目录
摘要Ⅱ
关键词Ⅱ
AbstractⅢ
引言
引言1
1文献综述1
1.1基础理论 1
1.2.1经典的Goodwin模型1
1.2.2多位点磷酸化2
1.2国内外研究进展2
1.3研究目标与意义3
1.3.1研究目标与意义3
1.3.2拟解决问题3
2方案论证3
2.1常微分方程3
2.2基因调控理论及振荡行为4
3过程论述 5
3.1 Goodwin模型与Hill函数5
3.1.1 详细的Goodwin模型5
3.1.2 平衡点及其稳定性6
3.1.3 酶守恒定律7
3.1.4 Hill函数8
3.2 Goodwin模型中的极限环振荡9
3.3多位点磷酸化10
4结果分析11
5讨论12
致谢13
参考文献13
附录A14
附录B15
附录C15
具有非线性降解率的Goodwin振子
摘 要
基因调控网络中普遍存在振荡现象，振荡组成了生命活动中大大小小的生物钟，包括生命周期以及其他有规律的周期性生命活动。Goodwin模型是研究基因振荡网络的经典模型之一，它是最简单的单基因自阻抑模型，内部系统是一个由三变量构成的负反馈系统，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。该原型模型及其变体已被普遍用于在生物中对生物钟和其他遗传振荡器进行建模。Griffith证明，该模型仅在Hill系数大于8时才会产生极限环振荡，而该阈值通常被认为是不现实的，因为在实际中很难解释如此高的Hill系数，所以Goodwin经常因为其合理性而受到质疑；生化反应繁多复杂，高的Hill系数很可能由其他因素造成，比如蛋白质磷酸化、时滞现象等。本文基于底物多位点磷酸化过程，建立修正的Goodwi *51今日免费论文网|www.51jrft.com +Q: *351916072* 
n振子模型。新模型仍然具有酶守恒律和底物产物守恒律。由于磷酸化速度足够快，拟平衡假设仍然可用。运用matlab和pathon定性分析和数值模拟证明，Hill系数低至4时，修正的Goodwin振子出现极限环振荡。因此，新的修正Goodwin振子模型更符合生物实际。
GOODWIN OSCILLATOR WITH NONLINEAR
DEGRADATION RATE
ABSTRACT
Oscillations are common in gene regulation networks. Oscillations constitute a large and small biological clock in life activities, including life cycles and other regular periodic life activities. The Goodwin model is one of the classic models for studying gene oscillation networks. It is the simplest singlegene selfsuppression model. The internal system is a threevariable negative feedback system that demonstrates a system based on delayed negative feedback at the molecular level The emergence of medium oscillations. The prototype model and its variants have been commonly used to model biological clocks and other genetic oscillators in biology. Griffith proved that the model will produce limit cycle oscillation only when the Hill coefficient is greater than 8, and this threshold is generally considered unrealistic, because it is difficult to explain such a high Hill coefficient in practice, so Goodwin often because of its rationality It is questioned; biochemical reactions are complex and complex, and the high Hill coefficient is likely to be caused by other factors, such as protein phosphorylation and time lag. In this paper, a modified Goodwin oscillator model is established based on the multisite phosphorylation process of the substrate. The new model still has the law of conservation of enzyme and the law of conservation of substrateproduct. Since the phosphorylation rate is fast enough, the pseudoequilibrium hypothesis is still available. Qualitative analysis and numerical simulation using matlab and pathon prove that when the Hill coefficient is as low as 4, the modified Goodwin oscillator has limit cycle oscillation. Therefore, the new modified Goodwin oscillator model is more in line with biological reality.

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