Name: Professor Reidun Twarock

Job Title: Professor of Mathematical Biology

Organisation: University of York

Qualifications: MSc in Mathematics; PhD in Mathematical Physics (both with distinction)

You have recently won the IMA Gold Medal for your work in Mathematical Virology.  Can you tell us a bit more about your research?

My research focuses on using mathematics to help solve problems in the study of viruses (virology). My techniques have contributed to important advances in our understanding of how viruses form, evolve and infect their hosts.

Most viruses have icosahedral symmetry, which means their symmetry is like that of an icosahedron which is a regular solid shape with 20 faces.

Figure 1: An icosahedron

Understanding the symmetries of icosahedral viruses has helped to develop new strategies to combat these viruses. In particular, I introduced Viral Tiling theory to explain the structures of cancer-causing viruses, and my mathematical results have also led to new applications in nanotechnology, for example in the context of malaria vaccines.  It is a really exciting time to work in this area!

What do you think is your most exciting or important discovery so far?

My work on virus structure has given a new insight into the lifecycle of viruses, and this could only have been achieved using viral geometry. A very exciting result is the discovery of the “virus assembly code”, a cryptic instruction manual contained within the genetic message of a virus, which has overturned what we thought we knew about how viruses assemble themselves.

How did you become interested in mathematical biology/virology?

My research career started in Mathematical Physics, but then in 2002 I attended a talk about icosahedral viruses and realised that my mathematical techniques could be useful in this area. The following summer, I had the opportunity to visit virologist Lars Liljas and he drew my attention to the structural puzzle of the cancer-causing viruses.  That summer I started to tackle this problem by using the mathematics of non-crystallographic symmetries and aperiodic tilings, and this was the beginning of Mathematical Virology.

Explain what you do on an average day at work.

There is no average day – luckily! Since last summer I am an EPSRC Established Career Fellow, which means that I currently don’t have any teaching commitments. But that doesn’t make my day any less busy. Running a large interdisciplinary team, whilst also pursuing research projects with many other colleagues across different countries and disciplines, guarantees that every day is eventful and fun. I love being hands on in my projects, and this can involve anything from mathematical work on paper, computational work, the writing up of results for publication, or the planning of new projects. Communication with project partners is important, and there is at least one call or Skype session with collaborators every day.

The mentoring of junior colleagues and research staff is also very important to me, and I take an active role in helping them to move forward in their careers.  Sometimes I also work on outreach activities with artists. For example, we are working with a team of computer artists at Goldsmiths, to create virtual models of virus structure based on our research.

Figure 2: A) A tiling model explaining the structure of the cancer-causing papillomavirus. B) A Hamiltonian path that has played a central role in understanding how viruses form. C) A nanoparticle used in vaccine design can be characterised using tiling theory.

The joy of solving mathematical puzzles, and creating mathematical concepts and approaches which can lead to discoveries in biology. I love taking a difficult biological question and using mathematics to solve a problem which seemed intractable.

What stimulated your interest in maths, and when?

I have been fascinated by shapes and numbers from a very early age. Apparently, I had a secret arrangement with children attending a nearby school to do all their maths homework, until I was found out… and told off! Generally, pursuing mathematics and solving puzzles makes me profoundly happy… I just cannot imagine a life without mathematics!

As long as I can remember I wanted to be a mathematician, apart from a short spell thinking about a career as a ballet dancer. However, when I told friends and family that I was going to study mathematics at university I was warned that this would mean I would eventually be without a job… But I just loved mathematics way too much to care – luckily!

Which skills do you consider to be essential for your job?

Mathematical creativity, analytical and lateral thinking, a joy of puzzles, and keeping going in the face of difficult problems are all equally important in my view. I often come across people thinking that creativity is more important in the arts than in science and mathematics. This could not be further from the truth!

In addition, the ability to communicate with people who work in different areas, curiosity, and intuition for biological concepts, are all vital for work in Mathematical Biology. As a leader of a large team, I also consider interpersonal skills and empathy for the people working with me as absolutely essential.

Do you have any advice for other individuals who are considering working as mathematical biologists?

Do come and join the party – it’s a wonderful career! There are so many exciting open problems where mathematics can make a real difference in our understanding of biology, and where biological questions can spur the invention of new mathematical concepts and approaches.

Do you think that mathematical biology will continue to grow in the future?

Absolutely. We are only beginning to see the enormous contributions that mathematics will make in biology in future.

It is so exciting to be part of these developments at this important time – the journey has only just begun…

Featured image: Image from page 271 of ”Elements of biol” (Public Domain) by Internet Archive Book Images