What makes a good mathematical biologist?

Last time I presented the life and times of Prof. Jim Murray FRS. Jim is actually my academic grandfather as he supervised Philip Maini (the current director of the Wolfson Centre for Mathematical Biology) and Philip supervised me.

Figure 1. Three generations of mathematical biologists. From left to right: Me, Philip Maini and Jim Murray. When I showed the picture to my wife she said that she loved the gradient in beard colour :).

The extended mathematical family tree can be seen in one of my previous posts.

This week we discuss Jim's work.

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What field of maths did you start in?

I was working on various types of fluid mechanics, such as magnetohydrodynamics and a theory of fluidisation but, except for the latter, nothing really caught my imagination. The last paper I wrote on fluids was on Burgers equation [an equation related to turbulence modelling]. I once met Burgers. I was giving a talk and he was sitting there seemingly asleep in the front row all during the lecture. At the end everyone applauded, he woke up and proceeded to ask a highly relevant question.

How did you get into mathematical biology?

A professor of botany approached the department and asked if they could recommend anyone who could help him quantify how oxygen got into pea nodules. When the guy phoned me up he thought I was a graduate student and said he could offer me $5 an hour! So, that was my introduction into mathematical biology: oxygen diffusion in pea nodules. After writing a few papers on it I found it quite interesting even though there was nothing too difficult about the mathematics as it was just singular perturbation analysis of the diffusion equation

I don’t know how, but someone from anatomy heard about me and got in touch. His problem was on pilot ejection seat injuries.

Please do expand on this problem. I’ve heard it involved dropping corpses down lift shafts.

I got interested and the model consisted of a one-dimensional compressible material on one end of which we applied a force to simulate the chair lifting rapidly. This lead to a wave travelling up the rod, but the wave equation was nonlinear and so a shock developed [shocks form when the solution tries to become multivalued. It’s like a wave breaking on the shore. See here for a simulation of the shock forming]. We then hypothesised that the shock might actually split the vertebrae.

We took this to the anatomist who wanted to test the theory. I asked him how he’d do this and he said that they strap a cadaver to a lift and dropped them. On stopping the lift suddenly they mimic the effect of an ejector seat and we can see what happens to the spine. He suggested that I come along to see how they do it, but I passed on that offer.

What has been your favourite experiment and what has been your favourite piece of mathematics?

Oh I don’t know. There have been so many and so diverse. I think animal coat patterns have been the most enjoyable. However, I’ve never thought that the model had anything to do with biology. It was phenomenological. I feel that the mechanochemical theory of morphogenesis (developed with George Oster from Berkeley) is much more relevant to biology since it made real biological predictions which were confirmed experimentally. Reaction-diffusion theory was taken over by mathematicians for the past 50 years: a morphogen was only found last year [click here to see my posts on Alan Turing’s chemical theory of morphogenesis].

In fact the person who should really be given credit for much of reaction-diffusion patterning is Daniel Thomas (university of Compiegne). He did experiments that produced reaction-diffusion spatial patterns, long before others in the early 1970s. It was his experimental reactions that I used for my animal coat patterning work. Yet no one has heard of him in the field, which is a real shame.

You are best known for being able to create models that are incredibly simple, yet are able to be strong enough to capture the relevant biology. How do you do it?

Well I would always start by talking to the biologist. Unless I get an intuitive argument to test from them I wouldn’t know what to do with the idea. I always want the mathematics to be as simple as possible. Then you can start adding in extra bits, if you need it to get closer to the biology.

In Oxford most of these interdisciplinary conversations have started as discussions over high table dinner in various Oxford colleges. So my advice on becoming a good mathematical biologist is to have haute cuisine dinners with as many interesting people as possible.

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Whilst Jim was in Oxford. Philip Maini got the chance to do a fuller interview that was recorded and is hosted by the Mathematical Institute of University of Oxford. It is called "Jim Murray - Reflections on a Life in Academia" and can be watched below.