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Spatio-TemporalModelling of the p53–mdm2 Oscillatory System

Published online by Cambridge University Press:  05 June 2009

K. E. Gordon ,
I. M.M. van Leeuwen ,
S. Laín  and
M. A.J. Chaplain
K. E. Gordon
Affiliation:
Department of Mathematics, University of Dundee, WTB/MSI-Complex, Old Hawkhill, DD1 5EH Dundee, Scotland, UK
I. M.M. van Leeuwen
Affiliation:
Department of Mathematics, University of Dundee, WTB/MSI-Complex, Old Hawkhill, DD1 5EH Dundee, Scotland, UK epartment of Surgery and Oncology, University of Dundee, Ninewells Hospital, DD1 9SY Dundee, Scotland, UK
S. Laín
Affiliation:
epartment of Surgery and Oncology, University of Dundee, Ninewells Hospital, DD1 9SY Dundee, Scotland, UK
M. A.J. Chaplain*
Affiliation:
Department of Mathematics, University of Dundee, WTB/MSI-Complex, Old Hawkhill, DD1 5EH Dundee, Scotland, UK
*
chaplain@maths.dundee.ac.uk
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Abstract

In this paper we investigate the role of spatial effects in determining thedynamics of a subclass of signalling pathways characterised by their ability todemonstrate oscillatory behaviour. To this end, we formulate a simple spatial model of thep53 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. Thetemporal changes in the total amounts of protein are also subject to spatial influences. The level of DNA damage required to induce sustained oscillations, forinstance, depends on the morphology of the cell. The model also provides a newinterpretation of experimentally observed undamped oscillations in p53 levels in single cells.Our simulations reveal that alternate sequences of high- and low-amplitudeoscillations can occur. We propose that the digital pulses may correspond to snap-shots ofour high-amplitude sequences. Shorter waiting-times between subsequent time-lapse fluorescence microscopy images in combination with lower detection thresholds may reveal the irregular high-frequency oscillations suggested by our spatialmodel.

Keywords

tumour suppressorcancersignalling pathwaylimit cyclepulse
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 4 , Issue 3: Cancer modelling (Part 2) , 2009 , pp. 97 - 116
Copyright
© EDP Sciences, 2009

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