Mathematical models of receptor mediated processes in vascular endothelial cells.

I present in this thesis a wide analysis of stochastic and deterministic models of the vascular endothelial growth factor (VEGF) and vascular endothelial growth factor receptor (VEGFR) on human umbilical vein endothelial cells (HUVEC).
Firstly, the analysis addresses the contribution of ligand induced dimerisation, receptor competition between VEGFR1 and VEGFR2 and immediate or delayed dimers phosphorylation in the overall behaviour of the VEGFR/VEGF system. The analysis is based on van Kampen approximation of the solution of the corresponding master equations and
matrix-analytic techniques to analyse different signalling hypotheses upon ligand stimulation.
Secondly two mathematical models are provided, with accompanying quantitative experimental data, for binding and trafficking properties of VEGFR on HUVECs, which propose a theoretical dependence of ERK phosphorylation and transport rate of receptors from the Golgi to the cell surface on these properties. The signal for ERK phosphorylation or perturbation of transport rate is generated by intrinsic VEGFR tyrosine kinase activation via VEGF binding at the cell surface, and terminated by receptor/growth factor complex internalisation and degradation. Presented in this thesis models consist of kinetic equations which describe the binding, internalisation, recycling and synthesis of VEGF and VEGFR, along with a simple expression for the dependence of ERK phosphorylation or receptor synthesis on
VEGFR/VEGF dynamics.