Tell us about your research
I am particularly interested in the mathematical modelling of biological systems. I have a deep interest in uncovering unifying principles which are able to explain properties and patterns emerging from the observation of biological systems. In doing so, I use tools borrowed from mathematics and physics.
How does your research bring together different disciplines?
I am a physicist by training, and when I was a PhD student I started studying some biology and ecology, which showed me that there are important unsolved problems that biologists and ecologists are not able to solve, simply because they do not have the necessary tools. On the other hand, physicists and mathematicians can make biology and ecology more quantitative and help in turning them into a more predictive science.
What is your background and how did you come to be involved in interdisciplinary research?
My PhD is in theoretical physics. I studied non-equilibrium statistical mechanics and stochastic processes, and during my PhD I realized that such tools could have been applied to many different areas in which traditional approaches have not much to say. So I started studying systems with many interacting species and tried to come up with models that were able to quantitatively explain their behaviour, at least under some interesting regimes.
Can you tell us about noteworthy discoveries you have made?
I mention just two of them. I devised a model which is able to predict the temporal evolution of ecosystems with hundreds of interacting species which live in tropical forests. This was also useful to understand how they react when they are affected by external perturbations. I also came up with a model that can predict how many species one can find in regions so large that cannot be exhaustively sampled, like the Amazon forest.
Have you been able to be involved in boundary-pushing research?
Yes. Several of my scientific contributions have been published in high profile journals such as Nature, Proceedings of the National Academy of Sciences USA, Review of Modern Physics and Physics Review Letters.
Why do you think interdisciplinary research is important?
Mathematics and Physics provide well-honed theories for shaping new concepts and structuring ideas, so that they can give us quantitative models that can be compared against empirical data.
Traditionally, Physics has largely tried to uncover the building blocks of nature, reducing complex features to its elementary elements and the simple rules which govern them. The reductionist approach has been highly successful; we know, for instance, that we are all made of the same basic building blocks, and the same fundamental forces act in the stars as well as in the living systems. This approach has strongly influenced life-science disciplines as well, including molecular biology, cell biology and genetics.
Over the last century, however, scientists have understood that living systems — from cells to tissues, from organs to organisms, from individuals to communities — involve a myriad of complex interactions over a large range of length, time and energy scales, which are highly intertwined. In such cases it is very difficult (or impossible) to identify the building blocks responsible for the emergent behaviour we observe. As a whole, a collection of elements may behave differently from its components, and a large scale pattern may be better explained in terms of such collections, instead of its basic building blocks.
Physics has developed a language for such “collective behaviour”, a conceptual system — complementing and strengthening the reductionist approach — which goes beyond the traditional quantities employed in the life-science disciplines. Scaling laws, phase transitions and non-equilibrium thermodynamics are becoming more and more common tools for describing collective organization, from living cells to social behaviour. Several fields of Mathematics provide rigorous methods and powerful theories which can underpin more general approaches and be fruitfully applied to many areas. Such broad methodologies are being used to describe processes from molecular level, up to large-scale patterns in ecological systems.
There are new fields which benefit from the mutual interaction between Physics and Mathematics on one hand, and biological sciences on the other. There are collaborative research programmes which commonly involve physicists, mathematicians and statisticians on one side, and biologists, ecologists and neuroscientists on the other.
These burgeoning approaches offer a great potential of innovation which industry is currently picking up (e.g., super-resolution microscopy, pathogen infection dynamics, magnetic resonance imaging, medical diagnostics…). Of course, this has triggered an increasing demand of new scientists with a cross-disciplinary training at the PhD level.
What interests you about interdisciplinary research?
Interdisciplinary research is a powerful source of new challenging problems that are usually as important as stimulating. Take the example of blood. The blood is a suspension of objects of various shapes and sizes. We know that red blood cells tend to migrate toward the centre of a blood vessel, whereas white blood cells and platelets are preferentially found near the walls. This phenomenon is called “margination” and is critical for some physiological responses. Even drug delivery is affected by margination in the bloodstream, but it is currently unknown how these phenomena influence the efficacy of drug particles. To answer such important questions it is essential to study fluid dynamics and apply its equations within a biological context. Biologists carry out experiments that are crucial to understand the correct regimes in which such equations have to be applied, and such specific regimes may stimulate the development of new theoretical tools in fluid dynamics to solve the biological problem at hand. In turn, the new mathematical techniques may reveal new and unexpected biological features of the components of blood that can be exploited to deliver efficiently drugs in the body.
This cycle or feedback between two fields is quite paradigmatic in interdisciplinary research and is a source of reciprocal improvement.
What is the Astbury Centre and how does it facilitate interdisciplinary research?
There are mathematicians in our School that use the Astbury Centre’s facilities to better understand biomolecules. These are molecules that are much larger than the atomic scale, but they are still affected by thermal fluctuations.
Why is interdisciplinary research strong at Leeds?
In the School of Mathematics we have several strong groups which build bridges between two or more different research fields. The Mathematical Biology and Medicine Group, which I belong to, is one of them.
Here are some examples. Statisticians study high-throughput genomic data to discover patterns in genomic profiles of cancer patients and discover genetic associations in complex diseases.
Some mathematicians of the group use models to study how the immune system works in health and disease. For instance, we know that the immune system is able to identify infectious organisms by recognising specific molecules of the pathogens. This is mediated by the so-called T cells, which are lymphocytes circulating in the blood. These cells can be grouped into a huge variety of distinct families, which are essential to combat pathogens. Mathematicians, in collaboration with immunologists, try to model how a healthy adult human is able to maintain such crucial diversity for years.
There are physicists and mathematicians who study macromolecules important in biology. These are much larger than a single atom, but still small enough to be affected by thermal fluctuations.
Finally, other physicists and mathematicians, including myself, try to understand, among other things, the mechanisms allowing the maintenance of species coexistence. In fact, there are biological theories which suggest that, in a given location, only one species should survive in the long run, because locally resources are finite. However, there exist communities with hundreds of species, from bacteria to tropical forests. How can that be? Evolutionary game theory and the theory of stochastic processes can help understanding the mechanisms of maintenance of biodiversity.
Nearly all these interdisciplinary researches have led to collaborations with industries, which are having an important impact on society. Our Mathematical Biology Group brings together researchers highly skilled in statistics, stochastic processes, evolutionary game theory, polymer science, condensed matter and statistical physics, and make use of a wide range of mathematical and computational techniques.
This century has seen a major expansion in interdisciplinary research, which was born to answer new pressing topical questions. Society has an urgent demand for scientists, trained up to the PhD level, who are problem solvers able to work in non-traditional multidisciplinary teams for tackling highly complex problems. Our School of Mathematics is at the forefront of such research and training.