Zhang Qi, Yu Yao, Zhang Jun, Liang Hua
Department of Statistics, Qingdao University, Qingdao, China.
Department of Biostatistics and Computational Biology, University of Rochester School of Medicine and Dentistry, Rochester, New York, United States of America.
PLoS One. 2018 Feb 23;13(2):e0192833. doi: 10.1371/journal.pone.0192833. eCollection 2018.
With the development of biotechnology, high-throughput studies on protein-protein, protein-gene, and gene-gene interactions become possible and attract remarkable attention. To explore the interactions in dynamic gene regulatory networks, we propose a single-index ordinary differential equation (ODE) model and develop a variable selection procedure. We employ the smoothly clipped absolute deviation penalty (SCAD) penalized function for variable selection. We analyze a yeast cell cycle gene expression data set to illustrate the usefulness of the single-index ODE model. In real data analysis, we group genes into functional modules using the smoothing spline clustering approach. We estimate state functions and their first derivatives for functional modules using penalized spline-based nonparametric mixed-effects models and the spline method. We substitute the estimates into the single-index ODE models, and then use the penalized profile least-squares procedure to identify network structures among the models. The results indicate that our model fits the data better than linear ODE models and our variable selection procedure identifies the interactions that may be missed by linear ODE models but confirmed in biological studies. In addition, Monte Carlo simulation studies are used to evaluate and compare the methods.
随着生物技术的发展，对蛋白质 - 蛋白质、蛋白质 - 基因和基因 - 基因相互作用的高通量研究成为可能，并引起了极大关注。为了探索动态基因调控网络中的相互作用，我们提出了一个单指标常微分方程（ODE）模型，并开发了一种变量选择程序。我们采用平滑截断绝对偏差惩罚（SCAD）惩罚函数进行变量选择。我们分析了一个酵母细胞周期基因表达数据集，以说明单指标ODE模型的实用性。在实际数据分析中，我们使用平滑样条聚类方法将基因分组为功能模块。我们使用基于惩罚样条的非参数混合效应模型和样条方法估计功能模块的状态函数及其一阶导数。我们将估计值代入单指标ODE模型，然后使用惩罚轮廓最小二乘法程序来识别模型之间的网络结构。结果表明，我们的模型比线性ODE模型更适合数据，并且我们的变量选择程序识别出了线性ODE模型可能遗漏但在生物学研究中得到证实的相互作用。此外，蒙特卡罗模拟研究用于评估和比较这些方法。
