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Abstract <p>Mathematical modeling of the dynamic oscillations in p53 response to DNA damage represents a significant area of research. Unlike conventional models that focus solely on reaction networks, this study incorporates two critical factors: the heterogeneity in cytokine concentration distribution of transcription factors and ubiquitin ligases between the nucleus and cytoplasm, and the time delay inherent in the negative feedback loop. Furthermore, a class of delayed reaction-diffusion models are developed to capture these dynamics. Using multi-scale analysis, we derive the amplitude equation of the system when a Hopf bifurcation occurs near the positive equilibrium, revealing rich spatiotemporal pattern dynamics. Our findings demonstrate that variations in time delay or diffusion parameters can induce periodic oscillatory solutions in both time and space, corresponding to supercritical (subcritical) Hopf and Turing bifurcations. Finally, numerical simulations are conducted to validate and further elucidate the theoretical results.</p> Graphical abstract <p></p>

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Oscillatory dynamics and regulatory mechanisms of the p53-Mdm2 reaction-diffusion systems driven by transcriptional time delay in DNA-damaged cells

  • 期刊论文

  • 发表日期：

    2026年4月22日

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  • Jianfeng Jiao,
  • Ping Li,
  • Hongcui Chang,
  • Can Chen

摘要

Abstract

Mathematical modeling of the dynamic oscillations in p53 response to DNA damage represents a significant area of research. Unlike conventional models that focus solely on reaction networks, this study incorporates two critical factors: the heterogeneity in cytokine concentration distribution of transcription factors and ubiquitin ligases between the nucleus and cytoplasm, and the time delay inherent in the negative feedback loop. Furthermore, a class of delayed reaction-diffusion models are developed to capture these dynamics. Using multi-scale analysis, we derive the amplitude equation of the system when a Hopf bifurcation occurs near the positive equilibrium, revealing rich spatiotemporal pattern dynamics. Our findings demonstrate that variations in time delay or diffusion parameters can induce periodic oscillatory solutions in both time and space, corresponding to supercritical (subcritical) Hopf and Turing bifurcations. Finally, numerical simulations are conducted to validate and further elucidate the theoretical results.

Graphical abstract