Mathematical models of cellular dysfunction

Abstract

Mathematical models provide a framework to confirm or reject hypotheses via the generation of quantitative predictions and offer rich insights into the processes that drive complex biological phenomena. In this thesis, we develop mathematical models that integrate experimental data and use these models to explore cellular dysfunction at different scales. The core of this thesis focuses on the selection of high-avidity T cells in cancer vaccines. High-avidity T cells, unlike low-avidity T cells, are adept at killing cancer cells and are essential for durable anti-tumour immunity. Using an ordinary differential equation (ODE) model, we show that we can optimise dosages to elicit high-avidity T cells. We find that increased numbers of immune cells known as immature dendritic cells, can also promote high-avidity T cells. We then reduce the complexity of our model and perform a thorough sensitivity analysis. We then study how immune cells regulate PD-L1 in the tumour niche. PD-L1 is an immunosuppressive molecule that tumours upregulate. Intriguingly, PD-L1 expression does not always correlate with tumour progression. To understand why we develop an ODE model that we calibrate to in vitro data. Using this model, we show that PD-L1 expression equilibrates in response to changes in immune activity via a feedforward circuit. This finding explains why some patients may respond to therapies targeting PD-L1 despite being PD-L1 negative. The last part of this thesis tests whether the spatial arrangement of cardiac mitochondria affects bioenergetics, as speculated by scholars. To test this, we develop an agent-based model of mitochondrial structure linked to a validated model of energy production and show that cardiac bioenergetics are robust to changes in fission and fusion over a physiological range. This thesis contains several foundational models. We expect the findings from this thesis to be a starting point for further interdisciplinary modelling and experimental work