Monday, 19 May 2014

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.

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.

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.

Monday, 5 May 2014

Prof. James Murray FRS: The founder of mathematical biology in Oxford

Although in the last post I said I would discuss rotational symmetric Venn diagrams we're going to take a short break in order to bring you an interview with one of the greats of mathematical biology.

On Tuesday 4th of March Prof. Jim Murray FRS came to Oxford to deliver the first annual Hooke lecture. When it comes to mathematical biology Jim, quite literally, wrote the book. Two books in fact! Not only has he had an extremely varied, interesting and hilarious career (dealing with everything from marriage to cannibalism and even having time to win the University of St Andrews first blue in table tennis and was captain of the university’s billiard team) but he founded Oxford’s Centre for Mathematical Biology.

Although he had a packed schedule I managed to catch up with him for a quick interview about his work, hoping that I could try and glean what makes a great mathematical biologist. This week we get a little bit of his background and biography

How are you?
Doing fine, just not as physically active as I used to be.

Still active on the lecture circuit though?
Oh yes, I still do a bit of teaching in Princeton and give colloquia around. My mind is still very much active.

Could you give me a brief overview of your early academic career?
Figure 1. Jim Murray.
I started in Moffat, a very rural and isolated part of Scotland, where there was only one non private school and you only attended until you were 14. After that everyone left to get a job. However, there were two of us that went off to Dumfries Academy. At the end of my three years there were only two of us who went on to university. The number going on to higher education back then was minute.

I was actually the first person in St Andrews University to get a PhD in Applied Mathematics. My supervisor, Ron Mitchell, who was also a professional footballer (known as “Elbows” Mitchell), wanted me to do numerical analysis on shear flow past shapes and in pipes. It was all associated with how aeroplanes measure their speed. Thankfully, I wriggled out of that by obtaining analytical solutions.

Based on this I did a summer internship in an aircraft industry, Fairey Aviation Company, near London. I worked in the theoretical division, but they had me doing the most boring jobs you could imagine. No wonder the company went bust! So, I decided against going into industry.

So did you go through this knowing that you wanted to be an academic?
Oh no. It was simply that from having polio I knew I was never going to be a plumber. I remember our maths teacher coming around the classroom giving his opinion on whether we would be able to do maths at university and he said,
“No, no, no Murray. You’d never make it”.
Well, I didn’t know any better back then and, so, I started doing chemistry at St Andrews. Thankfully, in the Scottish system you didn’t have to specialise at the beginning, which was good, as I found the field to be totally unexciting. By the end of that year I switched to physics. However, I also found that to be boring. Alongside this I did keep up the mathematics and found I kept getting prizes and medals in it. This, of course, made me think that perhaps the teacher hadn’t been right.

What did you do after your PhD?
I actually finished my thesis and had it all approved after two years, but I couldn’t graduate until after the third year. Thankfully, the university let me take a job for that third year at King’s College in Newcastle (then part of Durham University). I then got a post-doc and later a lectureship at Harvard University.

I came back to England, to University College London and two years later was elected Mathematics Fellow in Hertford College, Oxford. I actually got the position by mistake. The college fellow in charge of the appointment was a physicist who said to me that any person who gets a strong recommendation from Goldstein, must be good. It turns out the Goldstein he was thinking of was not the same Goldstein that had written my reference!

Who have you really admired?
Oh there are so many. For example, many of my students and postdocs are now major international figures in the field of mathematical biology. Several of the people I’ve collaborated with such as Jeffries Wyman (a biologist) just missed getting a Nobel prize (his collaborators did, however). I’ve always thought of these people as friends rather than just collaborators. I’m particularly fond of my extended collaboration with George Oster (Berkeley) a close friend with whom I worked for several years with on the mechanochemical theory of biological development. There are, of course, many many others.
Next time we discuss Jim's mathematics. Trust me, this is something that you don't want to miss, as we will be discussing the relationship between mathematics and dropping corpses down lift shafts. Also Jim shares his secret on how to be a great mathematical biologist.

In the mean time you can watch Jim's Hooke lecture "Why there are no 3-headed monsters, resolving some problems with brain tumours, divorce prediction and how to save marriages" below. This was recorded and is hosted by the Mathematical Institute of University of Oxford.