Berg Arthur, Li Ning, Tong Chunfa, Wang Zhong, Berceli Scott A, Wu Rongling
Center for Statistical Genetics, Pennsylvania State University, Hershey, PA, USA.
Methods Mol Biol. 2011;734:241-55. doi: 10.1007/978-1-61779-086-7_12.
Genetic networks underlying many biological processes, such as vertebrate somitogenesis, cell cycle, hormonal signaling, and circadian rhythms, are characterized by oscillations in gene expression. It has been recognized that the frequency and amplitude of gene expression oscillations vary among individuals and can be controlled by specific expression quantitative trait loci (eQTLs). In this chapter, we develop a dynamic model for mapping and identifying such eQTLs by integrating mathematical aspects of oscillatory dynamics into the functional mapping framework. The model can determine whether and how eQTLs regulate individual genes' activation kinetics and expression dynamics by estimating and testing Fourier series parameters for different eQTL genotypes. We incorporate a general autoregressive moving-average process of order (r,s), the so-called ARMA(r,s), to model the covariance structure for gene expression profiles measured in time course, broadening the applicability of the new dynamic model to mapping eQTLs in practice. The expectation-maximization algorithm (EM algorithm) was derived to estimate all parameters modeling the mean-covariance structures within a mixture model setting. Simulation studies were performed to investigate the statistical behavior of the model. The model will provide a powerful statistical tool for mapping eQTLs and their epistatic interactions that regulate oscillations in gene expression, helping to construct a regulatory genetic network for those periodic biological phenomena.
许多生物过程（如脊椎动物体节发生、细胞周期、激素信号传导和昼夜节律）背后的遗传网络具有基因表达振荡的特征。人们已经认识到，基因表达振荡的频率和幅度在个体之间存在差异，并且可以由特定的表达数量性状位点（eQTL）控制。在本章中，我们通过将振荡动力学的数学方面整合到功能定位框架中，开发了一个用于定位和识别此类eQTL的动态模型。该模型可以通过估计和测试不同eQTL基因型的傅里叶级数参数，来确定eQTL是否以及如何调节单个基因的激活动力学和表达动态。我们纳入了一个一般的（r，s）阶自回归移动平均过程，即所谓的ARMA（r，s），来对在时间进程中测量的基因表达谱的协方差结构进行建模，从而拓宽了新动态模型在实际中定位eQTL的适用性。推导了期望最大化算法（EM算法），以估计混合模型设置中对均值 - 协方差结构进行建模的所有参数。进行了模拟研究以调查该模型的统计行为。该模型将为定位调节基因表达振荡的eQTL及其上位性相互作用提供一个强大的统计工具，有助于构建那些周期性生物现象的调控遗传网络。
