Project: Building a theoretical framework to understand multidrug adaptive therapy for neuroblastoma.
Supervisors: Dr Kenneth Y. Wertheim and Dr Matishalin Patel.
Deadline: 2nd October 2023.
Applications are invited for individuals to apply for a PhD and Graduate Teaching Assistant position in Data Science. Neuroblastoma is a paediatric cancer arising in the peripheral sympathetic nervous system. It is the most common extracranial solid tumour of childhood, accounting for around 13 % of paediatric cancer mortality. This project aims to build a theoretical framework to understand Neuroblastoma progression by combining evolutionary game theory, population dynamics, and agent-based modelling. In the first stage, the PGR will design pay-off matrices to represent hypothetical relationships between cytotoxic activity and drug resistance. In the second stage, the PGR will search for evolutionary stable strategies (unchanging clonal compositions) in the corresponding replicator equations. Linked together, the games represented by the matrices, specifically their sequences of evolutionary stable strategies, constitute specific adaptive therapies. The main objective is to generalise the findings about two drugs. As the number of strategies accessible to a population of neuroblastoma cells undergoes combinatorial explosion, how do the effective adaptive therapies change? The answers will be tested with more realistic models from eco-evolutionary dynamics. For example, the logistic equation can describe a tumour’s carrying capacity, thus modelling clonal competition for finite resources. These details will in turn be used to finetune the pay-off matrices. In the third stage, the PGR will fit the models to experimental data about the synergistic effects of rapid COJEC and ALK inhibitors, such as a study combining lorlatinib with chemotherapeutic agents. In addition, Dr Taschner-Mandl (CCRI, Austria) is using an imaging assay to assess the effects of various drug combinations on neuroblastoma cell viability. She has also collected data about the clonal compositions of neuroblastomas at different time points of the standard treatment protocol. After revealing which of the theoretical adaptive therapies are clinically relevant, the PGR will solve the control problem of finding the drug doses necessary for steering the population dynamics through each sequence of evolutionary stable strategies corresponding to a relevant case. In the final stage, the PGR will implement these drug schedules in a graph-structured agent-based model to study the interactions between adaptive therapies, the unique vulnerabilities of small populations, and spatial effects.
Applicants should have a minimum of a 2:1 in a mathematical subject, such as applied mathematics, theoretical physics, chemical engineering, biological/biomedical engineering, computer science, and systems biology. They must possess Python programming skills to support DAIM teaching. If a candidate lacks proficiency in Python but is proficient in another language such as MATLAB or R, they will be conditionally accepted, on the proviso they learn Python before commencing their PhD, and continue their learning on arrival. Familiarity with ordinary differential equations, evolutionary game theory, numerical methods, or machine learning is desirable. Knowledge of biology is not necessary, but an interest in it is important.
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