To assess the natural variability in genome-wide gene expression levels, we computed F -statistics at each timepoint t for 4,973 genes g exhibiting significant mutational variance 2 (see Supplemental materials and methods in Additional file 1). Each F -statistic is defined as the ratio of natural (V_n ) to mutational (V_m ) variances within S. cerevisiae, scaled by the divergence times of the natural and MA lines (in generations) and degrees of freedom: F ( g , t ) = V n ( g ,   t ) V m ( g ) × 600 8.34 × 10 6 × 22 8 . F-values thus represent estimates per-generation natural variation in gene expression calibrated by neutral mutational variation. The genome-wide CDC median F -value is 1.56 × 10 ^-4 (cf. 31 ), indicating that variation among natural strains is roughly 10⁴-fold smaller than expected under mutation-drift equilibrium. (The median scaled natural and mutational variances are 2.40 × 10^-8 and 1.54 × 10^-4, respectively.) With a maximum F -value of 0.23, not a single gene shows evidence of positive selection for adaptive divergence at any timepoint. When tests are carried out for each gene at each timepoint (Figure 1A), 95.6% of hypotheses indicate stabilizing selection on expression level on average (FWER < 10^-5). The nine natural S. cerevisiae lines in our study are estimated to have diverged between 3.02 and 4.19 thousand years ago (95% confidence interval); therefore 94.4% to 96.4% of gene expression levels are under stabilizing selection. Moreover, the majority of genes (81.9%) exhibit expression trajectories consistent with complete stabilizing selection at every timepoint, while 742 genes (15.0%) exhibit low variability in at least half of the timepoints (partly neutral genes) and only 152 genes (3.1%) exhibit neutral variability in at least half of the timepoints (neutral genes) (Figure 1D, Table S2 in Additional file 1). No single trajectory appears to diverge completely neutrally. Thus, when analyzed in terms of gene expression levels only without considering the effect of CDC-dynamics, the overall pattern of our data is consistent with previous hypotheses that the expression levels of most genes are under strong stabilizing selection.

One might suspect that the broad lack of expression divergence among strains may be due to a general deficiency of CDC-temporal variation for many of the genes. To test this, we partitioned S. cerevisiae expression variation into relative contributions from strain and temporal effects using a linear mixed model analysis. 3,750 genes (59.9%) exhibit significant effects (FDR < 0.1 over all 6,251 × 2 hypotheses): 2,797 genes (46.6%) show significant strain variation (that is, divergence), 2,596 genes (43.3%) show significant temporal variation, and 1,643 genes (26.2%) show both effects. Averaging over these 1,643 genes, strain effects explain 39% and temporal effects explain 23% of the total variance in gene expression; combining these marginal effects explains 50%-90% of each gene's total variance. Strain and temporal variances show significant but mild correlation (R = 0.25, P < 10^-10; Figure S2 in Additional file 1), and temporal effects contribute 10⁴-fold more to overall expression variation compared to strain effects when scaled by divergence time (genome-wide medians σ t i m e 2 = 9.54 × 10 − 4   v s .   σ s t r a i n 2 = 7.43 × 10 − 8 ). Thus, considerable temporal variation in CDC-expression is present in the yeast transcriptome (see also Figure S3 in Additional file 1).

To relate evolutionary forces to yeast gene function, we computed the proportion of genes under stabilizing selection for eight broad life-cycle terms and 88 GO Slim terms over time, Q_j (t), where j indexes each term. The Q_j profiles of most terms appear qualitatively similar (Figure S4 in Additional file 1), and a comparison of average Q_j values for life-cycle terms reveals that periodic, meiotic, and CDC-specific genes (in that order) are the most neutral (Figure 1B). In particular, a significant number of neutral genes are periodically expressed (Fisher's Exact test, FDR < 0.05; Figure 1E). Of the 88 GO Slim terms, only 5 terms have average Q_j values less than 0.94 (the 95th percentile over Q_j ; Table S3 in Additional file 1): helicase activity (0.76), extracellular region (0.86), cell wall (0.91), cellular component (0.92), and pseudohyphal growth (0.93). Of these, cell wall and extracellular region terms are enriched among the 1,643 genes with significant strain and time effects (FDR < 0.05). Thus, while it is not clear whether there is a functional aspect to expression divergence in temporal trajectories, among genes with the most strain divergence, specific functional categories are enriched within the set of temporally variable genes.

A hierarchical clustering of the entire CDC-transcriptome data set shows a complex inter-relationship among strains and timepoints, such that no strain's entire CDC-temporal expression and no timepoint's entire strain expression form a single clade (Figure S5 in Additional file 1); however, different timepoints from the same strain tend to be more similar than the same timepoints from different strains, indicating a general pattern of strain divergence. Notably, 17 of 18 timepoints for our S. paradoxus strain (YPS3395) cluster as a single clade, indicating their general distinction from S. cerevisiae expression. Yet only 457 genes (7.5% of the genome) show significant differential expression between S. paradoxus and the 8 woodland S. cerevisiae lines (t-test, FWER < 0.1), and no gene shows greater than a three-fold change in expression level. Surprisingly, the S. cerevisiae laboratory strain exhibits the most divergent dynamic expression profile in this clustering, beyond the S. paradoxus outgroup, despite having only 248 genes (4%) that are differentially expressed compared to woodland strains (FWER < 0.1) with a maximum fold change of 4.2. Thus, compared to S. paradoxus, the laboratory S. cerevisiae strain shows only slightly greater expression level divergence from woodland strains but for fewer genes, yet it shows a more distinct pattern of temporal divergence. One possibility is that the laboratory strain's CDC molecular physiology has become adapted to laboratory growth conditions 32 , which is manifest in its CDC-transcriptome dynamics. Overall, these results indicate that while levels of expression show limited among-strain and between-species divergence, the dynamic pattern of expression displays significant temporal fluctuations, with broad among-strain and between-species divergence.

To evaluate the quantitative divergence in CDC-temporal expression following the qualitative patterns revealed by clustering analysis above, we first generated a 6,082 × 6,082 gene coexpression matrix for each strain by computing pairwise correlations between all CDC-temporal gene expression profiles and then calculated matrix correlation coefficients between coexpression matrices for all pairs of strains (Figure S6A in Additional file 1). Due to the extreme size of the matrices, all comparisons yield significant concordance in coexpression patterns (FDR < 0.01), but the degree of concordance is low (avg. R = 0.11), indicating most strains lack strong similarity in CDC-coexpression (that is, similar pairwise relationships between genes). Restricting these coexpression matrices to a subset of 266 transcriptional regulatory genes does not strengthen this pattern of weak association (avg. R = 0.12; Figure S6B in Additional file 1). Controls using replicated and simulated microarray data confirm this pattern (Text S1). As may be expected, S. paradoxus has the lowest coexpression correlation with other strains (avg. R = 0.047); however, S. cerevisiae strains YPS3137 and YPS2073 also have low correlations (0.055 and 0.068). The laboratory strain shows an average correlation of 0.12, indicating that its divergence in CDC-coexpression is typical compared to woodland strains. Thus, the laboratory strain appears to show pronounced divergence in overall CDC-transcriptome dynamics compared to other strains (see above) without markedly different coexpression relationships (that is, changes in regulation). Overall, we found considerable divergence in the genome-wide pattern of temporal coexpression.

To assess coexpression divergence in a time-specific manner, we grouped each strain's expression data into three overlapping CDC-phase groups (first, middle, and last nine timepoints). We first assessed coexpression matrix similarity between strains and between CDC-phase groups. This recapitulated the pattern of weak association between strains (R = 0.075; Figure 2A). Coexpression matrices consistently cluster by strain (Figure 2B), but cluster relationships between strains are unique to each CDC-phase group (Figure 2C). We also identified phase-directions of temporal covariation using a singular value decomposition (SVD) of each strain's expression data for each of the three CDC-phase groups. Within each group, the angular distance of major phase-directions between strains averages 75.8°, close to the maximum of 90° (Figure S7A in Additional file 1). Multidimensional scaling (Figure S7C in Additional file 1) and hierarchical clustering (Figure S7D in Additional file 1) indicate that similarity relationships between strains are phase-specific. These results indicate that the genome-wide pattern of coexpression divergence is time-dependent.

Since coexpression divergence may occur at different scales of transcriptome organization, we also assessed the pattern of modular temporal coexpression. We defined a coexpression k-module for every gene as its k most correlated genes within each strain. We assessed divergence in modular coexpression by computing the overlap of each gene's k-modules between strains and determining the degree of excess overlap compared to random expectation among significant genes. Less than two-thirds of genes exhibit significant overlap at any scale (from 25% at k = 25 to 65% at k = 2,500, averaging over all strain pairs, P < 1/250), suggesting that patterns of shared temporal coexpression cannot be identified for a large portion of the genome. While the average overlap among significant genes is consistently greater than expected by chance (Figure S8 in Additional file 1), the excess is generally low, averaging 8.24% with a minimum of 4.39% at k = 25 and maximum of 10.03% at k = 880 genes (Table 1). Thus, similar to the matrix correlation results, the pattern of modular coexpression shows low concordance between strains regardless of scale. Moreover, there is lower overlap at smaller scales, suggesting that temporal coexpression diverges more rapidly for genes that are more tightly coexpressed within a genome. To determine whether relationships of modular coexpression between strains change across organizational scales, we computed hierarchical clusterings of the 10 × 10 matrices of average module overlap between strains (Figure S9 in Additional file 1). A few strains, notably YPS3137 and YPS2073, show changes in overlap relationships across scales, suggesting that these strains differ in temporal coexpression at all scales of transcriptome organization. Thus, divergence in CDC-temporal coexpression is found genome-wide, in a time-dependent manner, and at all scales of transcriptome organization.

The gene-oriented analyses above indicate surprisingly large divergence in CDC-temporal expression, suggesting a broad potential for evolutionary divergence of expression dynamics despite stabilizing selection on expression levels. Changes in expression dynamics imply changes in the timing patterns of genome-wide gene regulation. To dissect the architecture of time-dependent gene regulation that underlies the observed pattern of transcriptome divergence, we analyzed multivariate (multi-genic) patterns of expression covariation among the S. cerevisiae lines, including time-dependent multivariate patterns. We first performed a canonical correlation analysis using genome-wide expression grouped by timepoint and found that expression can be correlated nearly perfectly between all pairs of timepoints using primary canonical variables (R ≈ 1.0, FWER < 0.05). This indicates that genome-wide expression at each timepoint shares the same sub-space (that is, fundamental directions of variation); however, particular directions of major variation may differ across timepoints. We next assessed the degrees of freedom of expression variation among strains by analyzing the covariation at each timepoint independently, using latent factor mixed model analysis (LFA) and principal component analysis (PCA). Compared to patterns seen in the mutation accumulation lines, natural time-specific covariation exhibits greater overall regulatory complexity, averaging 4.6 vs. 2 factors by LFA (Table S4 in Additional file 1), and restricted degrees of freedom of covariation, averaging 6.1 vs. 13 dimensions by PCA (Figure S13A in Additional file 1), at each timepoint. Combining all timepoints and strains, a total of 56 dimensions are required to explain 90% of the covariation in the natural strain CDC data (Figure 3). Surprisingly, these degrees of freedom do not simply separate into time and strain components: if each strain's expression is time-averaged, only five PCA factors explain the resulting among-line covariation; if each timepoint's expression is strain-averaged, ten factors explain the among-timepoint covariation. Thus, a much greater complexity of expression divergence is revealed when both CDC-temporal and strain covariation are taken into account.

Both LFA and PCA results strongly suggest the presence of differential constraints on transcriptome divergence as a function of CDC progression. We examined this by asking whether yeast strain covariance structure changes between different timepoints. We applied a SVD to the expression data at each timepoint for all S. cerevisiae strains, obtaining r = 9 multivariate directions of strain divergence U^r (t) for each of the 18 timepoints t 33 (see Supplemental materials and methods). We call these CDC-directions, which might reflect developmental constraints, mutational biases, or directions of selection (or combinations thereof), for example. We first computed angular distance between the major CDC-directions for all timepoint pairs (∠ U ¹ (s) U ¹ (t); Figure 4C). Adjacent timepoints as well as those in phase between cell-division cycles appear more similar than other timepoints, indicating that changes in covariance structure are both gradual and cyclic. Despite these similarities, angles average 50.4° and range from 19.4° to 88.9°. A random angles test failed to identify any significantly small angles (that is, significantly similar directions), even with a lenient cutoff (FWER < 0.15). Visualization of the major CDC-direction distance matrix by multidimensional scaling reiterates this pattern (Figure 4A). These results suggest that most major CDC-directions are distinct. Similar testing of each of the eight minor CDC-directions (Figure 4D) identified only eight significantly small angles out of 1,072 comparisons. Common principal component analysis of time-dependent covariation 34 revealed broadly consistent results (Text S2). Thus, we observe significant changes in the yeast transcriptome covariance structure across strains throughout the CDC.

To assess whether the CDC-directions correspond to biologically relevant axes of covariation, we identified the genes contributing the most to strain covariation in each major CDC-direction by correlation and determined the functional terms enriched among the top 5% of genes (Tables S6, S7 in Additional file 1). Significant terms vary by timepoint and include metabolic, periodic, ribosomal, and CDC life-cycle terms (FDR < 0.05). In addition, TATA regulatory motifs have been hypothesized to drive expression divergence via neutral drift 31 . We found that TATA-associated genes project onto major CDC-directions 4-fold less than genes lacking TATA motifs, which are over-represented among the top 5% of genes (P < 0.01, Table S8 in Additional file 1). Also, few of the 152 genes with neutral CDC-expression are found among the top 5% (P < 10^-5). This paucity of genes hypothesized to diverge neutrally argues against drift as a major force in strain diversification of CDC-directions. We also tested whether the major CDC-directions (of within-species covariation) are predictive of directions of between-species divergence, as might be expected for neutral species divergence 35 . For each timepoint we calculated angular distance between the major S. cerevisiae CDC-direction and the displacement vector of S. paradoxus expression, oriented within S. cerevisiae CDC-space (for example, Figure S14 in Additional file 1). All angles exceed 45°, and no angle is significantly small (FWER < 0.15). Thus, within-species covariation does not predict the direction of between species divergence. However, release from α-factor, S-phase, and the G₂/M transition have the smallest angles, suggesting that response to mating pheromone and DNA replication dynamics may be more constrained in evolutionary covariation.

We next evaluated whether the amount of variation projected onto the multivariate CDC-directions reveals a different, non-stabilizing pattern of selection compared to the pattern for individual genes. We computed F -statistics by comparing natural and mutational among-line expression variances projected onto each timepoint's CDC-directions. Although the average F -value over major CDC-directions U ¹(t) is 14.6-fold larger than the genome-wide average F -value (2.28 × 10^-3 vs. 1.56 × 10^-4, P = 1.5 × 10^-4), all F -values remain significantly low, including those calculated for minor CDC-directions (FWER < 0.05). Therefore, multivariate patterns of transcriptome divergence are also consistent with stabilizing selection. However, the temporal profile of major multivariate F -values, unlike that for individual genes, exhibits peaks in expression variability (87, 176, 260, and 345 min.; Figure S15 in Additional file 1); the average peak is 1.4-fold greater than that at all other timepoints (P = 0.018) and 19.1-fold greater than the genome-wide average (P = 0.006). Intriguingly, these peaks in expression variability are preceded by large changes in the major axis of CDC-covariation (63, 152, 251, and 301 min.), occur just prior to CDC-phase transitions (97, 218, 267, and approximately 350 min.), and coincide with drops in regulatory complexity (latent factors; 176, 260, 345 min.) (Table S4 in Additional file 1; see also Figure 4B). In addition, reductions in regulatory complexity generally coincide with the CDC-phase transitions G₁/S, G₂/M, and M/G₁ (48, 218, 260, 301 min.; except S/G₂ at 111 min.), suggesting greater constraint on gene regulation through the influence of CDC checkpoints. Thus, temporal fluctuations in strain variability might reflect multi-genic pleiotropic effects being channeled to varying dimensions and directions of gene expression through a regulatory architecture that changes dynamically across CDC-phases 7 .

Our multivariate analysis of the architecture of genome-wide gene regulation argues that the broad pattern of CDC-transcriptome divergence among yeast strains is heavily influenced by dynamical changes in control. However, if this architecture of timing control involves a global cascade of regulation, any changes in control could cause broad negative pleiotropic effects throughout the CDC 8 . Given our findings of strong stabilizing selection on both univariate and multivariate strain variation across the CDC, such a global, hierarchical architecture seems unlikely. Alternatively, this architecture may be organized into discrete modules of regulation that exhibit dynamically-autonomous timing control 36 . Moreover, superposition of regulatory timing patterns from different modules could combinatorially generate the regulatory complexity required for transcriptome-wide timing control while minimizing negative pleiotropic effects.

We evaluated this hypothesis of modular timing control by identifying genes that share patterns of expression heterochrony (evolutionary shifts in expression timing compared to the CDC) 27 37 38 , which can be used to delineate dissociable units of structure and function 29 39 . Briefly, we reasoned that if two genes are coregulated, their temporal expression trajectories might show similar evolutionary shifts in timing between strains and species, despite overt differences in the expression trajectories themselves. We tested for the presence of heterochrony in the yeast cell-division cycle by asking whether a time transformation (that is, heterochrony) model significantly explains a gene's divergence in temporal expression between two strains (Figure 5A). On average, our heterochrony model explains 61% of between-strain transcriptome variation (Figure 5B). We then computed a likelihood-ratio statistic for every gene by comparing the fit of the heterochrony model to the fit of a time-independent model. 64%-96% of genes show a significant time effect for any between-strain comparison (d.f.1, 3 and 14, FDR < 0.05; Figure 5C), indicating a broad pattern of heterochronic divergence. Each gene exhibits significant fit to the heterochrony model for an average of 33.1 of the ( 10 2 ) = 45 pairwise comparisons (Figure 5D). We retained 4998 genes showing consistent support for heterochrony (≥ 2/3 significant comparisons; Figure 5E) for the analysis of shared patterns of heterochrony. As expected, these genes tend to exhibit large dynamical fluctuations in expression level across the CDC: 85.8% belong to the set of 2,596 genes with significant temporal variation (P < 10^-10). At least 85% of the top 1,000 periodically expressed genes in our data set show significant heterochrony (Figure S16 in Additional file 1). In addition, functional analysis reveals significant enrichment for a variety of GO Slim terms (Text S3). These results suggest that the major mode of transcriptome divergence in the yeast CDC entails changes in timing (heterochrony) rather than changes in levels (heterometry) of expression.

We identified shared patterns of heterochrony among the 4,998 heterochronic genes by comparing their timing change curves (defined by the heterochrony model parameter estimates; Figure S17 in Additional file 1), such that two genes are similar if their timing change curves are concordant across the entire CDC (Figure S19 in Additional file 1). In this way we computed a distance matrix that characterizes the timing pattern relationships between all pairs of genes (Text S4). Clustering genes by their timing pattern relationships revealed seven significant timing modules, consistent with the hypothesis of modular timing control (Text S5). To identify the genes significantly associated with each timing module, we performed a pairwise analysis by counting the number of between-strain comparisons (out of 45) in which two genes exhibit the same pattern of timing change. We identified 5,393 significant interactions connecting 3,715 genes (binomial, P < 10^-4; see Additional file 2); 47.2% of the significant interactions connect genes within the same timing module. Genes sharing significant interactions display an average similarity of 0.46, compared to the genome-wide average similarity of 0.19 (Figure S24 in Additional file 1). Interacting genes also share functional ontology terms, on average sharing 95% of possible life-cycle terms (P < 10^-7) and 23% of possible GO Slim terms (P < 10^-19), consistent with a functional interpretation for divergence in expression timing. We partitioned genes sharing significant heterochronic interactions into two groups: 1,828 genes showing a majority of interactions within an individual timing module (module-specific genes), and 1,887 genes showing a majority of interactions across timing modules (between-module genes). Among these 3,715 genes, within-module interactions are found 5.6-fold more often than between-module interactions (P < 10^-10), indicating that module-specific genes comprise the inter-connected core of each timing module (Figure 6A). Functional enrichment of timing modules reveals five life-cycle terms and 21 GO Slim terms associated with four of the seven timing modules (Table S10 in Additional file 1), whereas analysis of between-module genes revealed no significantly enriched terms (FDR < 0.1). Thus, analysis of shared patterns of heterochrony reveals significant modular organization in the timing patterns of genome-wide gene expression and suggestive evidence that these modules are associated with cellular function.

Heterochronic modularity of gene expression timing suggests that each timing module could represent a distinct unit of temporal development, responsible for executing a particular timeline of gene expression events. In this case, each module's characteristic timing pattern might undergo dynamically-autonomous evolution without losing coherence in modular timing control. According to this hypothesis, a module's timing pattern may change during evolutionary divergence, increasing variation among modules; however, variation in the timing patterns of genes within a module should not change (or change more slowly), since this implies potentially deleterious changes in functional coregulatory relationships. We first used analysis of variance to test for differences in the mean timing pattern among modules, using the timing change curves of module-specific genes pooled from the 45 strain comparisons. Timing patterns differ significantly among modules (P < 10^-10), suggesting that timing modules undergo heterochronic divergence in a dynamically-autonomous manner. We then examined timing pattern variability within modules, by comparing the observed variance in timing change curves among module-specific genes to a distribution of random variances, produced by grouping timing change curves drawn randomly from the set of all observed curves. Within-module timing pattern variability is generally lower than expected and may be lower within species than between species (Text S6 and Figure S26 in Additional file 1). Linear discriminant analysis of the timing pattern relationships for module-specific genes illustrates this coherence of timing patterns within modules despite differences between modules (Figure 7). These results suggest that divergence in timing patterns may increase more quickly between modules than within modules, consistent with the representation of modules as distinct units of timing control.

Furthermore, robustness of the yeast CDC against genetic 40 , environmental 41 , and dynamical perturbations 42 suggests the possibility that timing pattern variability both within and between modules might be limited by a form of negative selection, potentially canalizing selection 43 44 45 , which could reinforce the coherence of modules as integrated developmental processes. Consistent with this, module-specific genes as a group show significantly low variation for timing change curves across strain comparisons (P = 0.0002), and when separated by module, their strain variation correlates with each module's estimated coherence (Spearman's r = -0.94, P = 0.0009). This suggests a relationship between within-module variability and among-strain variability in timing patterns (Text S7). In addition, variability among all timing patterns is also lower than expected and is time-dependent, suggesting the possibility of system-wide coordination and periodic synchronization of modular timing patterns (Text S8 and Figure S27 in Additional file 1). These results suggest that the CDC timing control architecture is comprised of a core of distinct, coherent, and dynamically-autonomous modules involving nearly 30% of the genome, combined with a layer of interactions between modules, which may potentially coordinate or synchronize expression timing globally.

While the prevalence of heterochrony is consistent with broad changes in gene coregulation, modularity in the patterns of heterochrony suggests that regulatory architecture itself could effectively constrain multi-genic strain variation into distinct channels of phenotypic expression. In this way, widespread divergence in transcriptome dynamics may be explained by predominantly quantitative changes in the expression patterns of module-specific regulatory factors, rather than qualitative changes in gene coregulation. Using the 1828 module-specific genes, we tested whether strongly shared heterochrony implies common transcription factor trans-regulation, as one possible mode of module-specific gene regulation. Genes sharing heterochronic interactions share more TFs than expected (P < 10^-100) and associate with TFs more strongly than pairs of genes without strongly shared heterochrony (P < 10^-10). The genome-wide pattern of TF-gene trans-regulatory interactions also associates significantly with the segregation of genes into timing modules (P = 0.014). We then sought to identify TFs that associate specifically with each timing module, using 2 × 2 contingency tables to summarize the interactions between each TF and module (Text S9). We identified 37 TFs showing 42 module-specific associations, averaging six TFs per module (FDR < 0.1); this represents significant association for 59% of the 63 TFs tested (the subset of 117 TFs showing ≥ 7 targets 46 ). These 37 module-specific TFs themselves exhibit significant patterns of heterochrony (Table 2; Figure S28 in Additional file 1); as a class, they show more extreme heterochronic shifts (distortion) compared to expectation from all heterochronic genes (76th percentile) and from all TFs (76th percentile). At least one TF from every module shows significantly large distortion compared to all heterochronic genes or all regulatory factors (P < 0.05); however, only one of these TFs (Cin5) is among the top 50 of all heterochronic genes genome-wide (rank-46 by distortion; Table S9 in Additional file 1). There do not appear to be differences in the distortion of these TFs among modules (ANOVA, P = 0.2). Thus, quantitative, heterochronic changes in the expression patterns of module-specific regulatory factors may drive divergence in CDC-transcriptome dynamics. While transcription factors were the only class of regulatory factors considered here, our results do not exclude the likelihood that additional factors, such as post-transcriptional RNA-binding proteins 47 or post-translational factors (kinases, methyltransferases, chromatin modifying enzymes, and so on) 48 49 , also contribute to the timing control of modular gene expression.

While we found 1,828 genes that strongly associate within individual timing modules (module-specific genes), another 1,887 genes (31%) instead show strong associations across timing modules (between-module genes); these between-module genes may exhibit a complex pattern of heterochrony. Our hypothesis of modular timing control suggests that negative pleiotropic effects due to changes in control may be minimized for genes with complex heterochrony by combinatorial regulation, using TFs with different timing patterns rather than the same timing pattern. First, we found no TF that significantly associates with the 1,887 genes with complex heterochrony compared to module-specific genes (FDR < 0.1). We also evaluated whether the number of module-specific TFs regulating a gene with complex heterochrony correlates with the number of timing modules represented by these TFs and obtained a rank correlation of 0.71 (P < 10^-10). While some correlation is expected by chance, we found only three genes (Erg11, Sis1, and YMR196W) that are strictly regulated by multiple TFs from the same timing module (three TFs for each), suggesting that this type of regulation may be rare. Thus, genes that associate with multiple timing modules tend to be regulated by multiple different timing patterns. This suggests that complex patterns of heterochronic divergence could be generated combinatorially while minimizing negative pleiotropic effects.

The ten natural S. cerevisiae and S. paradoxus strains are heterothallic haploid MATa derivatives of homothallic diploids. Woodland isolates were previously collected from state parks in Pennsylvania and New Jersey, USA 50 (Table S1 in Additional file 1). Laboratory strain YPS183 (HOΔ:kanMX, leu2Δ) derives from BY4741. Mating-type switching was prevented by homologous recombination of a Kanamycin resistance cassette at the HO endonuclease locus (YDL227C). The 23 mutation accumulation lines (provided by C. Zeyl 51 ) are diploid and were propagated asexually for 600 generations from a Y55 ancestor (leu2Δ).

Strains were inoculated from frozen stock and cultured overnight in synthetic dextrose (SD) minimal medium at 30°C (225 rpm). The next day cultures were diluted into fresh SD and upon reaching a culture density of OD ≈ 0.25, α -factor mating pheromone was added to a final concentration of 4 μM. Cultures were then incubated approximately 75 min. until arrested and synchronized in late G₁. The state of synchronization was determined by the appearance of < 10% shmoos and < 10% budding cells, visualized by light microscopy (100 ×, oil). Cultures were released from arrest by removing α-factor: 2 × wash with 4°C S medium (SD without dextrose) and resuspension of cell pellets with fresh 18°C SD medium. Approximately 25 ml aliquots of each culture were distributed into 18 flasks and incubated at 18°C (225 rpm). Incubation of cultures at 18°C in SD medium more than doubles the CDC-period, allowing a more accurate comparison of measurements across strains by reducing temporal sampling variation.

The sampling time course consisted of 18 samples, taken at average intervals of 19 min. (real time), starting at 0 min. (time of release from arrest) and ending at 345 min. The first sample (0 min.) was taken after all flasks were returned to the incubator. Upon sampling, each culture was placed on dry ice, mixed with 20 ml of -20°C 100% EtOH in a 50 ml Falcon tube, inverted, and placed immediately into a -80°C freezer.

Total RNA was extracted from each frozen cell culture sample using Qiagen's RNeasy Kit, following manufacturer's instructions. cDNA was prepared from 15 μg of each RNA sample using SuperScript III reverse transcriptase (Invitrogen) and compared directly to unsynchronized S. cerevisiae cDNA (YPS183 cultured at 30°C in YPD until reaching OD ₆₀₀ 1.1) on 2-channel spotted-oligo glass microarrays in a common reference design. Invitrogen AlexaFluor 555 and 647 fluorophores were used to label each cDNA sample. Hybridized slides were incubated for 24-65 hours at 42°C. Slides were prepared for scanning by serial incubation in wash buffers and dried using both a vacuum and high-purity, filtered N₂ gas.

Samples were hybridized to two dye-swapped microarrays. Unsynchronized MA line transcriptomes were produced with the same design. Corning UltraGAPS glass slides, spotted with the Operon AROS for Saccharomyces cerevisiae, V1.1, were used for all hybridizations. Each microarray targets 6388 protein-coding genes using two replicate spots per oligo, yielding four technical expression measurements per gene, strain, and timepoint. In total 378 time-series and 45 unsynchronized microarrays were produced for natural and MA lines, respectively. Data were quantified, filtered, and normalized, yielding expression measurements for 5879.9 genes per strain on average (92.4%). Measurements show a grand mean standard error (SE) of 0.175. Using two microarrays of the same strain independently cultured, synchronized, and sampled at 63 min., biological replicate measurement error was estimated as 0.554 (SE). Microarray data are available from the NCBI GEO database under accession number [GEO:GSE24237] and from the authors' web site 52 .

A set of 91 transposable (Ty) element genes were excluded from the final data collection. The remaining 6,263 gene expression trajectories were imputed for missing data and calibrated to a common CDC-period of 267 min. using budding index measurements. A common set of 6,082 genes have CDC expression for all ten natural strains. Custom software written in Python, R, SAS, and Mathematica was used to carry out computational analyses as described in the Supplemental Materials and methods.