拟南芥开花时间基因调控网路模型的比较研究

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背景：在拟南芥中,已经研发了几个光诱导花转变过程的基因调控网络的动态模型，它们可以刻画基因转录的行为，并基于实验观测的资料进行预测。已经证明，这些模型可以做出准确的和新颖的预测，产生可以检验的假设。本研究将解决两大问题。首先，建立基因调控网络的动态模型需要使用包括大量的参数的数学方程。第二，建立模型时，转录因子与DNA的结合机制需要详细考虑。第一个问题采用优化算法来解决。第二个问题需要比较三个替代的建模方法，即S-系统、米氏模型和质量作用模型。使用最小均方误差（O （ P） ）、平均相对误差（ MRE）和赤池信息准则（ AIC ）对参数估计的效率和模型性能进行评价。

结果：我们比较了3个描述拟南芥开花转型过程的基因调控模型。质量作用模型最简单的且参数最少。因此，使用最小AIC值法，计算量最少。缺点是它假设系统是一个简单的二级反应，这不符合我们的研究情况。米氏模型假设系统是同质的，而忽略了细胞内蛋白质的运输过程。S -系统模型表现最好，而且描述了扩散效应。S-系统的一个缺点是它含有大量参数。最大的AIC值也意味着在参数估计过程中出现过度拟合。

结论：三种动态模型描述了拟南芥开花转型过程的基因调控网络的动态。根据MRE、最小平方误差和全局灵敏度分析，S-系统表现最佳。但是，它具有最高的AIC值，表明在参数估计过程中可能会出现过度拟合。在模拟复杂的基因调控网络时，需要仔详细地使用本研究结果。

A model comparison study of the flowering time regulatory network in Arabidopsis

Wang CC, Chang PC, Ng KL, Chang CM, Sheu PC, Tsai JJ.

Abstract
BACKGROUND:
Several dynamic models of a gene regulatory network of the light-induced floral transition process in Arabidopsis have been developed to capture the behavior of gene transcription and infer predictions based on experimental observations. It has been proven that the models can make accurate and novel predictions, which generate testable hypotheses.Two major issues were addressed in this study. First, construction of dynamic models for gene regulatory networks requires the use of mathematic modeling that comprises equations of a large number of parameters. Second, the binding mechanism of the transcription factor with DNA is another factor that requires detailed modeling. The first issue was tackled by adopting an optimization algorithm, and the second was addressed by comparing the performance of three alternative modeling approaches, namely the S-system, the Michaelis-Menten model and the Mass-action model. The efficiencies of parameter estimation and modeling performance were calculated based on least square error (O(p)), mean relative error (MRE) and Akaike Information Criterion (AIC).
RESULTS:
We compared three models to describe gene regulation of the flowering transition process in Arabidopsis. The Mass-action model is the simplest and has the least parameters. It is therefore less computation-intensive with the smallest AIC value. The disadvantage, however, is that it assumes the system is simply a second order reaction which is not the case in our study. The Michaelis-Menten model also assumes the system is homogeneous and ignores the intracellular protein transport process. The S-system model has the best performance and it does describe the diffusion effects. A disadvantage of the S-system is that it involves the most parameters. The largest AIC value also implies an over-fitting may occur in parameter estimation.
CONCLUSIONS:
Three dynamic models were adopted to describe the dynamics of the gene regulatory network of the flowering transition process in Arabidopsis. Based on MRE, the least square error and global sensitivity analysis, the S-system has the best performance. However, the fact that it has the highest AIC suggests an over-fitting may occur in parameter estimation. The result of this study may need to be applied carefully when modeling complex gene regulatory networks.