The Goodwin model: behind the Hill function.
The Goodwin model: behind the Hill function.
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DOI：
10.1371/journal.pone.0069573
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发表时间：
2013
期刊：
影响因子：
3.7
通讯作者：
Abou-Jaoudé W
中科院分区：
文献类型：
--
作者：
Gonze D;Abou-Jaoudé W
Goodwin模型是一个3变量模型，展示了在分子水平上基于延迟负反馈的系统中振荡的出现。这种原型模型及其变体通常用于模拟生物学中的昼夜节律和其他遗传振荡。该模型中非线性的唯一来源是表征抑制过程的希尔函数。数学上表明，要获得极限环振荡，希尔系数必须大于8，这个值通常被认为是不现实的。确实很难用简单的合作动力学来解释如此高的系数。我们在此提出了标准Goodwin模型的分子模型，该模型基于转录因子的单位点或多位点磷酸化/去磷酸化过程，这些过程先前已被证明可以产生类似开关的反应。我们发现，当磷酸化/去磷酸化过程足够快时，以多位点磷酸化为基础的机制获得的极限环与古德温模型中观察到的振荡在定量上非常一致。给出了古德温模型能很好地近似详细机理的条件。Goodwin模型的一个变体显示出急剧的阈值和弛豫振荡，也可以用双稳态行为的双重磷酸化/去磷酸化机制来解释。这些结果不仅为古德温模型提供了合理的支持，而且突出了翻译后过程的速度在生化振荡中的关键作用，而翻译后过程的响应曲线通常是在稳态下建立的。
The Goodwin model is a 3-variable model demonstrating the emergence of oscillations in a delayed negative feedback-based system at the molecular level. This prototypical model and its variants have been commonly used to model circadian and other genetic oscillators in biology. The only source of non-linearity in this model is a Hill function, characterizing the repression process. It was mathematically shown that to obtain limit-cycle oscillations, the Hill coefficient must be larger than 8, a value often considered unrealistic. It is indeed difficult to explain such a high coefficient with simple cooperative dynamics. We present here molecular models of the standard Goodwin model, based on single or multisite phosphorylation/dephosphorylation processes of a transcription factor, which have been previously shown to generate switch-like responses. We show that when the phosphorylation/dephosphorylation processes are fast enough, the limit-cycle obtained with a multisite phosphorylation-based mechanism is in very good quantitative agreement with the oscillations observed in the Goodwin model. Conditions in which the detailed mechanism is well approximated by the Goodwin model are given. A variant of the Goodwin model which displays sharp thresholds and relaxation oscillations is also explained by a double phosphorylation/dephosphorylation-based mechanism through a bistable behavior. These results not only provide rational support for the Goodwin model but also highlight the crucial role of the speed of post-translational processes, whose response curve are usually established at a steady state, in biochemical oscillators.
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