"Vascular endothelial cells, that line blood vessels in mammals, make use of membrane-bound receptor molecules to bind extra-cellular molecules, such as growth factors, to regulate blood vessel development, new blood vessel sprouting, and vascular repair. While this vascular system is vital for the normal growth of tissue during development and wound-healing processes, it is also exploited by malign tumours through secretion of vascular endothelial growth factors that induce the growth of new blood vessels (angiogenesis), enhancing the perfusion of tumour mass. Moreover, imbalance in the regulation of this system has been linked to ocular and inflammatory disorders, ischaemic heart disease, neuro-degeneration, and other pathologies.This inter-disciplinary project aims to develop new stochastic mathematical models of the vascular endothelial growth factor receptor (VEGFR) and its binding to vascular endothelial growth factor, as well as receptor dimerisation, internalisation, signalling, trafficking, degradation, and subsequent regulation of endothelial cell fate. These models will be tested against experimental data obtained from the literature or generated within experiments to be designed and conducted during the execution of this project.The models will be constructed using a rule-based-modelling approach, analysed using Van Kampen’s system size expansion, and simulated using the Gillespie algorithm. Moreover, the models will be compared using a novel, sequential Monte-Carlo-sampling based Bayesian method that allows for the calculation of a posterior distribution over the models being compared, given the data.The insights derived from the analysis, simulation, validation and comparison of the stochastic models will advance our current understanding of the biology of the VEGFR receptor as one of the fundamental molecular mechanisms underlying blood vessel development, vascular repair and angiogenesis."