Spatio-Temporal Modelling of the p53–mdm2 Oscillatory System

¹ Department of Mathematics, University of Dundee, WTB/MSI-Complex, Old Hawkhill, DD1 5EH Dundee, Scotland, UK
² epartment of Surgery and Oncology, University of Dundee, Ninewells Hospital, DD1 9SY Dundee, Scotland, UK

Corresponding author: chaplain@maths.dundee.ac.uk

Abstract

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 changes in the total amounts of protein are also subject to spatial influences. The level of DNA damage required to induce sustained oscillations, for instance, depends on the morphology of the cell. The model also provides a new interpretation of experimentally observed undamped oscillations in p53 levels in single cells. Our simulations reveal that alternate sequences of high- and low-amplitude oscillations can occur. We propose that the digital pulses may correspond to snap-shots of our 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 spatial model.