Functional mapping of expression quantitative trait loci that regulate oscillatory gene expression.

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.