A random-periods model for expression of cell-cycle genes

We propose a nonlinear regression model for quantitatively analyzing periodic gene expression in studies of experimentally synchronized cells. Our model accounts for the observed attenuation in cycle amplitude by a simple and biologically plausible mechanism. We represent the expression level for each gene as an average across a large number of cells. For a given cell-cycle gene, we model its expression in each cell in the culture as following the same sinusoidal function except that the period, which in any individual cell must be the same for all cell-cycle genes, varies randomly across cells. We model these random periods by using a lognormal distribution. The variability in period causes the measured amplitude of the cyclic expression trajectory to attenuate over time as cells fall increasingly out of synchrony. Gene-specific parameters include initial amplitude and phase angle. Applying the model to data from Whitfield et al. [Whitfield, M. L., Sherlock, G., Saldanha, A. J., Murray, J, I., Ball, C. A., et al. (2002) Mol. Biol. Cell 13, 1977-2000], we fit the trajectories of 18 well characterized phase-marker genes and find that the fit does not suffer when a common lognormal distribution is assumed for all 18 genes compared with a separate distribution for each. We then use the model to identify 337 periodically expressed transcripts, including the 18 phase-marker genes. The model permits estimation of and hypothesis testing about biologically meaningful parameters that characterize cycling genes.