Philip Maini: Holding a mathematical lens to biological complexity
May 2, 2025 | Bharti Dharapuram
Philip Maini is a Professor of Mathematical Biology at the University of Oxford and the Director of the Wolfson Centre for Mathematical Biology. He uses mathematical models to understand biological processes such as embryogenesis, wound healing and cancer. On his recent visit to Chennai, he presented a public lecture on ‘A multi-disciplinary approach to understanding collective cell motion’ at IMSc. We caught up with him to speak about mathematical biology and the challenges of interdisciplinary research.
How did your interest in mathematics and mathematical biology develop?
In school, I specialised in mathematics, physics and biology when moving from O levels to A levels at 16 years of age. During the two years of my A level studies, I found that often the crucial information in one subject, such as simple harmonic motion in physics, can be encapsulated by a single equation in mathematics. I thought that was very beautiful. This inspired me to pursue mathematics at university.
At that time, I didn't know there was such a thing as mathematical biology, which wasn’t a well-known field in the 1970s. In the final year of my degree, I picked a course on differential equations and the lecturer was Jim Murray. I didn’t know at the time that he was a major leader in the field of mathematical biology. He motivated everything through ecology, epidemiology, physiology and biology, and that was the first time I was exposed to mathematical biology. Using mathematical models to understand how disease spreads or patterns form seemed very exciting to me so I did my doctorate with Jim.
One of the beauties of mathematics is that it is like an expert translator that can take information in one area of science and translate it to another.
In your talk, you gave an example of how model constraints can help us find new biological mechanisms. Can you elaborate?
Discovering new biology, to my mind, is the goal of a lot of the modeling that we do. We normally think in a very linear way but biology is much more complicated than that. And the complexity, with all its feedbacks, can only be understood through the language of mathematics. However, some of it can't be understood, even with present-day mathematics, because it is too complicated.
I always give the example of pattern formation by Alan Turing. We all know that diffusion destroys pattern. If you take a glass of water and pour a few drops of blue ink in it, you will initially see a nice pattern, which disappears after a while to give pale blue water. But Turing comes along and says that patterns on animals form by diffusion. He showed that our intuition based on a single chemical is an outlier. As soon as you have more than one chemical, diffusion can drive instability and give rise to patterns.
His model says that if you've got one chemical that activates itself and also activates another chemical that inhibits the activator then, under certain conditions, you can get patterns. This model has been validated experimentally in chemical systems and has stimulated a lot of work in biology. Instead of fishing blindly, the model allows you to look for mechanisms in some informed way.
Mathematical intuition can help us understand how processes interact to produce what we see. Importantly, while processes may be different than those proposed, the abstraction of mathematics allows insights into how seemingly different biology can give rise to the same outcome. A nice example of this is Kondo and Asai’s work. They found that in the angelfish Pomacanthus, a new stripe emerges when existing stripes grow roughly twice the distance apart. This is consistent with Turing’s theory, which predicts that you get more complex patterns as the domain gets larger. Kondo spent years trying to find the chemicals underlying this and he just couldn’t. Instead, he found that it was actually the cells themselves that aggregated to form patterns rather than responding to chemical cues. But the mechanism used by the cells followed the same principles as the Turing model.
You ended your talk with a comment about our plans to fly to Mars but a lack of understanding of how cells travel a few micrometers. What did you mean?
It is amazing to think that, on the one hand, we have learnt how to propel ourselves thousands of miles away from Earth but, on the other hand, we don't understand the basic science of how cells move. How cells move determines key processes in embryogenesis, wound healing and disease.
It is also to show that biology is much more complicated than people realise. The average person on the street has no idea about the complexity of medicine or biology while they think it is amazing that we can fly an airplane. But, how a multitude of processes combine to produce a living organism and enable it to survive is orders of magnitude more amazing than a vehicle that can fly.
For example, I tell students about the diffusion length scale of oxygen, which is about five cell lengths, or a little larger than that because of facilitated diffusion. We've got over a trillion cells in our body and our blood vessels form a network that delivers oxygen to all these cells on a daily basis and for eighty years. How on earth does the system set itself up to have the right distance apart from each blood vessel so that every cell can get a bit of oxygen? You think it just happens, and then you realise all the different things that make it happen. It is incredible!
How do you find a common language to communicate with your collaborators in biology?
There are two collaborations I have had that have been the most fruitful. The one on neural crest cell biology was with Paul Kulesa [who very sadly passed away this March], who was trained as an engineer and did a doctorate in mathematics. Frustrated that nobody was testing the predictions of his mathematical models, he learnt biology to do the experiments. Paul already knew what mathematics can and cannot do and where a mathematical model might help. Likewise with Bob Gatenby who studies mathematical oncology. He was a physicist who went into medicine and became a clinician. As with Paul, the common language was already there.
There are doctoral training centers in the UK, which are now called Landscape Awards. I am involved in one called the Interdisciplinary Life and Environmental Sciences Landscape Award (ILESA). Students apply to come into the program under different themes, including some in mathematical biology. In this program, students are taught modules in basic science in the initial period to establish a common language amongst everybody before they start their doctoral projects. I have noticed that when mathematicians coming from these programs read biological papers, they have more of an insight into how to interpret and critique the results instead of taking them at face value.
Has funding been a challenge in your area of research?
There are challenges in that many of the usual funding avenues in mathematics mainly look for mathematical advances. They see if you are coming up with new mathematics, and the biological funding agencies look for novelty in experimentation. Another thing I would like to point out is that in interdisciplinary proposals, each discipline has only half the space to present the problem and expertise. So you have to miss out on several details and are already at a disadvantage as the reviewers from each field flag this missing information.
When everyone was kicking up a fuss about this in the early 90s, the two main funding bodies in the UK said that they would have a joint program where they would look for the novelty in bringing mathematics and biology together. That worked brilliantly and was a great success. But they scrapped it five years later because a new set of people came in and wanted to show that they are doing something different. But it is getting a bit easier now because there are programs that will put forward a theme and you can apply if your ideas fall within that theme.
What are you excited about going ahead?
One of the exciting things is phenotypic heterogeneity, the fact that cells are dynamic and can change their responses. It opens up a lot of richness in the behaviour of systems and mathematics is beginning to uncover this. Another area is the spatial analysis of transcriptomics data and trying to see if you can make predictions from a spatial perspective. The problem I am thinking of is in terms of things like cancer, but you can imagine many different areas including embryogenesis.
Do you have any advice for young researchers looking to pursue interdisciplinary research?
There is far more interdisciplinarity in industry now, where it can actually be a positive to have done a bit of mathematics and a bit of experimental work and be able to combine the two. I think that in most academic institutions you probably still have to sell yourself as being a mathematician or a biologist. If you want to find a faculty position in mathematics and spend half your time in mathematics and half the time in biology, then you are competing with someone who spends all their time doing mathematics.
Maybe you should still specialise in one discipline, either as an experimentalist or a mathematician. It is difficult to be an expert in one subject, let alone two. You may want to be an expert in one of the subjects but speak the language of the other and collaborate with an expert in the other field. I would advise that you specialise in one area but be open to learning stuff in the other.
The other thing that I would like to say is do it for the enjoyment, because it is difficult. In the early days, there certainly was a lot of antagonism towards interdisciplinary research in mathematical departments. Pioneers like Jim Murray got a lot of criticism from colleagues. I got quite a bit of criticism as well. I think it is a part of human nature that if you see somebody who is different from you–think of racism–you think they are not as good as you. But there is a bit less of that now and it is safer going in. And the real enjoyment of your work more than compensates for the difficulties.
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