Thomas Reuben, Mehrotra Sanjay, Papoutsakis Eleftherios T, Hatzimanikatis Vassily
Department of Industrial Engineering and Management Science, Northwestern University, Evanston, IL 60208-3120, USA.
Bioinformatics. 2004 Nov 22;20(17):3221-35. doi: 10.1093/bioinformatics/bth389. Epub 2004 Jul 9.
Identification of the regulatory structures in genetic networks and the formulation of mechanistic models in the form of wiring diagrams is one of the significant objectives of expression profiling using DNA microarray technologies and it requires the development and application of identification frameworks.
We have developed a novel optimization framework for identifying regulation in a genetic network using the S-system modeling formalism. We show that balance equations on both mRNA and protein species led to a formulation suitable for analyzing DNA-microarray data whereby protein concentrations have been eliminated and only mRNA relative concentrations are retained. Using this formulation, we examined if it is possible to infer a set of possible genetic regulatory networks consistent with observed mRNA expression patterns. Two origins of changes in mRNA expression patterns were considered. One derives from changes in the biophysical properties of the system that alter the molecular-interaction kinetics and/or message stability. The second is due to gene knock-outs. We reduced the identification problem to an optimization problem (of the so-called mixed-integer non-linear programming class) and we developed an algorithmic procedure for solving this optimization problem. Using simulated data generated by our mathematical model, we show that our method can actually find the regulatory network from which the data were generated. We also show that the number of possible alternate genetic regulatory networks depends on the size of the dataset (i.e. number of experiments), but this dependence is different for each of the two types of problems considered, and that a unique solution requires fewer datasets than previously estimated in the literature. This is the first method that also allows the identification of every possible regulatory network that could explain the data, when the number of experiments does not allow identification of unique regulatory structure.
识别遗传网络中的调控结构并以线路图的形式构建机制模型,是使用DNA微阵列技术进行表达谱分析的重要目标之一,这需要开发和应用识别框架。
我们开发了一种新颖的优化框架,用于使用S系统建模形式识别遗传网络中的调控。我们表明,mRNA和蛋白质种类上的平衡方程导致了一种适合分析DNA微阵列数据的公式,其中蛋白质浓度已被消除,仅保留mRNA相对浓度。使用该公式,我们研究了是否有可能推断出一组与观察到的mRNA表达模式一致的可能的遗传调控网络。考虑了mRNA表达模式变化的两个来源。一个源于系统生物物理特性的变化,这些变化改变了分子相互作用动力学和/或信息稳定性。第二个是由于基因敲除。我们将识别问题简化为一个优化问题(所谓的混合整数非线性规划类),并开发了一种算法程序来解决这个优化问题。使用我们的数学模型生成的模拟数据,我们表明我们的方法实际上可以找到生成数据的调控网络。我们还表明,可能的替代遗传调控网络的数量取决于数据集的大小(即实验数量),但对于所考虑的两种类型的问题中的每一种,这种依赖性是不同的,并且唯一解所需的数据集比文献中先前估计的要少。这是第一种方法,当实验数量不允许识别唯一的调控结构时,它还允许识别每一个可以解释数据的可能的调控网络。