Biomathematics: the great frontier of the 21st century?

Once upon a time, biology meant zoology and botany, the study of animals and plants. The invention of the microscope shifted the emphasis to the level of cells, and more recently the focus has been at the molecular level. Traditionally, the life sciences were attractive for young people who were passionate about science but who disliked mathematics or felt they were not good at it. But mathematics now plays a vital role in biology, and students need mathematical skills.

Biological systems are hugely complex, but simple mathematical models can isolate and elucidate key elements and processes and predict crucial aspects of behaviour. Many problems in biology have been solved using mathematics already developed in other areas – network analysis, group theory, differential equations, probability, chaos theory and combinatorics – but completely new mathematical techniques may be required to solve some tough problems in the life sciences.

The shape of a protein is an essential factor in determining its functions. For example, haemoglobin has a complex folded shape that enables it to “pick up” an oxygen molecule and “drop it” where it is needed. The folding and tangling of protein molecules is being modelled using the branch of topology called knot theory.

Complex behaviour

Network analysis shows us that a large network of simple components – whether transistors or neurons – can exhibit astonishingly complex behaviour. The human brain has 100 billion nerve cells, linked together by a biological wiring system of axons and dendrites. The number of interconnections is vast, something like a thousand million million. This is “big data” with a vengeance.

One simple element can do little. Link a large number together and you can get fantastically complex behaviour. For the brain, this includes thinking. Many questions in neuroscience remain to be answered, such as "how does memory work?" How is information from the senses interpreted and stored? Bio-informatics deals with the enormous data sets produced in biological research.

Systems biology is a rapidly developing interdisciplinary field of biological research. It focuses on complex interactions using a holistic approach aimed at discovering and understanding emergent properties of organisms. Such properties are difficult or impossible to understand using a reductionistic approach – breaking them down into basic constituents. Systems biology makes extensive use of mathematical and computational models.

Body networks

The communication networks in the human body involve millions of interlinked cells. Occasionally, these networks break down, causing diseases such as cancer. Systems Biology Ireland, at UCD, is designing new therapeutic approaches based on a systems-level, mechanistic understanding of cellular networks. Researchers at Systems Biology apply mathematics and computer science to enormous data sets arising from biological techniques. Their research aims to find out what genes do, how they work together, what goes wrong in diseases, and how to cure them.

Just as astronomy gave rise to spectacular developments in mathematical analysis in the 18th century, biology may have a profound effect on mathematics in the future. Some commentators see biomathematics as the great frontier of the 21st century, and argue that by 2100 biology and mathematics will have changed each other dramatically, just as mathematics and physics did in earlier centuries.

Peter Lynch is professor of meteorology at University College Dublin. He blogs at thatsmaths.com