Mahaffy J M, Pao C V
J Math Biol. 1984;20(1):39-57. doi: 10.1007/BF00275860.
Two models for cellular control by repression are developed in this paper. The models use standard theory from compartmental analysis and biochemical kinetics. The models include time delays to account for the processes of transcription and translation and diffusion to account for spatial effects in the cell. This consideration leads to a coupled system of reaction-diffusion equations with time delays. An analysis of the steady-state problem is given. Some results on the existence and uniqueness of a global solution and stability of the steady-state problem are summarized, and numerical simulations showing stability and periodicity are presented. A Hopf bifurcation result and a theorem on asymptotic stability are given for the limiting case of the models without diffusion.
本文提出了两种通过抑制进行细胞控制的模型。这些模型采用了来自隔室分析和生化动力学的标准理论。模型包含时间延迟以考虑转录和翻译过程，以及扩散以考虑细胞中的空间效应。这种考虑导致了一个具有时间延迟的反应 - 扩散方程的耦合系统。给出了对稳态问题的分析。总结了关于全局解的存在性和唯一性以及稳态问题稳定性的一些结果，并给出了显示稳定性和周期性的数值模拟。对于无扩散模型的极限情况，给出了一个霍普夫分岔结果和一个关于渐近稳定性的定理。
