Computational Challenges in Biochemical Networks: Multiscale Modelling and Inverse Problems

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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.