PhD Studentship: Applied Mathematics: Computational Modelling and Optimisation of Anti-body Drug Conjugates for Tumours

Anti-cancer drugs can be classified into small- and large-molecule drugs. One of the more complex types of novel anti-cancer drugs are antibody-drug conjugates (ADCs), in which several molecules of a cytotoxic drug are attached to an antibody via chemical linkers. The antibody component binds to the antigen on a tumour cell, after which the cytotoxic drug is released to kill the tumour cell. ADCs are designed to combine the tumour cell-killing effects of cytotoxic drugs with the targeted specificity of antibodies, to provide a more effective therapy. However, ADCs are challenging drugs to develop, because all of the features associated with the small- and large-molecule drug components must be optimised together. Computational mathematical modelling is used to make the optimisation of ADCs more efficient by identification of the critical processes and parameters. 

In this project, we aim to develop mathematical and computational models to predict the spatial distribution of concentrations of intact antibody-drug conjugates (ADCs) and released cytotoxic drugs over time in a tumour after dosing ADC to a patient, and how they relate to the spatial distribution of antigen in the tumour. The effect of the cytotoxic drug to kill tumour cells will be included to simulate the response of the tumour to ADC treatment. Stochastic or agent-based approaches will be used to describe the heterogeneity of antigen expression in the tumour. The models will be calibrated against pre-clinical data and compared to literature models that are based on ordinary differential equation systems without a description of spatial heterogeneity. Simulations and sensitivity analysis of the model will be used to identify optimum dosing schedules or ADC properties that maximise the anti-tumour response. 

This project is in collaboration with experts from AstraZeneca. 

The Departments of Mathematics is part of the Computational Foundry, a world-class centre for computational research, part-funded by the European Regional Development Fund through Welsh Government. The brand-new building of the Computational Foundry provides an ideal environment for doing a PhD.

Funding Comment: Covers full tuition, £20,780 stipend (2025/26), plus up to £1,000 yearly for research costs.

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