It is well accepted that genes are simultaneously involved in multiple biological processes and that genes are coordinated over the duration of such events. Unfortunately, clustering methodologies that group genes for the purpose of novel gene discovery fail to acknowledge the dynamic nature of biological processes and provide static clusters, even when the expression of genes is assessed across time or developmental stages. By taking advantage of techniques and theories from time frequency analysis, periodic gene expression profiles are dynamically clustered based on the assumption that different spectral frequencies characterize different biological processes. A two-step cluster validation approach is proposed to statistically estimate both the optimal number of clusters and to distinguish significant clusters from noise. The resulting clusters reveal coordinated coexpressed genes. This novel dynamic clustering approach has broad applicability to a vast range of sequential data scenarios where the order of the series is of interest. 1. Introduction Microarray and next-generation sequencing (RNA-seq) technologies enable researchers to study any genomewide transcriptome at coordinated and varying stages. Since biological processes are time varying [1], they may be best described by time series gene expression rather than by a static gene expression analysis. Acknowledging the nature of genes that are involved in dynamic biological processes (e.g., developmental processes, mechanisms of cell cycle regulation, etc.) has potential to provide insight into the complex associations between genes that are involved. Functional discovery is a common goal of clustering gene expression data. In fact, the functionality of genes can be inferred if their expression patterns, or profiles, are similar to genes of known function. There are published clustering methods that include into the analysis the duration of the experimental stages, or the staged dependence structure of gene expression. The results from these approaches are certainly more informative and realistic than groupings that are gained from static clustering methods (i.e., clustering at a single-staged experimental point), but their results are limited in interpretation. The seminal work from Luan and Li [2] is a good example of a clustering application that takes the time dependent nature of genes into account. More realistic, though, is the fact that some biological processes typically start and end at identifiable stages, or time points, and that the genes in a process may be dynamically regulated at
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