When Biology and Math Collide

Biology and mathematics—the practical and the theoretical—can be surprisingly uneasy bedfellows, but their union could help uncover the mysteries of life.
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Small fruit fly seen through extreme magnification. (Photo: Sebastian Janicki/Shutterstock)

Small fruit fly seen through extreme magnification. (Photo: Sebastian Janicki/Shutterstock)

The story of Turing patterns is about more than proving whether Turing’s reaction-diffusion mechanism is responsible for creating fingers, fur, and fins. It’s about the meeting of maths and biology: two traditionally uneasy bedfellows. And, like anyone who’s observed a testy relationship between two ill-suited partners, some people are concerned.

It was Turing’s own kind—mathematicians and others based in the physical sciences—who kept his idea alive when the biologists stopped believing. At that time the two fields were moving along completely separate tracks. Biologists didn’t see what benefit mathematical models could bring compared to their experiments in the lab (and probably didn’t understand the maths either), while mathematicians found real life a bit too messy for their sterile equations.

At the University of California-Berkeley, professor Mike Levine has built up an extremely distinguished career dissecting the complex genetic instructions that turn a fruit fly egg into a maggot. He’s a larger-than-life character devoted to beautiful embryology, and holds strong opinions about it. When a team of U.K. researchers published a paper detailing a mathematical model to explain the formation of particular stripes in the fly embryo, Levine launched a broadside. He accused them of “computing away the magic,” saying, “I cannot help but complain that the new models for the regulation of [gene] expression described by Nicholas Luscombe and co-workers ... seem to strip the mystique from [it].”

"It’s not cool as a mathematician to be working in this kind of area—it’s not like people think we’re the shit because we do mathematical biology. The pure mathematicians are still saying, 'What are you doing? Why are you getting your hands dirty?'"

Others feel that computer simulations are little better than pretty animations, and don’t have much to give "real" biologists slaving away in their labs. As professor Jeremy Green of King’s College London says, “A lot of people in biology think that models are just a fudge, just a descriptive animation that tells you nothing about what’s actually going on in a real-life situation. Of course, the best model for any piece of biology is that thing itself—the best model of an embryo is an embryo. But the question is not how do you know whether the model represents reality or not—the real question is what do you have to do to make your model in the first place, so that it matches what you see in real life.”

Researchers like Green make their models by thinking about how a biological system ought to behave—for example, by being driven by a Turing mechanism—gathering as much lab data as they can, putting it all into the computer and pressing "go." The fun starts when the output from the simulation looks nothing like what the cells actually do in real life.

Green explains: “That tells you that your assumptions about what’s going on are wrong. So you scratch your head and think, ‘What will make this system work? How do I change my model to make it more closely match reality?’ And it’s this process of the model failing that tells you something about how the system works—and it tells you what to go back and look for experimentally. If it worked perfectly, there’d be no need to bother with the model.”

James Sharpe of the Centre for Genomic Regulation in Barcelona, Spain, agrees. “It was clear to me that the best thing to do is to have one lab, split between experimental biologists and theoretical researchers. Theoretical biology in the old sense is not that valuable—you have to go back and forth between the model and the lab, and that should just be how we do biology now. In many ways this is just a natural evolution of how scientists have always worked—we’ve always had models but they’ve just been in our heads.” (Or, more likely, scribbled on a beermat in the pub.) “The difference now is the complexity, and you can’t just rely on thinking about it to come up with the correct predictions.”

Two people who represent the new melding of maths and biology are British fruit fly embryologist Robert Drewell and American mathematician Jackie Dresch, professional and personal partners at Amherst College in Massachusetts.

“As soon as any biologist sees an equation, there is that knee-jerk reaction,” says Drewell. Dresch jumps in. “He basically said the same thing to me when we first met at a fly conference. He was all, ‘Can you explain your poster to me, because it all looks like bullshit equations?’” It was the worst pick-up line ever, but it worked.

Dresch feels the stigma goes both ways, with theoreticians shying away from the messy business of real biological systems in the lab. “Mathematicians have been busting their asses for hundreds of years to get to this point,” she says. “So why not converge and bring biology and maths together to make more progress? It’s not cool as a mathematician to be working in this kind of area—it’s not like people think we’re the shit because we do mathematical biology. The pure mathematicians are still saying, ‘What are you doing? Why are you getting your hands dirty?’”

Sharpe has a similar story about his modeling career. He did his Ph.D. at the National Institute for Medical Research at Mill Hill in London—a haven for some of the world’s leading embryologists. “When I finished, I knew I wanted to go into computer modeling. The people in the lab said, ‘This is scientific suicide—you’ve had an incredible opportunity in one of the best labs in the world, and you could go off and have an amazing career being a developmental biologist.’ They thought going into modeling was going to ruin me, but 15 years later no one would say that. The perception of the need to be doing this has completely changed.”

Sharpe believes we’re on the verge of a paradigm shift. There may still be some people who think modeling isn’t useful, but this isn’t the general attitude any more. “Biology is more like computing—it’s about information processing and decision making. By using computers to tackle more complex questions we can actually study biology, rather than reducing biology to physics. It’s very exciting.”

This post originally appeared on Mosaic as “When Biology and Maths Collide” and is republished here under a Creative Commons license.

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