The heterochrony model of time-dependent changes in gene expression trajectories between strains. The model was fit to single period, Z-standardized CDC-expression data for a single gene measured in two strains. (a) Formulation of the time-independent (null) and heterochrony regression models. The heterochrony model estimates a timepoint mapping between strains using the Beta cumulative distribution function, which generates smooth and invertible transformations on [0, 1] according to parameters α and. β. This model also allows translation of expression trajectories using the phase parameter γ. Transformed timepoints were modulated around 1, so that transformations are defined with respect to a single cell-division cycle. Estimates of α, β, and γ were bounded within [1/3, 3], [1/3, 3], and [-260/2, 260/2], respectively, where 260 is the CDC period. The light blue line (α = 1; β = 1; γ = 0) describes the null (time-independent) model, where t = t' = Beta (t, 1,1) + 0. (b) Distributions of R2 values for the time-independent (top) and heterochrony (bottom) models, over all 45 comparisons per gene. Both models were fit identically, except that parameter values for the null model were fixed at (α = 1; β = 1; γ = 0). (c) Distribution of the proportion of significant F -values (genes) over the 45 strain comparisons (FDR < 0.05). (d) Distribution of the number of significant strain comparisons over genes. (e) The number of genes significant in at least k comparisons versus k. A cutoff of 30/45 = 2/3 was used to classify a subset of 4998 genes as heterochronic.
Simola et al. Genome Biology 2010 11:R105 doi:10.1186/gb-2010-11-10-r105