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Professor Heather Harrington
University of Oxford
Philip Leverhulme Prize
2020

Applied mathematics: algebraic systems biology and topological data analysis

Heather Harrington’s advances in data analysis have led to new, robust methods for dealing with noisy data

Modern science generates data at an unprecedented rate. Many measurements often track multiple molecules or cells in time, and their location within a single tissue. In quantitative biology we seek to understand the processes that generate these data by exploring hypotheses that are articulated as mathematical models. The main focus of my research is to create a mathematical framework to understand large classes of models in different scenarios, and with varying amounts of data. Oxford is the ideal institution to carry out my research; it hosts world class mathematicians in algebra, topology, computation, data science, applied mathematics, as well as experimentalists.

One promising research direction is to combine algebra and topology for studying high-resolution spatio-temporal biological data and models. For example, as shown in Figure 1 above, in a collaboration between mathematicians and clinicians, we have been investigating the spatial organisation of different immune cells such as T cells and macrophages, and whether their location plays a role in the tumour microenvironment. We have two possible inputs into the data analysis pipeline (Fig. 1A): data simulated from a mathematical model (describing how immune cells infiltrate a tumour spheroid), or data from histology slides of immune cells in cancer. With noisy or mislabelled data, which is often the case in pathology, we showed that two parameters are needed to analyse the spatial patterns of immune cells using topological data analysis (a bifiltration, Fig. 1B). With this statistical topological data analysis pipeline, we found a significant difference in spatio-temporal data as model parameters changed, and validated existing trends of immune cell locations in the clinical data of head and neck tumours (see Figure 1C). Furthermore, we proposed that this bi-filtration is a good proxy for the oxygen level within the tissue. This is joint work with Oliver Vipond, Joshua Bull, Philip Macklin, Ulrike Tillmann, Christopher Pugh and Helen Byrne.

The Philip Leverhulme Prize will enable me to hire a research assistant to continue to explore new mathematical descriptions of biological mechanisms, and develop methods for integrating and analysing multiscale data with mathematical models. I also plan to support students interested in research careers at the interface between pure and applied mathematics by hosting the 2022 Summer session of Enhancing Diversity in Graduate Education in Oxford.

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