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Over the past decade or so, there have been a large number of modelling approaches aimed
at elucidating the most important mechanisms affecting the formation of new capillaries
from parent blood vessels — a process known as angiogenesis. Most studies have focussed
upon the way in which capillary sprouts are initiated and migrate in response to
diffusible chemical stimuli supplied by hypoxic stromal cells and leukocytes in the
contexts of solid tumour...
In this paper we investigate the role of spatial effects in determining the
dynamics
of a subclass of signalling pathways characterised by their ability to
demonstrate
oscillatory behaviour. To this end, we formulate a simple spatial model of the
p53
network that accounts for both a negative feedback and a transcriptional delay.
We show that the formation of protein density patterns can depend on the shape
of the cell, position of the nucleus, and the protein diffusion rates. The
temporal...
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