A dynamic p53-mdm2 model with delay kernel

TL;DR

This paper develops a dynamic model of the p53-mdm2 gene interaction incorporating delay kernels, analyzing how delays influence stability and oscillations, with numerical examples supporting the theoretical findings.

Contribution

It introduces a novel p53-mdm2 model with distributed delays and weak kernels, analyzing bifurcation behavior and stability in gene regulation dynamics.

Findings

Delay parameters induce bifurcations leading to oscillations.

Stability of gene activity depends on delay and kernel coefficients.

Numerical examples confirm theoretical bifurcation analysis.

Abstract

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 transcripion factors should explain the different stable or sometimes oscillatory gene activities characteristic for different tissues. In this paper, the dynamic P53-Mdm2 interaction model with distributed delays and weak kernel, is investigated. Choosing the delay or the kernel's coefficient 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.