Oscillations and DNA Repair in a Spatio-Temporal Model of the p53 Signalling Pathway

Division of Mathematics, University of Dundee, Dundee, DD1 4HN, UK.

^⋆ Corresponding author. E-mail: aterry.maths@outlook.com

Abstract

In mammalian cells, the p53 pathway regulates the response to a variety of stresses, including oncogene activation, heat and cold shock, and DNA damage. Here we explore a mathematical model of this pathway, composed of a system of partial differential equations. In our model, the p53 pathway is activated by a DNA-compromising event of short duration. As is typical for mathematical models of the p53 pathway, our model contains a negative feedback loop representing interactions between the p53 and Mdm2 proteins. A novel feature of our model is that we combine a spatio-temporal approach with the appearance and repair of DNA damage. We investigate the behaviour of our model through numerical simulations. By ignoring the possibility of DNA repair, we first explore the scenario in which the cell has a very inefficient DNA repair mechanism. We find that spatio-temporal oscillations in p53 and Mdm2 may occur, consistent with experimental data. We then allow p53 to be directly involved in repairing DNA damage, since experimental evidence suggests this can happen. We find that oscillations in p53 and Mdm2 can still occur, but their amplitude damps down quickly as the DNA damage is repaired. Finally, we find that a minor change to the location of the DNA damage can notably change the spatial distribution of p53 within the nucleus. We discuss the biological implications of our results.