SCIENTIFIC ACTIVITIES - Fields Institute - University of Toronto

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IN CONVERSATION IN LATE MAY, LEAH KESHET (UBC) PRESENTED a lecture at the Centre for Mathematical Medicine entitled Adventures in Mathematical Biology. She spoke mainly about recent progress in cell motility modelling using a systems biology approach. (Cells typically move by a process called chemotaxis, and proteins regulate cell movement by enabling this process.) Keshet described the progression of her model from inception, using three simple partial differential equations to model the protein dynamics, to a more robust model including proteins that stay relatively dormant during movement. This expansion led to the addition of three differential equations to the model. Keshet’s lecture outlined the symmetry breaking that occurs during initiation of cell polarization, as well as the related cell signaling systems. She summarized her research, presented the mathematical models she has developed, and hypothesized underlying biological mechanisms produced from the insight she has gained from her models. The key points of her talk were related to the relevant developments in biotechnology and their implications for the modelling and understanding of cell motility. After her introduction she showed movies made through microscopes that illustrated cell motility. She then gave a general description of the approach to understanding cell motility mechanisms. She noted that using genetic circuit diagrams to identify the relevant proteins involved in the process is the only way to study it. After this, she explained the process of research in this field 18 FIELDSNOTES | FIELDS INSTITUTE Research in Mathematical Sciences Leah Keshet and the importance of interactions between mathematicians and biologists. From making initial biological observations and producing a preliminary model, Keshet was able to validate it and make the necessary modifications to produce more accurate explanations. Her preliminary model consisted of three coupled partial differential equations corresponding to the active proteins: phosphoinositides, GTPases, and the actin cytoskeleton. To capture the characteristic wave movement of the cells, she improved the preliminary model by including inactive proteins. Keshet noted that her understanding of the phenomenon has been produced from the ground up and that it has taken off to a great start. Keshet has given follow-up directions to some of her collaborators, graduate students, and post-doctoral fellows. They are creating a stochastic version of the model to include inherent biological instabilities, a scheme of fluid based computations to study the motion of shapes, and some biological directions to study the cell’s ability to diffuse and re-orient itself. Keshet was a student of applied mathematician Lee Segal. In the 1960s, Segal pioneered many of the asymptotic and quasi-steady state methods used to study complex mathematical models in a more tractable format. Following her lecture, Keshet sat down with Sivabal Sivaloganathan, Co-Director of the Center for Mathematical Medicine, to answer a few general questions about mathematical biology.
Richard Cerezo: From my understanding of the lecture, you characterized cell motility by its activity with three proteins. Leah Keshet: That was one aspect of a bigger project in which the three proteins play a major role, this is absolutely true. When I give this lecture to biologists, I tend not to do it quite in the same order… Since I am giving the talk at the Fields Institute I wanted to have a centerpiece which was more mathematical. RC: Are you a biologist or mathematician by training, or both? Siv Sivaloganathan: Her mother was a pure mathematician and her father was a biologist, so it was inevitable that she was… LK: …stuck in between. RC: I guess that comes across when you have to tailor your talks to different audiences. LK: I try to, although you sometimes get the opposite attitude and some people say that to be in a field like this, you need to be able to sit in two chairs, and you need to have a very big bottom, because biologists will say, ‘This is completely too simplified’ and there is nothing biological here. And mathematicians will come along and say, ‘This is too soft, there is nothing mathematically interesting here.’ So it’s tricky. SS: When you’re looking at a problem that is essentially biological, how do you go about thinking ‘what’s the crux of the mathematical problem?’ How do you go about formulating a problem mathematically? LK: Well it’s not trivial. It took many years before we got to even asking the right questions. We were stumped for a while at the point where we saw, ‘these are the three proteins, and these are the reactions. We’ve simulated them but we don’t get polarization. What’s going on here? Why don’t we get what we want?’ To begin to see what was happening took a long time. To begin to formulate a simpler problem that we could pursue analytically took even more time. It’s been a total of seven or eight years from when we began thinking about these proteins. SS: Would you say that apart from experience, it’s a whole universe of things outside the realm of mathematics that you need to feel through to get a handle on the problem? LK: For the first five or six years, a lot of the work is reading the literature and figuring out what it means, rather than having a biologist to work with directly. This is because biologists rarely see the value of models. The biologists who have these values are rare and it takes a while for us to build up enough of a background to publish. I have collaborations with Condilis in New York, which arose because I gave a similar talk in Minnesota and he was one of the people in the audience. He could see that there was some value in those directions. RC: Was this approach to the problem out of necessity or was this something that you were trained during your PhD? LK: I think it’s more a matter of luck. That is, having the right people come together at the right time. So when I began thinking about this, I had a postdoc Stan Moray [...] and he was a person who already had these two dimensional simulations for moving cell platforms—not so much as for many cells interacting with each other, but he could immediately see that this could be done. While some students were working out the biochemistry, we could then go to them and say, ‘Here’s what we found,’ and he could go then and make 2D simulations. If we had to do everything from scratch, it would have taken a long time. RC: For the future generation of math biologists, what attitude should we foster? Since this is a highly non-traditional field in mathematics. LK: The good thing is that the field has become more central and nowadays, biologists typically have to show some type of modelling component in their grant proposals. They cannot simply apply for NIH or NSF funding without this balance. They have to show that they have some way of taking that data from their experiments and making sense of it by working with theorists. Therefore, they have much more motivation to be connected to young people who’ve got quantitative techniques. So I think it’s important both to get the good math background, which means PDEs, ODEs, numerical simulation, a bit of computer programming, knowing how to use MATLAB, as well as taking the necessary background courses in biology that you’re interested in like immunology of cell biology in my case, and then being very open to talking to and finding people in those fields to talk to. SS: Because in many ways, biology up until now has been just observation and acquiring of lots of data. But trying to do mathematics with objects that are not in your chemical equations is something that is just slowly sinking in. RC: In what way, if any, did Professor Lee Segal influence your work, your approach, and your philosophy? LK: Good question. I think first of all that he was a great applied mathematician. And I have to say that, despite all his good intentions, he did not get me all excited about asymptotic analysis. But I did appreciate its usefulness, so other people working with me deal with those things. He had a way of taking problems and saying, ‘How can we simplify this as a first cut? How can we take something very complicated and try and write down what are the key things that we’ll go after as a first version? Once we understand that, we’ll add extra details.’ He was very good at that. [...] there are many scientists in every area who are extremely possessive and have the attitude of saying ‘this is my idea, this is how it works’, ‘everybody else is a fool’, ‘this is the only way’. Segal was very much willing to see all kinds of points of view and debate, ‘well this kind of model can explain this, the other kind of model is not so good at explaining that’ and vice versa. He was known in the field as being a great man, almost a father figure, and I think that is really important. RC: So a human aspect was very important, as well as his ability to relate to other people, not only his ability to be solely a scientist? LK: To bridge between different perspectives and not be too put off if someone thought that ‘no actually, things work a different way’, to be tolerant of different points of view and be open. SS: This is interesting because we had a workshop a couple of weeks ago on Mathematical Oncology and one of the students of Weinberg at MIT was speaking and I was talking to him afterwards and he was saying how he got to work with Weinberg. Weinberg said to him ‘anybody could be a great scientist, I want you to be a great human being’ and I thought that was a wonderful thing to say. FIELDS INSTITUTE Research in Mathematical Sciences | FIELDSNOTES 19
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SCIENTIFIC ACTIVITIES - Fields Institute - University of Toronto

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