Statistical resynchronization and Bayesian detection of periodically expressed genes

Abstract

We propose a periodic-normal mixture (PNM) model to fit transcription profiles of periodically expressed (PE) genes in cell cycle microarray experiments. The model leads to a principled statistical estimation procedure that produces more accurate estimates of the mean cell cycle length and the gene expression periodicity than existing heuristic approaches. A central component of the proposed procedure is the resynchronization of the observed transcription profile of each PE gene according to the PNM with estimated periodicity parameters. By using a two-component mixture-Beta model to approximate the PNM fitting residuals, we employ an empirical Bayes method to detect PE genes. We estimate that about one-third of the genes in the genome of Saccharomyces cerevisiae are likely to be transcribed periodically, and identify 822 genes whose posterior probabilities of being PE are greater than 0.95. Among these 822 genes, 540 are also in the list of 800 genes detected by Spellman. Gene ontology annotation analysis shows that many of the 822 genes were involved in important cell cycle-related processes, functions and components. When matching the 822 resynchronized expression profiles of three independent experiments, little phase shifts were observed, indicating that the three synchronization methods might have brought cells to the same phase at the time of release.

Figure 1

Transcription profiles of five typical groups of stage-specific genes. Solid lines represent the transcription profiles of stage-specific genes. The line of asterisks represents the average transcription profile of the genes within each group.

Figure 2

The periodic–normal mixture model fitting of the CLN2 profiles in the three data sets: cdc28, cdc15 and alpha. Columns 1–3, transcription profile fitted with one, two and three sinusoids; column 4, the PNM fitting (K = 3 with normal mixture) to real observations. Solid curves are the PNM model and the asterisks are observations.

Figure 3

The PNM model fittings of four periodically expressed genes in the three data sets: cdc28, cdc15 and alpha. Solid curves denote the PNM model and the asterisks denote observations.

Figure 4

Histograms of model fitting residual sum of squares of the three data sets (cdc28, cdc15 and alpha) overlaid with the fitted mixture-Beta distributions.

Figure 5

Clustering of the 822 PNM-identified periodic transcripts into the five stage-specific groups.