that’s not true of all places,” says Glass. “I have always been in a very nurturing environment and my colleagues have always been fantastic. That is something I appreciate enormously. I am very fortunate, and I think we all feel very fortunate that the people in our department are so supportive and collegial.”


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