Mechanistic mathematical models of tumour/host interaction

Primary supervisor: Benny Chain, UCL

Secondary supervisor: Jo Spencer, King’s College London

Tertiary supervisor: Alessia Annibale, King’s College London

Project

The immune system plays a major role in regulating tumour growth, and can be effectively manipulated for therapeutic benefit. However, the interaction between tumour and host immunity remains incompletely understood. A better understanding is likely to contribute to improved strategies for immunotherapy, and also to improved immune-focused approaches to predict and monitor disease progression and therapeutic outcome. We and many others have contributed to creating large multi-modal data sets which capture different aspects of immunity within tumours e.g. T cell receptor repertoires (1), bulk and spatial transcriptomics and high parameter immunophenotyping (2) to define the intra-tumoural immune response in great detail. However, these data sets are invariably snapshots which define the tumour/host interaction at a single (or at best a few distinct) moments of time. The challenge is how to use this static data to infer the dynamics of tumour/host interactions. A well-established approach to this general challenge is to use mathematical modelling to capture the key parameters of the dynamics. Comparison of predictions of different models to static data can then be used to illuminate underlying dynamic features which are otherwise not observable. Mathematical modelling provides a rigorous and quantitative way to test our hypotheses on how complex biological processes work. This approach, based on branching process models of cancer evolution, has been very successful in identifying key features of cancer development (3) . However, the extension of the models to incorporate innate or adaptive immunity is still in its infancy (4) .

In this interdisciplinary project, the student will work with computational immunologists (primary supervisor), experimental immunologists with special expertise in spatial proteomics (secondary supervisor) and mathematicians (tertiary supervisor) to develop mathematical models which incorporate immunity into established models of cancer evolution. The student will start by implementing established cancer evolution models, focusing on non-small cell lung and colorectal cancer where enormous data sets of multi-region DNA sequence and epigenetics are already available to the supervisory labs. The branching models will be extended using graph-based evolutionary models (5) to incorporate immune selection, especially T cell immunity, leveraging the large available data sets on clonal T cell expansion collected by the primary supervisor. Once the preliminary models have been implemented, the project can develop in several directions. One option is to extend the models to incorporate spatial heterogeneity, leveraging the rapidly expanding sets of spatial transcriptomics and proteomics which are being generated. Bespoke datasets, designed to link and validate mathematical predictions and place them in the context of tissue microanatomy will be created using 10x Genomics Visium spatial transcriptomics and imaging mass cytometry. The migration of cells between tumour and blood (since matched blood samples are available) is also an important potential area of investigation. We envisage that the modelling will combine mathematical formulations with computational simulations and will be coupled with in situ validation. The project will provide a rare and exciting opportunity to train in cutting edge inter disciplinary research, at the interface of mathematics, computers, big data and the functional microanatomy of cancer.

Candidate background

This project would suit students with a degree in mathematics or computer science, who are keen to apply their knowledge to problems of fundamental biological and medical importance.

Potential Research Placements

1. Francesca Cicciarelli, King’s College London/ Francis Crick Institute
2. Trevor Graham, ICR
3. The Centre for Physical Life Science, King’s College London

References

1. Joshi, K., de Massy, M. R., Ismail, M., Reading, J. L., Uddin, I., Woolston, A., Hatipoglu, E., Oakes, T., Rosenthal, R., Peacock, T., Ronel, T., Noursadeghi, M., Turati, V., Furness, A., Georgiou, A., Wong, Y., Ben Aissa, A., Sunderland, M. W., Jamal-Hanjani, M., Veeriah, S., […] Chain, B. (2019). Spatial heterogeneity of the T cell receptor repertoire reflects the mutational landscape in lung cancer. Nature medicine, 25(10), 1549 – 1559. [link]
2. Bortolomeazzi, M., Keddar, M. R., Montorsi, L., Acha-Sagredo, A., Benedetti, L., Temelkovski, D., Choi, S., Petrov, N., Todd, K., Wai, P., Kohl, J., Denner, T., Nye, E., Goldstone, R., Ward, S., Wilson, G. A., Al Bakir, M., Swanton, C., John, S., Miles, J., […] Spencer, J. and Ciccarelli, F. D. (2021). Immunogenomics of Colorectal Cancer Response to Checkpoint Blockade: Analysis of the KEYNOTE 177 Trial and Validation Cohorts. Gastroenterology, 161(4), 1179 – 1193. [link]
3. Sottoriva, A., Kang, H., Ma, Z., Graham, T. A., Salomon, M. P., Zhao, J., Marjoram, P., Siegmund, K., Press, M. F., Shibata, D., Curtis, C. (2015). A Big Bang model of human colorectal tumor growth. Nature genetics, 47(3), 209 – 216. [link]
4. Łuksza, M., Sethna, Z. M., Rojas, L. A., Lihm, J., Bravi, B., Elhanati, Y., Soares, K., Amisaki, M., Dobrin, A., Hoyos, D., Guasp, P., Zebboudj, A., Yu, R., Chandra, A. K., Waters, T., Odgerel, Z., Leung, J., Kappagantula, R., Makohon-Moore, A., Johns, A., […] Balachandran, V. P. (2022). Neoantigen quality predicts immunoediting in survivors of pancreatic cancer. Nature, 606(7913), 389?395. [link]
5. Hathcock, D., & Strogatz, S. H. (2019). Fitness dependence of the fixation-time distribution for evolutionary dynamics on graphs. Physical review. E, 100(1-1), 012408. [link]