The haploid laboratory strain S. cerevisiae CEN.PK113-7D was grown at steady state in aerobic chemostat cultures on a synthetic minimal medium with glucose as the limiting nutrient. Cells were cultured at six different specific growth rates, namely μ = 0.02, 0.05, 0.10, 0.20, 0.25, and 0.33 per hour, corresponding to doubling times between 2 and 35 hours (Figure 1a). To assess the transcriptional program underlying growth, we analyzed the whole-genome transcription profiles from all cultures and thereby identified a signal from 5,930 out of 6,091 annotated open reading frames (ORFs; Additional data file 1). The detectable transcripts were then grouped using a robust and signal insensitive algorithm for clustering of coexpressed genes, whereas genes with noisy expression profiles were discarded (Figure 1b-d) 12. Consensus clustering algorithms 131415 take advantage of the randomness in K means or Gaussian clustering solutions to produce a robust clustering. By averaging over multiple runs with different number of clusters K, common patterns in each clustering run are amplified whereas nonreproducible features of individual runs are suppressed. Consequently, it is possible to cluster large expression datasets without conservative fold change exclusion 12.

In the present case we extracted the consensus clusters from 50 scans with Gaussian mixtures in the interval K = 10 ... 40, leading to a total of 31 × 50 = 1,550 clustering runs. The results from the multiple runs were used to calculate a cooccurrence matrix C. This matrix describes the empirical probability of observing each pair of transcripts (n,n') in the same cluster throughout the 1,550 clustering runs (Figure 1). The probability of transcript co-occurrence was then used to generate the consensus clusters (Additional data file 2). The co-occurrence matrix was converted into a transcript-transcript distance matrix as D_nn' = 1 - C_nn'; that is, a high probability of co-occurrence is equal to a short distance between the expression profiles of a pair of transcripts. The number of clusters in the dendrogram was finally determined as the average over the 50 repetitions of the Gaussian mixtures with the greatest likelihood. This criterion was found to be a pragmatic, conservative starting point for biologic validation. We reduced the 27 clusters to 13 by merging biologically similar clusters adjacent in the consensus dendrogram. Transcripts that could not be assigned to a cluster with at least 80% probability (P_a < 0.20) were discarded and collected in a 'trash' cluster (Figure 2a, cluster 14; Additional data file 2).

Among the 1753 ORFs (Figure 2a, clusters 1-4) with increasing transcript level as a function of the specific growth rate were mainly genes involved in RNA metabolism and in the biosynthesis of novel cell material. More specifically, these genes are involved in the synthesis of RPs, respiration, amino acid biosynthesis and lipid biosynthesis, as well as in nucleobase, nucleoside, nucleotide, and nucleic acid metabolism (Table 1). Ribosome-related genes were found to be over-represented in clusters 1, 3 and 7, and were almost absent in clusters with decreased or complex transcript patterns (Figure 2b). This observation was in good agreement with the over-representation of the regulatory ribosomal protein elements (RRPEs) GAAAA(A/T)TT in clusters 1 and 2 (Table 1). Comparing the genes of clusters 1-7 with a transcription factor binding study 16 showed that 70% of the RAP1 targets were found in these clusters, in particular clusters 2, 4, and 6 (P < 10^-2). RAP1 is a highly abundant transcription factor 17 that is involved in transcriptional activation of the highly expressed genes, including genes encoding RPs and glycolytic enzymes 18. The over-representation of RAP1 targets in clusters 2, 4, and 6 therefore suggests that this factor may be an important determinant of positive growth rate regulation.

A higher specific growth rate may be obtained by shortening steps in the cell cycle, and we therefore expected to identify cell cycle regulated genes among the growth rate affected genes 19. Comparing a list of 430 cell cycle regulated genes 202122 with genes regulated by the specific growth rate showed that this also was the case. Both clusters 1 and 2 exhibited significant over-representation of genes expressed in the G₁ (P < 10^-2) of the cell cycle. This observation, together with the finding of the M-G₁ regulated RRPEs in genes of clusters 1 and 2, suggests that a change in the specific growth rate affected the length of G₁ rather than other steps in the cell cycle.

Many genes involved in stress response had decreased mRNA level as a function of the specific growth rate (Figure 2a, clusters 12 and 13). A signal that could be mediated by the TOR (target of rapamycin) pathway 2324 via the corresponding stress response element, namely AGGGG, found to be over-represented among members of clusters 12 and 13 (Table 1). Genes in clusters 11 and 12 were mostly involved in chromosome organization and RNA processing, whereas cluster 13 typically contained stress response genes, for instance genes encoding heat shock proteins and genes involved in autophagy. To investigate the overlap between cluster 13 and genes found in stress response studies, we compared the present data with a core of 1,000 stress response genes that have been denoted the environmental stress response (ESR) genes 7. Transcript data from cells going into lag phase 5, growing under postdiauxic conditions 5, or exposed to 12 stress conditions revealed a strong correlation with transcript profiles from cells at different specific growth rates (Figure 3). Eighty percent of the transcripts that decreased upon stress showed the same response to slower growth, whereas 89% of the transcripts that increased upon stress also increased upon slower growth (Figure 3). This overlap between growth rate regulated genes and genes responding to stress indicates that the stress response shares a component with the response to changes in the specific growth rate.

The analysis also revealed that the responses to stress and growth rate are independent of carbon source. Cells grown on galactose are inhibited when exposed to 10 mmol/l LiCl 25. Besides a specific inhibition of phosphoglucomutase 25, lithium also inhibits the specific growth rate from 0.15 to 0.025 per hour over 140 minutes while the transcript level of 1,390 genes changed more than twofold 6. The transcript profiles of these genes have a considerable overlap with those of glucose grown cells (Figure 3), and suggest that they relate to the growth rate rather than the choice and amount of carbon source.

Almost 50% of the members of cluster 13 (Figure 2) belonged to the group of ORFs with unknown process (Table 1). Overall, only 25% of the ORFs in S. cerevisiae have not been assigned to a biologic process, and the lack of annotation was therefore a clear trait of ORFs in cluster 13. The strong transcriptional response argued against these ORFs being dubious genes. Our results suggest that the cellular role played by these ORFs may be unclear because they are poorly expressed at the high specific growth rates at which phenotype and function are normally inferred.

Some clusters appeared bell or valley shaped, showing that many transcripts did not follow a simple dependence on the specific growth rate (Figure 2a, clusters 6 and 8-11). Genes in clusters 8 and 10 exhibited an abrupt change in transcript level at μ = 0.33 per hour, where the specific growth rate was above the so-called 'critical dilution rate' (μ = 0.30 per hour) at which the Crabtree effect sets in 26. At this high specific growth rate the cells change from a respiratory metabolism to a mixed respiratory-fermentative metabolism, resulting in ethanol production (2.4 ± 0.1 g/l). The change in metabolism also correlated with induction of genes that are involved in vesicle transport and glucose transport (Figure 2a, cluster 8) and repression of genes that are involved in sporulation and carboxylic acid metabolism (Figure 2a, cluster 10). Most notable in the latter group were ICL1 and MLS1, which encode the key enzymes in the glyoxylate shunt; ALD4 and ADH2, which are involved in metabolism of ethanol; and FBP1 plus PCK1, which encode key gluconeogenic enzymes. FBP1 and PCK1 are previously reported to be subject to transcriptional repression at high glucose concentrations, although the mode of regulation is unclear because repression is not dependent on the MIG1 and Ras/cAMP pathways 27. These observations suggested that increased glucose uptake, together with downregulation of genes that are involved in ethanol catabolism, gluconeogenesis, and the glyoxylate shunt, could be involved in a shift from pure respiratory metabolism to mixed respiratory-fermentative metabolism at high growth rates.

The cluster analysis also revealed that gene pairs had much greater probability of being coexpressed than would be expected if they were randomly distributed across the genome (Figure 4a,b). The exception to this pattern was genes in one of the upregulated clusters and genes that changed expression abruptly around the critical dilution rate of μ = 0.30 per hour (clusters 1, 8, and 10); otherwise, all other clusters had an over-representation of gene pairs or genes in close vicinity to each other on the chromosomes.

Short chromosomal domains of coexpressed genes have previously been reported for S. cerevisiae and the Drosophila genome 2829. It has been suggested that gene expression within a chromosomal domain behaves as a 'square wave' (a discrete opening of the chromatin gives the transcriptional machinery increased access to several neighboring promoters) 2930. Opening of the chromatin occurs when the nucleosomes are remodeled by factors such as RAP1 31 and during DNA replication. We therefore speculated that the coexpression of growth-rate regulated genes (Figure 4a,b) could be influenced by replication and tested if there was a significant over-representation of these genes around the replication origins. In S. cerevisiae, 429 replication origins have been determined by chromosome immunoprecipitation 32 and 332 origins have been found by replication timing experiments 33. Between these two sets, 294 replication origins were overlapping within 10 kilobases (kb) 34.

Comparing the chromosomal position of the growth-related genes in clusters 1-13 (Figure 2) with the 294 replication origins revealed a positive correlation (P < 10^-3) between the genes and distance to the nearest replication origins. The average distance for a gene in these clusters to the nearest replication origins was 16.41 kb, whereas the average distance expected by chance was 16.81 ± 0.15 kb (average/standard deviation). Within the group of growth-regulated genes it was observed that genes in downregulated cluster 13 were found to be positioned closer to the replication origins than would be expected by chance (Figure 5). The average distance for a gene in cluster 13 to the nearest replication origins was 13.57 kb, whereas the average distance expected by chance was 16.43 ± 0.88 kb (average/standard deviation; P < 10^-3). One explanation for this phenomenon could be that some of the genes in cluster 13 are direct neighbors to the replication origins, whereas the remaining ones are distributed on the chromosomes as would be expected based on chance. Because of the correlation between transcript profiles from different growth rates and stress conditions (Figure 3), we speculated that genes responding to stress, postdiauxic shift, and stationary phase would also be closer to origins than expected by chance (see Table S5 in the report by Radonjic and coworkers 5, published elsewhere). Interestingly, this appeared to be the case for genes with altered expression in response to the stationary phase after diauxic shift (see Table S5 in the report by Radonjic and coworkers 5, published elsewhere). The average distance of the upregulated genes was 15.27 kb whereas the average distance expected by chance was 16.81 ± 0.65 kb (P < 10^-2). If growth-regulated genes are closer to the replication origins, then it would be expected that non-growth regulated genes are further away from the replication origins. This indeed was also the case when comparing the genes with marginal changes in expression under different growth conditions (see cluster F in Figure 3 in the report by Radonjic and coworkers 5, published elsewhere) to the position of the replication origins (P < 10^-3).

We also included a sensitivity analysis to evaluate the influence of the number of replication origins used in the analysis. The sensitivity analysis showed that the P values decreased with increasing number of replication origins (Additional data file 4). The number of replication origins is based on two datasets including 429 and 332 origins. Thus, the true number of replication origins is expected to be higher than 294. If the true number of replication origins is higher then the P values in the analysis are very conservative, and this would add further confirmation of our conclusions.

CEN.PK113-7D MATa was grown at dilution rates of 0.02, 0.05, 0.10 (in triplicate), 0.20 (in triplicate), 0.25, and 0.33 (in triplicate) per hour. The strain background and the aerobic continuous cultivations were described previously 5253.

The cRNA synthesis, hybridization to Affymetrix S98 arrays, and scanning were performed as described previously 54 with the only exception that the hybridization signal was not amplified, because we found that this step conferred substantial noise on the expression data. Affymetrix Microarray Suite v5.0 (Affymetrix Inc., Santa Clara, CA, USA) was used to generate CEL files of the scanned DNA microarrays. The normalized expression levels of the 9335 probe sets were subsequently calculated using the Perfect Match model in dChip v1.2 55, and this dataset was used to extract the expression level of 6091 annotated unique ORFs (updated March, 2004) 56. The data have been deposited at ArrayExpress 57 with the accession number E-MEXP-593.

To compensate for a drop in the mRNA level at different growth rates 58, we identified 42 ORFs that decreased linearly with specific growth rate (P < 0.05) with an average ratio of 1.8, and we used this information to scale the dataset such that the 42 selected ORFs had constant expression for all specific growth rates (Additional data files 1 and 5).

For all experiments done in triplicates, the geometric average was calculated as follows:

Y = [ ∏ m = 1 3 Y m ] 1 / 3 MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbhv2BYDwAHbqedmvETj2BSbqee0evGueE0jxyaibaiKI8=vI8tuQ8FMI8Gi=hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciGacaGaaeqabaqadeqadaaakeaacaWGzbGaeyypa0ZaamWaaeaadaqeWbqaaiaadMfadaWgaaWcbaGaamyBaaqabaaabaGaamyBaiabg2da9iaaigdaaeaacaaIZaaaniabg+GivdaakiaawUfacaGLDbaadaahaaWcbeqaaiaaigdacaGGVaGaaG4maaaaaaa@40F7@

The transformed expression level (n = 1 ... N transcript index, and m = 1 ... M chip index) was used for visualization:

X n m = ( Y n m − Y ¯ n ) / ∑ m = 1 M ( Y n m − Y ¯ n ) 2 MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbhv2BYDwAHbqedmvETj2BSbqee0evGueE0jxyaibaiKI8=vI8tuQ8FMI8Gi=hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciGacaGaaeqabaqadeqadaaakeaacaWGybWaaSbaaSqaaiaad6gacaWGTbaabeaakiabg2da9iaacIcacaWGzbWaaSbaaSqaaiaad6gacaWGTbaabeaakiabgkHiTiqadMfagaqeamaaBaaaleaacaWGUbaabeaakiaacMcacaGGVaWaaOaaaeaadaaeWbqaaiaacIcacaWGzbWaaSbaaSqaaiaad6gacaWGTbaabeaakiabgkHiTiqadMfagaqeamaaBaaaleaacaWGUbaabeaakiaacMcadaahaaWcbeqaaiaaikdaaaaabaGaamyBaiabg2da9iaaigdaaeaacaWGnbaaniabggHiLdaaleqaaaaa@4D5A@

Here Y¯n MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbhv2BYDwAHbqedmvETj2BSbqee0evGueE0jxyaibaiKI8=vI8tuQ8FMI8Gi=hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciGacaGaaeqabaqadeqadaaakeaaceWGzbGbaebadaWgaaWcbaGaamOBaaqabaaaaa@3542@ is the average expression level for the nth transcript and the denominator is the Euclidean norm over the M experiments. Hence, the transformed transcript level Xnm is confined to the interval [-1,1]. A value of 0 corresponds to the mean average level over all six specific growth rates. The dataset was clustered R = 31 × 50 = 1,550 times, K = 10 ... 40 clusters and 50 repetitions for each size, with the variational Bayes mixture of Gaussians 59. For each run r this gave a cluster label matrix label(n,r), along with a likelihood, which was used to calculate the co-occurrence matrix C_nn' (i.e. the empirical probability that two transcripts n and n' were in the same cluster).

C n n ′ = 1 R ∑ r = 1 R δ ( l a b e l ( n , r ) , l a b e l ( n ′ , r ) ) MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbhv2BYDwAHbqedmvETj2BSbqee0evGueE0jxyaibaiKI8=vI8tuQ8FMI8Gi=hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciGacaGaaeqabaqadeqadaaakeaacaWGdbWaaSbaaSqaaiaad6gaceWGUbGbauaaaeqaaOGaeyypa0ZaaSaaaeaacaaIXaaabaGaamOuaaaadaaeWbqaaiabes7aKbWcbaGaamOCaiabg2da9iaaigdaaeaacaWGsbaaniabggHiLdGcdaqadaqaaiaadYgacaWGHbGaamOyaiaadwgacaWGSbGaaiikaiaad6gacaGGSaGaamOCaiaacMcacaGGSaGaamiBaiaadggacaWGIbGaamyzaiaadYgacaGGOaGabmOBayaafaGaaiilaiaadkhacaGGPaaacaGLOaGaayzkaaaaaa@53A2@

where δ (l,l') = 1 if l = l', and δ (l,l') = 0 otherwise 131415. Contrary to a distance matrix calculated directly in 'expression level space', the 'consensus distance' D_nn' = 1 - C_nn' was not suffering from outlier effects. Thus, based on the consensus distance, data could be clustered reliably with hierarchical clustering using the Ward algorithm (Additional data files 2 and 3). Second, the likelihood was used to estimate the initial number of clusters to 27 (number of leaves in the hierarchical clustering). A thorough description of the cluster algorithm and the biological validation for reducing the number of clusters to 13 can be found in Additional data file 2 and in the report by Grotkjær and coworkers 12.

The expected distance between two coexpressed genes was calculated by assuming that a given gene belongs to a given cluster with probability P = Z/N. Here, Z is the number of transcripts in the analyzed cluster, and N denotes the total number of transcripts in the DNA microarray analysis found in the systematic sequence of S288C (6081). The distance between two genes belonging to the same cluster follows the negative binomial distribution (r = 1, P = Z/N). Z genes distributed on 16 chromosomes give rise to (Z - 16) intervals between genes. Hence, the expected number of times, Z_D, the distance D between two co-expressed genes is encountered is as follows:

Z D = ( Z − 16 ) Z N ( 1 − Z N ) D MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbhv2BYDwAHbqedmvETj2BSbqee0evGueE0jxyaibaiKI8=vI8tuQ8FMI8Gi=hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciGacaGaaeqabaqadeqadaaakeaacaWGAbWaaSbaaSqaaiaadseaaeqaaOGaeyypa0JaaiikaiaadQfacqGHsislcaaIXaGaaGOnaiaacMcadaWcaaqaaiaadQfaaeaacaWGobaaamaabmaabaGaaGymaiabgkHiTmaalaaabaGaamOwaaqaaiaad6eaaaaacaGLOaGaayzkaaWaaWbaaSqabeaacaWGebaaaaaa@425C@

The statistical significance between the position of replication origins and ORFs in each cluster was determined by randomization tests. For all genes in a particular cluster, the average distance between the start codon in base pairs to the nearest of the 294 replication origins 34 was calculated. The average distance for clusters with genes evenly distributed over all chromosomes was repeatedly determined, and a P value (the probability for observing the average distance in the cluster by chance) was calculated. The number of replication origins used in this study is less than the 429 replication origins determined by chromosome immunoprecipitation 32 and 332 found by replication timing experiment 33. A sensitivity analysis revealed that the P value increased for less than 294 replication origins and so the calculated P values should be considered conservative estimates.

The cumulated hypergeometric distribution was used to test for over-representation of cluster members among both cell cycle regulated genes and the transcription factor RAP1.

P = 1 − ∑ i = 0 X − 1 ( K i ) ( N − K Z − i ) ( N Z ) MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbhv2BYDwAHbqedmvETj2BSbqee0evGueE0jxyaibaiKI8=vI8tuQ8FMI8Gi=hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciGacaGaaeqabaqadeqadaaakeaacaWGqbGaeyypa0JaaGymaiabgkHiTmaaqahabaWaaSaaaeaadaqadaqaauaabeqaceaaaeaacaWGlbaabaGaamyAaaaaaiaawIcacaGLPaaadaqadaqaauaabeqaceaaaeaacaWGobGaeyOeI0Iaam4saaqaaiaadQfacqGHsislcaWGPbaaaaGaayjkaiaawMcaaaqaamaabmaabaqbaeqabiqaaaqaaiaad6eaaeaacaWGAbaaaaGaayjkaiaawMcaaaaaaSqaaiaadMgacqGH9aqpcaaIWaaabaGaamiwaiabgkHiTiaaigdaa0GaeyyeIuoaaaa@4BB1@

Here, X is the number of transcripts in each phase of the cell cycle found by the cluster analysis and K is the total number of analyzed ORFs in each phase of the cell cycle. N and Z are defined as above. We tested over-representation and under-representation of all 14 clusters in each phase of the cell cycle, and corrected the P value for multiple testing 60, leading to a cut-off of P < 0.01. Cell cycle regulated genes were compiled by selecting genes appearing in at least two of four lists, one containing genes known to be involved in the cell cycle based on literature studies and three lists arising from independent, numerical analyses 202122. A list of 5,421 overlapping genes was compiled by comparing the current dataset with that reported in the transcription factor binding study conducted by Lee and coworkers 16. The transcription factor RAP1 was found to affect 288 genes (P < 0.01). The genes were distributed in the clusters as follows: clusters 1-7 contained 132 genes, the 'trash' cluster 101 genes, and other clusters 55 genes.