A Conversation with Dr. Christine Heitsch 
by Andrew Kerr
January 2008

I chatted with Dr. Christine Heitsch about her work as a mathematician exploring questions in biology. She describes the value of interdisciplinary collaboration, her personal reasons for preferring to work in mathematics as opposed to experimental science, and A Wrinkle in Time.

Q - Your dad is also a mathematician. Do you and he ever sit down and just talk math?

A - We certainly talk about mathematics, or the social aspects of mathematics. But detailed conversations? Not so much.

I think [my dad] was impressed the first time that I knew something mathematical that he didn't already understand. It took me a long time to get to that point.

He's a topologist. One of first times I asked him what he did, he explained how to a mathematician a coffee cup and a donut are both the same things, because they both have one hole in them. Topologists study the structure of things that aren't changed under squishing and stretching and things like that. So if you have your coffee cup with the handle, you can take the cup part of it and basically squish it down and merge it into the handle so that all you have is the circle, but it's the same shape as your donut. In fact I have a coffee cup from graduate school that has hazard striping on it and says "Caution: Not a Donut!"

When I was nine, my dad had a sabbatical. We went traveling. We were on a beach outside of Rome when I asked him why we counted by ten. So first he held up two hands, and then he found a stick and started drawing ones and zeros in the sand. He explained to me how we would count if we only had two fingers. He explained to me what the binary number system was and how you convert between digital and binary number systems.

What I imbided was the idea that there is structure and that one of the things that any scientist does is to study and try to understand structures. Biologists started with structures they could see and smell and touch. Now we've got nanoscale; they've gone well beyond that realm. Mathematicians have always thought a little bit more abstractly and study things like why a donut and a coffee cup are actually the same thing. But [still,] it's all about structure.

Q - I can see how math helps scientists. But what do mathematicians get out of that relationship? Seems the laws of nature would be more limiting to the imagination.

A - Typically, mathematicians (as a gross generalization) are not interested in the applications of mathematics. They're interested in developing new mathematics and pushing the boundaries of our discipline. But we become very interested in applications of mathematics when it's clear that thinking about those problems coming out of other sciences pushes mathematics forward.

The interaction of mathematics with physics is well known to be fruitful for both sides. Not only does physics need mathematics to understand the problems that come up in physics, but mathematics benefits from this interaction because it generates new and interesting questions in mathematics.

The laws that people were looking for were more apparent in physics and astronomy, so it was easier for mathematicians to think about those types of problems. But biology is messy. It resists abstraction and simplification in many ways. And that makes it much more challenging and interesting to work on.

What's interesting about this emerging interface between mathematics and biology is that it is starting to generate new and interesting mathematical questions. Mathematicians are getting increasingly excited about the interaction with biology because it's becoming clear that there's interesting mathematics there.

Q - So what do you do?

A - One of the basic divisions between mathematics is the division between analysis and algebra. Analysis grows out of calculus and looks at things that are basically continuous; you describe a system in terms of the ways that it changes. On the algebraic side there is algebra, group theory, number theory, coding theory, graph theory, discrete math--all these sort of things that tend to concern the study of structures that are more discrete as opposed to continuous.

Now of course that's a gross over-simplification, but it's one way of sort of situating what I do within the broader areas of mathematics.

So the mathematics of what I do is on the algebraic side of this. It's a newly emerging interface of mathematics and biology. The sort of work that I do has been described as discrete mathematical biology, sort of in contrast to continuous analytical biology. I focus on the interaction of combinatorics with molecular biology. Combinatorics is a broad area of mathematics; molecular biology is a broad area of biology.

What I'm interested in is understanding how structure and function are encoded in RNA virues. It turns out that there is a lot of mathematical structure there if you understand enough of the biology to strip away a lot of the details (Einstein has this wonderful quote: things should be made as simple as possible--but no simpler). Just coming up with the mathematical question that you want to answer is a huge step in doing research in this, because you start with this very messy, complex biological system and you have to decide at what level of resolution are you going to focus? The level of resolution that I work at is looking at the genomes of these viruses. They are typically single-stranded RNA sequences.

Q - My last interview was with Dr. Patricia Sobecky, who works with plasmids, which are effectively "weird" DNA (when compared to the more familiar chromosomal DNA model). What are the differences between RNA and DNA?

RNA, just like DNA, is a nucleotide sequence. So [in DNA] you've got A, T, G and C [adenine, thymine, guanine and cytosine]--and in RNA it's a U [uracil] instead of T. [Unlike single-stranded RNA,] DNA forms this canonical double stranded helix. So in some sense DNA exists in a perfect world; every base in a DNA segment can pair with its perfect compliment.

But RNA is typically a single-stranded nucleotide sequence [here is a comparison]. These nucleotide bases, which behave like little bits of Velcro, are looking to stick to their correct pairing partner. DNA has this perfect complement, so it does the best thing possible: it sticks to its perfect complement. But RNA, because it's single-stranded, these nucleotide bases pair within the sequence. So you have this linear structure. You start with what is essentially a linear sequence, and then bases within that sequence pair with each other so the sequence folds to form what's known as a secondary structure. So you go from a one-dimensional structure to basically a two-dimenstional structure. And then that two-dimensional structure exists in three dimensions.

RNA is this interesting hybrid, or most likely precursor, of both DNA and proteins. It has a nucleotide sequence like DNA, but the sequences form complex three-dimensional structures that perform functions like proteins do. It's reasonable to treat these sequences as combinatorial objects. So I think about them as strings over a finite alphabet. I just have a set of letters, my A, C, G, and U, and I can align those letters to get strings, and those strings interact with themselves to form planar structures that I represent as a trees. Then I analyze what those trees do to try and understand better what the biological molecules are doing.

Not only do I use these combinatorial structures to model the biological molecules, but thinking about these biological problems has generated new insight into open questions about these combinatorial structures. I was able to solve a problem that had been open for more than 30 years. And it turns out to be a surprisingly elegant solution, because the standard way of looking at it was more complicated than it needed to be.

Q - Do you spend all your time in the mathematics department, or do you go outside your department to do this research?

A - One of the great things about coming here to Georgia Tech is I've found a number of collaborators since arriving here. So I'm currently working with Steve Harvey, who is in the School of Biology. He's a structural biologist, so he looks at the three-dimensional folding of these molecules and models them. And David Bader, who is a computer scientist and does computational science and engineering in the College of Computing. We are trying to understand these viral RNA secondary structures, focusing on the analysis, so that's sort of the more mathematical aspect. It's a nice three-way interaction going. And then I've also been recently talking with Lauren Williams, who is in the Chemistry and Biochemistry department, and Alberto Apostolico and Concettina Guerra, who are again in computational science and engineering.

Q - Why are such interdisciplinary collaborations important?

A - There are a few rare examples of people who have enough expertise in biology and computation and in mathematics to have it all in one research group. But a much more standard model is to have sort of a particular area of expertise and an understanding of other fields, and then to build collaborations with other experts to have the expertise to tackle these challenging problems.

Steve was assigned to me by the Dean's Office as my College of Sciences faculty mentor. We met at the beginning of last year. He starts telling me about this problem that he's been working on where there is a particular virus that is known experimentally to fold into a dodecahedron. The virus traces out the edges of the dodecahedron, and then the rest of it is packaged in the midde. But this experimental data is not at a level of resolution that we can determine how that's done. It would be kind of like me taking off my glasses. So you see the blurry outline of a shape, but you can't see any of the details of it. Our goal is to use these mathematical approaches and computational tools to basically be our glasses, to try and focus on what this sequence is doing and to understand how that's folding. So Steve is describing this problem to me saying we have the sequence and we have this three-dimensional structural data, but we need the secondary structures in order to be able to bridge between the known one-dimensional structure and what we know about the three-dimensional structure. And it's terrible to describe things in terms of advertising, but it was one of those, "You've got peanut butter on my chocolate!" sort of moments, because I'm sitting there saying "I honestly cannot believe you are describing this problem to me, because that's exactly what I do. If I had to say what type of problem some biologist would come up to me with I wouldn't even dream of this, because it's just too perfect!"

There's a society for industrial and applied mathematics; they have a conference on discrete mathematics. I had gone to that the spring before coming here, and been speaking to someone who also works on RNA problems, and I was saying how I needed to forge a collaboration with somebody who was interested in the computational aspects of these problems. And the person I was speaking to at this meeting said, "You're going to Georgia Tech? You have to meet David Bader! He's the perfect guy for you!" And it turns out that this is exactly the case. Much like my interaction with Steve, we have enough commonalities in terms of our interests to be able to articulate a question that we're interested in working on together, but enough differences so that all three of us bring different expertise to the table. We are more than the sum of our parts.

Q - "Virus" is a word that to the average person is associated with disease. Is the ultimate objective of your research to find ways to fight and defeat viruses in the human body?

A - So that is certainly part of it.

In some sense we can think of viruses as perhaps the simplest form of life. They exist, they replicate, they perform functions, they evolve. But it doesn't make sense to talk about them as being living.

Just as a model biological system, viruses are interesting regardless of their impact on us or anything else. However we are also particularly interested in studying viruses precisely because of their impact on us and the rest of our environment. We would like to do a much better job of understanding the structure of viruses so that we can decipher the functions that they perform with the goal of disrupting those functions, ideally. The work that I do is very far on one end of that pipeline, but you can see just this little pinpoint of light at the end of the tunnel where you might say, OK, someday we might be able to do something better in terms of prevention or control, create better vaccines, just do something that would have a profound biomedical impact through the type of work that we are doing here.

Q - Where you always interested in going into mathematics?

A - A salient detail is that my father is a mathematician. However, for a very long time I thought I would be a biologist. There's this children's book, A Wrinkle in Time, by Madeleine L'Engle. An image that has stuck vividly with me for my entire life is the description of the mother, who I believe is a biochemist and who has a laboratory sort of set up in an annex of their house, cooking dinner over the Bunsen burner while she babysits her experiments. And so I at first thought that that was the direction that my career would take, that I would be an experimental scientist.

Part of this was also that I never found the [high school] mathematics classes particularly interesting. I pretty much went through the standard mathematics curriculum. I was fortunate that I went to very good schools, so the standard curriculum was at a reasonably high level. I had taken AP Calculus by the time I had graduated from high school. But frequently you hear about these math prodigies who were doing research when they were 14. I was not one of them.

But the biology classes were very interesting. In high school you get to dissect things and study plants and do experiments and do interesting things even at that level. So I was far more interested in the biological sciences than I was in the mathematical ones when I started college. I don't know if this is true overall, but it feels somehow shameful starting college being undeclared, so I think there's a lot of subtle pressure to have a major and to have a plan in mind when you start college. So I just picked biology. It seemed like a reasonable thing.

I was fortunate because I was an undergraduate at the University of Illinois at Urbana-Champaign, and they had a biology honors program that one could apply to at the end of your freshman year. If accepted you were enrolled in a very small program involving about 30 students, sort of as a seperate track of biology major. That was what I did. But at the same time I was always taking math classes and just started essentially pursuing a mathematics major in parallel with the biology, and added physics to the mix at some point because you also have to take all these introductory physics classes. So I think in my sophomore year, if not officially, at least unofficially I had three different majors: math, physics, and biology.

Perhaps in my freshmen year I had said to my father, "Maybe I'll be a math major." And he had said, "Wait until you've taken a real math class first! Calculus doesn't count! You have to take abstract algebra at least!" And so I said, "OK" and took the abstract algebra class.

In your first two years you can sort of simultaneously major in three things because there's a huge amount of overlap between all of the requirements for these majors, but you have to specialize a bit more as you go into your junior and senior years and start taking these advanced classes. I remember walking across the Quad and thinking, "I have to pick one." I realized, "Wait a minute, what I want to do is mathematics, what I like is mathematics, I should major in mathematics! I can always apply it to physics or to biology, if that's what I'm interested in doing."

Now having had that insight I will say that the career path that I took veered very far away from any interaction of mathematics with other sciences. I became a math major, took all of these math classes, but there was essentially no real interaction of mathematics with biology or physics or anything else. I went to graduate school in mathematics at Berkeley and ended up doing my PhD there. My advisor is an expert in semi-groups. This is an area of algebra. But again, no applications, no interaction with biology or anything else. However, there is a natural connection. The particular area that I was interested in is known as "combinatorics on words." This refers to strings over finite alphabets and their properties and representations and analyzing them, and it's an area that is already at the interface between mathematics and computer science, and has increasingly important biological applications because biology has a lot of strings over finite alphabets.

So when I finished my PhD I thought I might want to move into computer science from mathematics. I was invited to do a post-doc in theoretical computer science at the University of British Columbia, which I did. There I was introduced by Anne Condon and Holger Hoos to a lot of these new problems that were emerging in computational biology. Anne said it was not exactly what I had been working on, but there were these underlying commonalities thinking about strings and sequences and trying to understand, and would I be interested in working in such things? I said, "Well, the irony is that I started college as a biology major." And I'd come all the way back around now to thinking about these biological questions, but from a completely different perspective than one that I would have anticipated doing!

Q - There does seem to be a sort of inevitability with regards to your decision to go into math. But I'm still curious as to why you detoured from biology, which you obviously were enjoying when you first entered college.

A - Experimental science requires a very different sort of patience and perseverence than theoretical work does. Experimental work is very different because you are dealing with physical things. Much of it is out of your control. It requires a different sort of personality than I have to deal well with that.

One of the first labs that we had to do in this honors program involved monitoring E. coli growth under a variety of conditions. We were divided up into groups and each group had a different set of conditions that you were growing your bacteria under. Every 15 minutes you had to take the test tube with the bacteria to the spectrometer and measure how many bacteria were currently in the tube. Then we made plots. The experiment started at 1, finished at 11--10 hours in lab--and that was only because the TA's had started it for us a couple of hours earlier, and in fact stayed late until 2 or 3 o'clock in the morning to finish it for us!

So you can't leave. And there's nothing you can do to speed it up. This was exacerbated by the fact that we all had an organic chemistry exam the next morning at 9 o'clock.

At 11 [the next day] we went into our biology lecture. Our professor said, "We figured out what the problem was." It turns out that dead bacteria scatter light much the same way that live ones do, so the original innoculation of bacteria had half as many viable bacteria in it as it was supposed to. So there was this five or six hour lag where the bacteria were not growing the way they were supposed to be growing because there weren't enough of them. And she says to the class, "If it bothered you, get out of lab science! This just happens!"

Now I didn't get out immediately, but this stuck in my memory.

And I think it was that summer, I had done an interenship in the MNR laboratory of Paul C. Lauterbur. This was through the chemistry department, and they had particularly chosen...there were two reason for placing me in his lab. One was that it was more biological chemistry and there were mathematical aspect to it, so that fit well with my research interest. But also they said to me, "He'll win a Nobel Prize one day." And he did [in 2003--ed].

There were two things that I learned from the experience. One was that the more that you progressed along a career in the experimental sciences the less hands-on science you do. So if you are faculty in an experimental discipline, and particularly if you are this leading researcher, then you are in some sense running a small business. And your job description as head of this business is to have the great idea and to secure the funding for it and to manage everything at a high level of detail. But you're not doing the science--the stuff that you presumably went into the discipline to do. I've known faculty or PI's who are quite proud of the fact that they've managed to eke out a few hours a week where they do experiments. This is extraordinarily unusual. And that is the model in the experimental sciences.

I contrasted this with my [mathematician] father who always was doing research, always was involved with what he went into the discipline to do, who was always thinking about problems, talking with collaborators, doing research, and who wasn't as worried about all of the administrative aspects of managing a large research group.

The post-doc that I was working most closely with...I went in one day to observe him doing an experiment. And he had been waiting for weeks, months, for these specially-labeled cells to arrive so that he could run his experiment, get the data, write a paper, apply for jobs and whatever. And we got in to do the experiment and the machine was broken! And so he was desperately trying to figure out how to fix it as quickly as possible while his specially-labeled cells that he'd been waiting who knows how long for were dying! And I just stood there and I was like, "I would not deal well with this sort of situation."

He was frustrated and he was tense and he was upset, but he was coping with it, managing to move forward and try and make the best of it. And I thought, my head would explode! This is not for me!

These were incidents and experiences that I had that were what led to my, I don't see myself having a career in the experimental sciences. I can't picture myself being that kind of scientist. But I can easily picture myself being a mathematician. So that was sort of a more pragmatic, professional calculation.

But then it's just the math that I like. I think about things mathematically, I am most interested in the mathematical aspects of problems. It's incredibly frustrating in some sense. And so it has to be something that you love, and not in a roses and hearts and rainbows kind of way, but in an almost obsessive "I can't NOT do this" sort of way. Because most days you make a little progress, if at all, and it's a lot of slogging through it for those brief "A-ha!" moments where you realize, "Oh, wow! This is even cooler than I ever thought!" But it has to be something that you're willing to get up and do every day. The most important thing I think is to find what that is. For everybody it's going to be different.