A dynamic P53-MDM2 model with time delay

Specific activator and repressor transcription factors which bind to specific regulator DNA sequences, play an important role in gene activity control. Interactions between genes coding such transcription factors should explain the different stable or sometimes oscillatory gene activities characteristic for different tissues. Starting with the model P53-MDM2 described into [Mihalas GI, Simon Z, Balea G, Popa E. Possible oscillatory behaviour in P53-MDM2 interaction computer simulation. J Biol Syst 2000;8(1):21–9] and the process described into [Kohn KW, Pommier Y. Molecular interaction map of P53 and MDM2 logic elements, which control the off–on switch of P53 in response to DNA damage. Biochem Biophys Res Commun 2005;331:816–27] we enveloped a new model of this interaction. Choosing the delay as a bifurcation parameter we study the direction and stability of the bifurcating periodic solutions. Some numerical examples are finally given for justifying the theoretical results.