MODELS OF GENETIC-CONTROL BY REPRESSION WITH TIME DELAYS AND SPATIAL EFFECTS
MODELS OF GENETIC-CONTROL BY REPRESSION WITH TIME DELAYS AND SPATIAL EFFECTS
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DOI：
10.1007/bf00275860
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发表时间：
1984-01-01
影响因子：
1.9
通讯作者：
PAO, CV
中科院分区：
文献类型：
--
作者：
MAHAFFY, JM;PAO, CV
本文提出了两种细胞阻遏控制模型。该模型使用来自房室分析和生化动力学的标准理论。这些模型包括考虑转录和翻译过程的时间延迟，以及考虑细胞中空间效应的扩散。这种考虑导致一个耦合系统的反应扩散方程的时间延迟。稳态问题的分析。总结了该问题全局解的存在唯一性和稳定性的一些结果，并给出了数值模拟结果，证明了该问题的稳定性和周期性。对于无扩散模型的极限情况，给出了Hopf分支结果和渐近稳定性定理。
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.