A computational approach to the functional clustering of periodic gene-expression profiles

Abstract

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 in a time course. Here, we present a statistical model for clustering periodic patterns of gene expression in terms of different transcriptional profiles. The model incorporates biologically meaningful Fourier series approximations of gene periodic expression into a mixture-model-based likelihood function, thus producing results that are likely to be closer to biological relevance, as compared to those from existing models. Also because the structures of the time-dependent means and covariance matrix are modeled, the new approach displays increased statistical power and precision of parameter estimation. The approach was used to reanalyze a real example with 800 periodically expressed transcriptional genes in yeast, leading to the identification of 13 distinct patterns of gene-expression cycles. The model proposed can be useful for characterizing the complex biological effects of gene expression and generate testable hypotheses about the workings of developmental systems in a more precise quantitative way.

Figure 1.—

Component number-dependent AIC and BIC values of model fitting by a Fourier series function of order 1–3 for 800 genes collected from the yeast genome.

Figure 2.—

Thirteen periodic patterns of gene-expression profiles approximated by a first-order Fourier series function for 800 genes collected from the yeast genome.

Figure 3.—

Component number-dependent AIC and BIC values of model fitting by a first- and a second-order Fourier series function for 1000 simulated genes under different residual variances.