Clustering Periodic Patterns of Gene Expression Based on Fourier Approximations

DNA microarray analysis has emerged as a leading technology to enhance our understanding of gene regulation and function in cellular mechanism controls on a genomic scale. This technology has advanced to unravel the genetic machinery of biological rhythms by collecting massive gene expression data during a time course. In this article, we have proposed a two-step procedure for clustering periodic patterns of gene expression in terms of different transcriptional profiles. In step 1, a least squares approach was used to estimate the coefficients that determine periodic gene expression profiles based on Fourier series approximation. In step 2, the estimated Fourier coefficients were employed to cluster genes into different expression patterns with a traditional clustering analysis and mixture model-based maximum likelihood method implemented with the EM algorithm. Applying our procedure to a case study published in Spellman et al. (1998), 632 cell-cycle regulated genes measured at a multitude of different time points were sorted into five distinct groups. The advantages of this procedure lie in the biological relevance of results obtained and the construction of a general framework within which the interplay between gene expression and development can be tested.