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Math professor James Keener tells how math enhances understanding of life's processes.

Your body is full of math. From the constant flow of molecules in and out of your cells to the nerve signals zipping through your brain, your physiological processes can be described in terms of mathematical terms and models. It’s an approach to biology and physiology that moves from observational science into fundamental physical principles, according to some mathematicians, including the University of Utah’s James Keener. This week, Keener and his fellow mathematical biologists gather at the U for the 2017 annual meeting of the Society for Mathematical Biology. As part of the proceedings, the society will award Keener the inaugural John Jungck Prize for Excellence in Education. Keener recently spoke with @theU.

What is the significance of the Jungck prize to you?

I’m incredibly honored. John Jungck was very influential in developing ideas for communicating mathematical biology to all audiences. He was a really great communicator. The society established this prize in his honor. The fact that they chose to make me the first recipient — I was incredibly surprised and shocked by that and highly honored. I never thought my contributions were anywhere close to being recognized like that.

How do you describe the field of mathematical physiology?

Mathematical models help us describe and understand how physiological and biological processes work. There are myriad cell functions, and we’re trying to put numbers and equations to these processes, thereby helping understand the basic mechanisms by which cells work better than purely empirical methods would allow us to. It’s trying to provide a theoretical basis for the way living organisms function.

Why are biological processes well-suited to mathematical modeling and study?

Biology is basically physics and chemistry writ large. There are things moving around according to very basic physical principles. If I can count it or measure it, then I should be able to measure how that changes over time in a quantifiable way. As some chemical level is going up rather than down, I should be able to describe the process by which it’s going up. If something is changing and I can count it, then maybe I can track it in time with mathematics.

What is an example of the understanding math can add to a physiological process?

The classic example was the stunning achievement in 1952 when Hodgkin and Huxley used mathematics to describe how nerves work. They won a Nobel Prize for their work, and deservedly so, but they wrote down equations for how nerve action potentials work. To say that that revolutionized the field is an understatement. The principles they used have been applied in myriad other ways since then but that stands out as one of the most spectacular achievements in the field.

How did you become interested in this field?

It’s been 35 years now. I was interested in the field of chaos. I read an article that claimed that the heartbeat was chaotic. Being a mathematician, I wanted to know if this statement held any mathematical validity. I started to study the heartbeat. I became interested in cardiac physiology, just because of my curiosity to know if the mathematics associated with chaos theory applied at all to cardiology. That opened the door.

You quite literally wrote the book on mathematical physiology, a 2008 textbook with New Zealand mathematician James Sneyd. How has that book affected the field?

I had a very good collaborator. That book has been very well-received. It’s novel in the field of mathematics, because it takes a biology-first approach to mathematics. Most math texts try to walk you through the material from a math perspective. We took a different perspective. We wanted to rewrite a physiology book from a mathematical point of view. We took two physiology books and looked at their outlines and we wrote our chapters in a similar order, but we simply mathematized it, so we gave the mathematical understanding of what the physiology books were trying to teach. It was a little bit unusual in its perspective. I think that captured some attention.

What are the U’s strengths in mathematical physiology?

We have a substantial group of people and have lots of different projects going on with my colleagues and our graduate students. One of my colleagues is a leading expert in understanding how blood clots form and are regulated. Another is into the evolution of cancer and how the dynamics of cancer are affected by various mutations, protein levels and so on. Some of my colleagues are studying the dynamics of interactions of the immune system with cancer. I could list 25 projects that I think are exciting.

What is a frontier of mathematical physiology in which you hope to see significant progress?

The real frontier is in developing rich and productive collaborations with more and more biologists. There’s a huge cultural difference between mathematicians and biologists. In order to make genuine contributions to biology, it is crucial that we collaborate with real biologists. The real cutting edge is gradually developing more and more interactions between biologists who are not just sympathetic but enthusiastic about the use of quantitative methods in their field. I genuinely believe that quantitative methods can be very valuable in the coming decades to solidify and deepen our understanding of these very complex biological processes. That’s what we’re trying to do.