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Spatio-Temporal Modelling of the p53–mdm2 Oscillatory System

K. E. GordonI. M.M. van LeeuwenS. LaínM. A.J. Chaplain — 2009

Mathematical Modelling of Natural Phenomena

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...

Modelling the Impact of Pericyte Migration and Coverage of Vessels on the Efficacy of Vascular Disrupting Agents

S. R. McDougallM. A.J. ChaplainA. StéphanouA. R.A. Anderson — 2010

Mathematical Modelling of Natural Phenomena

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...

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