Computational Challenges in Biochemical Networks: Multiscale Modelling and Inverse Problems

In the last 20 years, technologies have been developed which allow biologists to observe, in real time, the reactions which are occurring in a single cell. These new developments have the potential to give us a whole new understanding of how cells function. In particular, it gives us a tool with which we can make great leaps in our understanding of how our genes operate and affect the way cells behave, multiply, and die. The understanding of these mechanisms is key in developing treatments for conditions for when they go wrong, for instance in cancer. As such, this relatively young area of science could be very important for the future of the health of humankind.

The use of these technologies is increasing rapidly amongst biologists, but the problem remains as how best to interpret this data, and allow us to understand what we have observed. What is more, the observational methods are far from perfect, and are full of small errors which could cloud our conclusions. Therefore it is important that we understand the underlying mathematics within these problems, in a bid to extract as much reliable information from this data as possible.

The aim of this project is to study the mathematical theory behind, and develop new computer algorithms for, the analysis of this type of data. The Bayesian philosophy is a mathematical framework which allows us to not only identify likely biochemical mechanisms which could have caused the phenomena we observe in the experiments, but also to quantify how much we should believe our own results. This project will have significant impact on this area, and help to cement the UK's position as one of the leading places to conduct biological and pharmaceutical research, which plays such an important part in our economy. Furthermore, it will enhance the UK's reputation for high quality interdisciplinary applied mathematics research.

This project is motivated by a genuine need within the biotechnology sector to be able to process and make the best use of the huge amounts of data that are emerging from new technologies. The technologies in question allow biologists to observe the biochemical reactions which are occurring in a single cell, in real time. The analysis of this data is a crucial step in furthering our understanding of how our genes alter the way cells behave, proliferate, and die. A greater understanding of how things can go wrong in cells is key to the development of new treatments for a whole range of different conditions. What is more, it will aid the development of the science and technology behind individualised treatments for conditions such as cancer, leading to far better survival rates.

Therefore, this project has a clear objective in impact, in terms of helping biologists and pharmaceutical researchers to further their understanding of biological reactions and then go on to develop new treatments. This will lead to several significant benefits to the UK in the long term. New treatments will help people to live longer, healthier and more active lives in future generations. The average life expectancy in developed countries has soared in the last 100 years, not least because of the advances in healthcare and pharmaceuticals. In order for this improvement in the quality and length of people's lives to continue, we must continue to conduct cutting edge research in a range of disciplines, including the underlying mathematical problems, as in this project.

The pharmaceutical sector is a huge contributor to UK PLC. The UK has a strong record of cutting edge research into the development of new treatments and drugs. AstraZeneca and GlaxoSmithKline are two of the world leading pharmaceutical companies, both having originated, and with a strong continued presence, in the UK. Further to this, other multinationals such as Pfizer, Novartis, Hoffmann-La Roche and Eisai also have a major presence in the UK. In 2007, the pharmaceutical sector employed approximately 72,000 people, and generated £8.4 billion towards the UK's gross domestic product. The continued health of this sector in the UK is important for the future health of our economy, as well as the future health of the population. This project will contribute to the development of a new area of science which will help to secure the future of this vital part of our economy.

The scope of this project is not just limited to the applications mentioned above. The mathematical methodologies developed within the project can also be applied to a whole range of problems in science and engineering. Wherever we make observations to try to understand or quantify something, whether it be observations of an oil well, or the weather, or in an MRI scanner, the methods developed in this project will aid scientists to better understand what they are observing. The breadth of impact of this area of mathematics, called the study of inverse problems, is significant.