Mathematical modelling of cellular receptor-ligand dynamics

In this thesis, mathematical models are presented which are used to study cellular signalling pathways, initiated by the interaction between receptor molecules, residing on the surface of a cell, and ligand molecules, diffusing in the extra-cellular medium. Cell signalling pathways ultimately determine the fate of a cell, be it to divide, differentiate, migrate or even die, and the eventuality with occurs can be dependent on the receptor-ligand pairing. Different mathematical and statistical techniques are employed in this thesis, to study specific cell signalling pathways for which experimental data has been produced. Data collection has been carried out for such pathways due to their involvement in human disease when dysregulated, where disease progressions include autoimmune diseases and many types of cancer. As well as analysing mathematical models for specific pathways, new methodologies are developed in this thesis to analyse properties of a general model of the competition between multiple receptor types for a common ligand variety, which could be applicable to many cell types and signalling pathways. Both deterministic and stochastic models are used in this thesis, since the expression of different receptor and ligand types can be hugely variable, ranging from low copy numbers per cell, to very high copy numbers. This thesis aims to explore the role of receptors and ligands in different healthy and disease scenarios.