This is the second in a series of interviews I have been doing for the Association for Women in Mathematics. (You can read my first interview, with dynamicists Laura DeMarco and Amie Wilkinson, here.) In my interviews, I'm "listening in" on a conversation between two women mathematicians. I talked with mathematical biologists Victoria Booth and Trachette (Tracé) Jackson of the University of Michigan at the AWM research symposium in March, where they co-organized a special session on mathematical biology. We talked about how they got involved in mathematical biology, some of the research questions they are most excited about, and why Jackson thinks that now is a great time to be getting into mathematical oncology. This is an edited transcript of our conversation, and it first appeared in the September/October issue of the AWM newsletter (subscription required).

**EL**: So how did you get into math? Were there any pivotal moments when you thought, yes, I'm going to be a mathematician, or a math biologist?

**TJ**: For me, I think, when you talk to people who are doing mathematics as their career, they often start with, "I was always good at math." That was true of me, but I never thought of pursuing it as a career. I just thought it was something that I liked and that I was good at, until I got to college. I wasn't even majoring in math. One of the professors in the math department actually called me to his office and said, "you're taking all these classes, and you're doing really well. I think you should major in math." And I said, "I'm majoring in engineering." And he said, "No, you really need to change your major to math." And we had this conversation, and it was almost like an invitation to join the discipline. Even as an undergraduate, not really knowing what that meant, it felt like I was extended this really wonderful invite to try this, to see if I could do this, to see if I could love this. So that kind of invitation to the discipline, I think, really helped shift the direction I was going in. Since then, it's sort of been like, what area? I knew math was what I was going to do, and figuring out what area came a little bit later. I was going down a very pure math track. I thought I might end up going to graduate school and studying some very pure math topics for a long time.

The second story of the change of direction in my life was seeing flyers around my math department walls saying that someone was coming to visit, and he was going to tell us how the leopards got their spots, using math. And I kept seeing this poster, and every time I walked past it, I would just shake my head. There's no way math has anything to do with that! And so I went and sat in on the talk, and I didn't understand much. I was still an undergraduate. But what I took away was that mathematics has the potential to really understand biological phenomena and make a difference in how biologists view their experiments and the theories that they're making. That was the "aha" moment for me, that mathematical biology was going to be my field.

**VB**: So was that Jim Murray?

**TJ**: That was Jim Murray, who ended up being my Ph.D. advisor.

**VB**: Ah. For me, I think, similarly to Tracé, I didn't have dreams of being a mathematician. Going into college I took math and did well in it, and it turned out that the advisor that I was assigned in college happened to be a math professor. It was just sort of random, but he kept saying, "Oh, you should take more math." He pushed it. I was generally interested in all different sciences, and I took a lot of different science classes and math sciences but ended up focused on math. After undergrad I knew I wanted to do applied math, but I didn't have a specific application in mind. But when I was in graduate school, in thinking about what kind of applied math I wanted to do, there were a lot of the classic areas of applied math that other professors and students were interested in, like fluid dynamics, wave propagation, combustion. Somehow all those applications didn't really turn me on very much. But then one professor gave a short research blurb about some neuroscience he was doing, and I thought that sounded like an interesting thing to try. So I worked with that professor, but he only did a little neuroscience. It wasn't his main area of research. So I did a problem that was more a math problem, kind of abstract to neuroscience. But then went to the National Institutes of Health as a postdoc. There I collaborated with neuroscientists and learned the neurobiology really well.

**EL**: Does the University of Michigan have a big math bio program, or is it just kind of random that you're both there?

**VB**: Well Tracé's been there longer, and she's really developed the math bio program. We have an undergraduate major in mathematical biology and a couple of core courses that Tracé's developed and added to over the years.

**TJ**: We're really proud of the fact that mathematical biology is growing in terms of the number of undergraduates interested in it and the number of graduate students we're able to attract now. There is a nice group of us who do mathematical biology in the department. Some of us do it as our "bread and butter" day job, and others sort of do it as an application here or there, joint with a student or something. It's really a great environment to do mathematical biology, I think. We have a really top medical school, where a lot of collaborations are found. In other departments throughout campus, there are just so many people who are interested in quantitative biology. So it's nice to be able to draw upon a much wider pool of people interested in the subject.

**VB**: Yes. We have this core group of faculty. Some are in the med school, and in the physics and biology departments. They have these quantitative interests and quantitative approaches. Michigan has a strong history of interdisciplinary work, so people are very open to collaboration and talking across groups and disciplines. I think that helps a lot to, to have that institutional history of collaborations across schools and departments.

**EL**: Do you ever feel like you're being pulled in two directions? The math people might be saying you're a biologist, or vice versa?

**VB**: I think there is a balance that you have to maintain. I don't find it in my colleagues or the department so much, but at funding levels. Certain funding agencies are more math-focused, and others are less math-focused. You're trying to apply for grants, which are so important these days. You try to gear your proposal to the agency. You want to have some type of real mathematics that you're doing, but you also want to have what you're doing be really applicable so experimentalists can understand it and apply it. In that way, there is a tension.

**VB**: Yes, that's definitely still a challenge, especially in terms of writing grants and trying to get your work funded. Finding that balance, and maybe even shifting that balance to match what the funding agencies want, is something that we all learn to do quite early on. I think it's really nice that our department in particular really values the application and the impact that our work has on our field, as opposed to nitpicking whether it was in a math journal or not. Do you agree?

**VB**: Yes, I think so. The department has been very supportive of the applied aspect of our work, which is what we enjoy.

**EL**: Can you talk about what some of these cool applications have been? For me, a geometer, I think, oh all math biology is the same!

**TJ**: No, not quite!

**VB**: Actually our sessions, I think, really highlighted just how diverse it is, not just the topics of biology, but the math techniques people use.

**TJ**: You might think, math bio is kind of uniform, but it's very broad. I am in the area of cancer modeling, computational cancer research. I've worked on a variety of problems looking at developing mathematical tools for understanding the growth and control of tumors. Lately my research has had two threads. One is more along the lines of molecular therapeutics, looking at models that can help with new drugs being developed at Michigan and trying to help optimize how those drugs should work in terms of delivering them and how tumors will respond to them.

The second aspect of my work is more of a basic science kind of question. In the last few years, how tumors initiate blood vessel formation has become a big topic. We are looking at the mechanistic aspects of blood vessel formation in response to tumors. We're asking questions about how the biomechanics and biochemistry connect in order to give this strange conglomeration of vessels—that doesn't look anything like normal vessels—that tumors tend to generate. We always have an eye towards using that for therapy. If we can understand that, maybe we can stop it from happening and shrink tumors by attacking blood vessel cells, which is less harmful than attacking rapidly dividing cells. More than just cancer cells are dividing in your body, and if you give traditional chemotherapy, you're not targeting anything. If you could target something like blood vessel formation, it would hopefully have fewer side effects.

**VB**: Most of my work is in basic understanding of neural systems. One area is this modeling we've been doing on the neural control of sleep-wake states. What we're motivated by is the fact that in the experimental sleep field, there's a lot of controversy and non-consensus about what are the regions of the brain that are promoting the different sleep and wake states, and how those regions of the brain are connected to cause transitions between the sleep and wake states.

In the sleep literature, there are a number of different hypotheses for this network of neuronal populations that control sleep and wake states. The proposed structures are completely different. They don't have the experimental techniques available to actually monitor the activity in different neural populations on a timescale where you can see changes in sleep state. There's a gap between what's possible to observe or measure experimentally in an animal and where the theory is.

We're trying to use modeling to bridge this gap and to test these hypotheses that have no way to experimentally test them. We're hoping that we're helping the experimental community to at least identify targets to explore further. When they propose some network structure, what really are the implications of that network structure?

**EL**: Do you have any advice for people who might be starting in math or applied math?

**TJ**: I have a tidbit for someone who knows they're interested in applied math and who thinks that biology might be the application that they're interested in. There are at least two camps for training in mathematical biology. One camp is that you should learn a lot of mathematics first and then learn the biology you want to apply it to, and the other is to learn modeling and learn the biology, and learn everything dually.

I think both ways of training have merit, but in my experience and in my opinion, if you build your mathematical foundation to be very solid and very strong, and you increase your mathematical toolbox, you can use all of those skills throughout any type of application, as opposed to limiting yourself first with one or two mathematical tricks that you've learned. So I'm more aligned with the camp of really getting that mathematical foundation in order to help you apply those mathematical skills more broadly.

**VB**: I definitely would agree that just in terms of your training and what you study in school, getting the training in the quantitative techniques, and all the mathematical skills, rather than an application—the engineering or the physics or the biophysics—is better. It's harder to learn the other way. It's harder to try to pick up the theory of stochastic differential equations on your own, in your spare time.

**TJ**: Light reading!

**EL**: How did you get the idea to do this session at the AWM symposium, or were you approached?

**TJ**: I'm actually on the executive committee of the AWM, so I was asked by one of the organizers if I would put together a session on something to do with mathematical biology, and they said it would be nice if I had a colleague who was also in mathematical biology to put together the session with. I thought of Victoria because she's in my department. Our research areas are complementary, but they don't really overlap, so I thought we could get a diverse group of speakers, which I think we did.

**VB**: Yes, we did.

**TJ**: I thought it was successful, and everyone gave really great talks.

**VB**: I think it worked out well.

**TJ**: It was wonderful to see so many young women, mostly assistant professors and postdocs, who gave really, really polished, wonderful research talks that really highlighted the field of math biology, and how broad and diverse it is. It was great to see women in this setting.

**VB**: I agree, it was great. It was nice to see so many young women starting out.

**TJ**: It kind of brought back memories.

**EL**: How long have you been colleagues, and have you done other projects together before?

**TJ**: I've been at Michigan since 2000, and you came in 2004?

**VB**: Yes, 2004.

**TJ**: So we've been at Michigan together for quite a while. Since our research doesn't necessarily overlap, one of the things that we both enjoy is making sure that there is a community of people that can get together in some form or another for mathematical biology talks. So we started a mathematical biology research group, which Victoria has taken over and turned into a really nice mathematical biology-biophysics seminar, and we also started our undergraduate research program in mathematical biology. We had some money from the NSF to do that, and Victoria was a mentor to some students who came through that program as well. We try to do some of those educational kinds of things together as a group. Just making sure that there's a pipeline of students and making sure we and the rest of the faculty interact with them.

**EL**: Has the AWM, or an informal network of other women, been particularly important to you in your careers?

**TJ**: That's a really good question. I think we're lucky in our department that there is a definite presence of the women. When I first came in in 2000, at least three of the women faculty personally took me under their wings. I had wings all over me! They kind of took me under their wings, and it was really, really wonderful. I know in some departments, there are maybe one or two women. We're lucky enough to have double digits.

**VB**: We do have a big presence.

**TJ**: In terms of AWM, of course their travel grants and things like that have helped me throughout my early career. Certainly my graduate students have made use of that when appropriate and necessary. I even had an early career assistant professor come and visit me through an AWM mechanism. That was very helpful for her. She was at a teaching college and needed some research time. She came and worked with me for a while and got some time just to do research. AWM's programs are phenomenal in terms of hitting critical transition points for women.

**VB**: We recently had one of our undergraduates as an honorable mention for the Alice T. Schafer award.

**TJ**: Oh, that's right! And she started our women in math club.

**VB**: Yes, we have an undergraduate women in math club at Michigan as well. I'm having a "women in math" moment teaching my class this semester. I'm teaching linear algebra, which is an engineering type service course. There are 30 students, and two women.

**TJ**: You're kidding!

**VB**: No, it's the worst ratio I've ever had. And one of the women never comes to class. So it's just that one poor woman sitting in there with all those guys.

**EL**: I'm sure she appreciates that you're up there.

**VB**: Yes, it's good that I'm up there. But I think that [unbalanced ratio] might be an anomaly.

**EL**: Is there anything else you'd like to share?

**TJ**: For my field of research, computational cancer modeling, it's a really nice time for students to be getting involved and getting excited about it. Although people have been using mathematics to try to understand cancer for years and years, we as a community, we haven't been a real presence in the discipline, or force in the discipline. If you look at computational neuroscience, they have Hodgkin and Huxley.

**VB**: They laid the foundation.

**TJ**: And won a Nobel Prize, and really solidified the field. Comparatively, we don't have those foundational results.

**VB**: Or something that people are really able to build on.

**TJ**: Right, there's no one building block.

**VB**: That's been able to propel the field forward.

**TJ**: Exactly. But now, there's just so much going on and so much research being done that we're on that verge.

**VB**: Oh really? That's interesting. Because cancer is so complex. Every cancer is different. It's not just one disease.

**TJ**: Right. It's certainly a myriad of diseases.

**VB**: Maybe in some types, there's sort of an understanding.

**TJ**: But in many there's not.

**VB**: How do we even approach it? What kind of model works? It won't be one thing.

**TJ**: It won't be one thing that fits all. That's true. Every organ of origin is different, every mutation that generated that particular tumor is different. There's a lot of variation. But we're on the verge of something big.

**EL**: Thanks for taking the time to talk with me.

**TJ** and **VB**: Thank you.