Hans Othmer on Mathematical Biology

Newsletter 2003

HANS OTHMER ON MATHEMATICAL BIOLOGY: IN INTERVIEW WITH PETER WEBB,
PROFESSOR OTHMER EXPRESSES SOME THOUGHTS

Peter Webb: Hans, first of all let me thank you very much for agreeing to be interviewed for the Departmental Newsletter. Before I ask you any questions I would like to congratulate you, because we have heard that you have received an award from the Alexander von Humboldt Foundation, which is a notable distinction and evidently is in response to your work and your various activities. Congratulations! I wonder if you could just tell me a little bit about it? It comes with some money, which I suppose will support work that you do with people in Germany. Do you have to do the work in Germany? Will you do it in certain places?

Hans Othmer: No, not strictly. As the director of the Max Planck Institute where I am staying emphasized, this is a prize, so there are no fixed requirements, but the purpose of it is to stimulate in part research between people in Germany and the rest of the world, and so I've made a commitment to stay there for about 6 months, and they also gave me generous travel funds to go back and forth and I can invite visitors and so forth. It's just perfect. It's out of the blue. It's very nice!

PW: Let me ask my first question about mathematical biology, which is a big question. It is really if you could give some sort of overall snapshot of how you see mathematical biology at the moment, where you see the current activity. We would have to have been blind and deaf not to appreciate in recent years that mathematical biology is receiving a lot of attention and that there is a lot of funding coming into mathematical biology. How do you see the overall picture at the moment?

HO: Well, given that I've been in the area for 30 years, I consider that it has changed very dramatically. When I started at Rutgers, 30 years ago last year, there were real, real hard questions. Is this a legitimate intellectual exercise? a), and b) does it belong in a mathematics department? Some of those questions people still ask, and that's perfectly legitimate. But I see it as coming into a golden age, because what has really changed fundamentally is that biologists have begun to realize that they need mathematics to understand these complex biological systems. Thirty years ago when a lot of the new molecular biology techniques started in, the attitude was: I will take the watch and I will dissect it, put its pieces on the table, and I will then understand how a watch works. Of course anybody could say that isn't true. You will understand how the pieces work, but you won't understand how the watch works. That realization has really sunk in full-force, because the more people understand about biology the more they realize how complex it is. Mathematics is the natural language that deals with extracting essential pieces and discarding what isn't so essential, and analyzing those essential pieces.
I think there are enormous possibilities for mathematicians in mathematical biology, just as there were 150 years ago in physics. Much of analysis came out of people trying to understand heat conduction, fluid flow, gas dynamics. Everything evolved into the field of PDEs, functional analysis and all these things. They all came out of very concrete problems long ago. It's interesting to ask, what would have happened to mathematics had people really started understanding biology first, rather than physics. How would mathematics have developed?

PW: Could you be specific about what parts of mathematics in technical terms have particular application in biology. I am aware of some things. So I think there is quite a lot of mathematical modeling using differential equations, there's that kind of thing. I understand also there's a certain amount of combinatorics, trying to understand DNA structure perhaps. What areas might a mathematician who is interested in moving in to mathematical biology focus on?

HO: Well, I think there are areas of biology in which almost any area of mathematics that I can think of has been used. Certainly differential equations and dynamical systems, ordinary differential equations, partial differential equations, those are the bread and butter of modeling in much of biology. We also need to know about stochastic processes. We are discovering that if we talk about gene control networks we have to worry about individual molecules. We can't treat things as continua the way we think of when we do a differential equation model. And so stochastic processes are going to be much more important in the future. In understanding languages one uses a lot of algebraic structures. Maybe DNA strings are a kind of a formal language.

PW: I have the impression that there is more emphasis on continuous phenomena than discrete. For instance, I do representations of groups, often-finite groups, and I am not aware that that particularly has application in mathematical biology.

HO: Well it actually has had some, in the form of symmetry groups. So there are huge issues about pattern formation. If you look at any issue of Nature you see people are trying to understand how the spatial structure of things evolves. To summarize it, how do you read out the information of the genome at the correct point in space at the correct time, so as to build an organism like me? And so, finite groups and group theory and group representations and so forth have been used in analyzing symmetry and symmetry breaking, pattern formation and so forth. In the area of bifurcation theory, one subarea is symmetric bifurcations. The point is that one should never say that a particular area of mathematics is never going to be useful. Wait! Somebody will find a use.

PW: How do you view the mathematics department here, at the University of Minnesota, in terms of mathematical biology, the people who are here at the moment, what courses we have, and the gap that probably exists between what there currently is and what you might hope for in the future?

HO: Yes, OK. Let me start answering that by backing up one step and emphasizing that mathematical biology is still a very interdisciplinary subject, and that's because we're not at the stage people are in fluid mechanics, for example, where the Navier-Stokes equation is very well-established. You don't have to justify working on Navier-Stokes to people doing fluids. There are well-established questions everybody agrees are very important, so you go off and look at them. In biology it's different, so people really have to learn some of the biology as well as the mathematics. You don't just go to someone and say, 'Give me an equation of a type I am very familiar with and let me work on it.' because that will frequently lead to nonsense. So it's an extremely interdisciplinary subject. As to how that plays out, it means for the students that they have to learn things in addition to various mathematical techniques. My students will take courses on differential equations, dynamical systems, PDE's numerical analysis, stochastic process, and then perhaps a biology course or two so that they have some grounding at least in the biological aspects of the problems that they are trying to understand.
As you know last year we hired someone in neuroscience, so now I would say roughly speaking the two areas which are represented here are pattern formation, developmental biology, physiology type of problems including gene control, all the complex networks issues; and then Duane Nykamp does theoretical neuroscience, which is a huge area in itself, and which I would hope more mathematicians would get interested in thinking about, because it is the canonical example of what mathematicians do very well, i.e. thinking about abstract ways to understand things. That's needed there, but it has to be grounded in some understanding of what the basic physiology of the brain is. You can't just think of it as an abstract machine, although the abstraction could help enormously.

PW: Do you think the courses that are available currently are well set-up to allow somebody who is a mathematician to obtain a knowledge of the biology that he or she needs?

HO: Well I give some courses the intent of which is to accomplish that in part, but let me also emphasize that it's an awful lot easier learning the biology as a mathematician, than it is learning the mathematics as a biologist. So we have an enormous advantage. I've never taken a biology course, I've learned it all by reading. I send my students to some courses so that they get a more formal introduction to it, but if one is sufficiently dedicated, you can read it and learn it, and by talking to people in the area understand it. So it's an asymmetric situation, and I would emphasize that people learn the mathematics first, and well, because they can learn the biology later.
One thing I find interesting here, and which surprised me when I came here is the latent need that exists on campus for people to have someone with more mathematical training to talk to. I could collaborate with 15 people at any given time, simply because there is so much interest in having mathematicians who know enough of the background to be able to converse, but can also do the mathematics. That's why people from other departments come here. And so, you know, many of our colleagues could probably do similar things.

PW: Do you think you need more people in your area in the department?

HO: I think so. I think in a department of this size, given the demand in terms of training Ph.D.s, given the possibilities for enhancing mathematics through interactions with other departments, I think it's an easy thing to justify.

PW: It's a difficult thing to run a program when you have one or two people and you are trying to do everything yourself.

HO: Well, believe me, the first four years here were very tough. I was doing a new graduate course every year, and now we're beginning to have a program, so people can see an intellectual path that will take them through courses and into the research, and that's good. I would also say that people have to realize that mathematics is by and large a service organization within the university. That's the reality. If we were only teaching our own progeny, there would be far fewer of us. That is the reality. And so, having people who understand some of the issues that people outside of the department are facing when they want to use mathematics, I think, is again healthy for mathematics. We can serve as a kind of bridge to people outside, and they can say, 'Yes, there's somebody who has some inkling of what we do when we struggle in trying to apply mathematics, and why our students struggle with the way mathematics is taught.' It all comes together. I think what we have to do is build on this and see that biology does as much for mathematics as mathematics can do for biology, because then both sides win, and that's the most interesting outcome.