Perspective on mathematical biology - Going back to go forward

This post by the Director of the WCMB, Prof. Philip Maini, is an extended version of his recent article in the SMB Newsletter.

James D. Murray

This year marks the 30th anniversary of the Oxford Centre for Mathematical Biology (now renamed the Wolfson Centre for Mathematical Biology). Such landmark birthdays naturally make one pause for thought. The Centre was founded by Professor J.D. Murray, FRS. He was awarded a grant from the Science and Engineering Research Council (SERC) to set up a centre to promote mathematical biology in the UK. The freedom he was given is unimaginable in today’s government funding environment. Basically, if he came into contact with someone (via a conference or research paper) who looked interesting, he could invite them to come to Oxford and pay for them out of the grant.

Thirty years on and the Engineering and Physical Sciences Research Council (EPSRC – which is what SERC became) announced a new model for funding graduate studies in the UK, called Centres for Doctoral Training (CDT), with over 60 theme areas. The only one that contained the words “mathematics” and “biology” was the one: “New mathematics in biology and medicine”. To my mind, this totally misses the point as mathematics should be used to discover new biology and medicine and, in the process, inevitably new mathematics arises. The “winners” were announced three weeks ago and of the over 70 CDTs awarded, not one was for mathematical biology. So, is this a bad time for mathematical biology in the UK? One can argue both ways – several of the CDTs will implicitly use mathematical biology for applications in industry and healthcare, so does this mean that mathematical biology is now such an integral part of science that it does not need special treatment, or that it is having to be slipped in under the radar? Only time will tell, but the fact is that, just as the subject area is growing at its fastest rate, so the number of UK graduates in the subject will fall.

Both mathematics and biology have changed enormously over the past 30 years. For example, computing power has increased so much that one can do in seconds what would previously have taken months. At the same time, advances in biotechnology have led to huge amounts of data, and “big data” is the phrase everyone uses nowadays. However, mathematical biology has not kept pace with these advances. Why? I would argue that most data that are being generated are not appropriate for the sort of mathematical biology practised by the SMB community. We focus on mechanism and develop models that are typically spatiotemporal in nature, yet most data are static. This, I feel is one reason why we have been overtaken by bioinformatics where the methodology can use the data presently being generated and great advances have been made in this field. However, I feel that we are now on the threshold of very exciting times in mathematical biology, as advances in imaging and staining etc. now mean that, for the very first time, there is the chance that we will acquire the data that our models need.

To take full advantage of this new opportunity will, in many cases, involve us having to go back to go forward. Certainly in my area of mathematical biology (developmental biology, wound healing and cancer) many of the models proposed over the past 30 years were way beyond what could be verified experimentally and therefore they could not be validated. Now that they will, in principle, be verifiable, we must revisit them. This poses a challenge, as we are always under pressure to move “forward” in developing new mathematics, new models and collect new data. Under this system, funding to revisit old models would not be granted. But, we are the system, and we must do something about this!

There are many positives regarding mathematical biology. In more and more talks, it is becoming difficult to spot where the mathematics ends and the biology begins, such is the close integration. We also publish more in scientific journals, so that our work reaches the application areas. Certainly in many Mathematics Departments, this is very unusual, even for “applied” mathematics. The journal Cancer Research has several mathematical biologists on its Editorial Board.

Alexander "Sandy" R. A. Anderson

The Moffitt Cancer Center in Tampa has, within it, the Integrated Mathematical Oncology Department, chaired by Dr Sandy Anderson, a mathematician.They sit next to experimentalists and work closely with them. Then there is the recent appoint of Dr Kristin Swanson (a mathematician) as Professor in Neurological Surgery and Vice Chair of Research for Neurosurgery at the Northwestern School of Medicine.

Kristin R. Swanson

These are just two examples of the growing number of mathematical research groups embedded in medical schools/institutes, adding to the numbers embedded already in the more traditional haunts of physiology, zoology, ecology and epidemiology departments. In Europe, BIOMS in Heidelberg is just one of the growing numbers of institutes in which mathematicians and experimentalists work side by side. The subject is informing government strategies on epidemiology and general ecological management. Mathematical biologists are beginning to be invited to present at biology/medical/healthcare conferences and departments. In this day and age when there is so much political, as well as social, ignorance of relevance of mathematics in the real world, I think that the engagement of mathematical biology with the “user” partners (most mathematical biology is not done in mathematical departments) is an excellent riposte.

Then of course there is NIMBioS and the MBI, two centres that have greatly contributed to the growth of mathematical biology. I remember when I started as a graduate student in 1982, my supervisor, Professor Jim Murray, handed me a small number of papers and told me that I should be able to read them by Christmas and then I would basically be able to start research as I would know all the important literature. In those days, one was aware of everything going on in the subject. Now, it is impossible to keep up even in one’s own very specialised part of mathematical biology.

As well as being interdisciplinary, mathematical biology is becoming more intradisciplinary. For example, understanding network requires ideas from graph theory; work on viral capsids requires group theory; fitting models to data requires ideas from algebra, probability and statistics. Therefore I see a further exciting era of more pure mathematicians getting involved in mathematical biology. One of our responsibilities is to find a way to make this community aware of these exciting opportunities.

As the subject area continues to grow in breadth and depth there are inevitable questions about training. Should there be undergraduate degrees in mathematical biology, or is it at the graduate level, or postdoctoral level that a student should broaden out. I would say that for interdisciplinary research one should have at least a discipline and so it is at graduate level that one should begin interdisciplinary research, but I know many people who disagree with that, arguing that this is too late or, indeed, too early.

Then there is the question of at what level can the sort of mathematics we do be applied. My own approach more recently has been, by and large, to focus on a particular biological question that cannot be answered purely by experiment and then work closely with experimentalists in a predict-test-refine-predict iterative cycle. I have tried to resist the temptation to include too many things in the model as I feel that such models are difficult to parametrise and that it is also difficult to learn a great deal from them. The models that have been the most influential to date (for example, Lotka-Volterra, Fisher, Hodgkin-Huxley, Turing, to name only the classical ones) have all had few equations but have changed the way people think. Of course, this is an unfair comparison as these models have been around a lot longer than the more detailed models presently being developed. For example, some of the heart modelling is now being incorporated by some drug companies are part of their drug testing protocol. It remains to be seen how these more detailed models develop.

In my first year back in Oxford as a faculty member I was sitting at lunch one day and overheard a senior colleague paraphrasing Max Planck, “science advances one funeral at a time” (according to Wikiquote, the full statement is, “A new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die, and a new generation grows up that is familiar with it.”). I must admit that, at the time, this made no sense to me and I felt it totally irrelevance. Twenty- three years on, I think it is one of the most enlightened statements I have ever heard and it has become as sort of mantra – especially when faced with the sort of problems I mentioned at the beginning of this piece.

I think that the new generation of scientists coming into this field are more open and, while there undoubtedly are challenges in the immediate future (particularly of a financial kind faced by all of society, and caused by another field of mathematics), the fact that the number of people in the non-mathematical sciences who feel mathematics is important is growing, the future looks promising for our field.