With the foregoing regression framework, we further investigated whether the combined effect of various histone acetylation sites could be approximated by a simple cumulative model, or a more complex 'combinatorial histone code' is needed. To gain a qualitative overview, we grouped genes according to their upstream histone acetylation patterns, each corresponding to a combination of high (greater than 60th percentile) or low (less than 40th percentile) histone acetylation levels at three acetylation sites. To avoid ambiguity due to measurement noise, the middle 20% of genes was not included in any groups. This coarse-grained partition method results in eight groups of genes with distinct upstream acetylation patterns. For example, one of these eight groups contains genes with high H3K9, high H3K14, and low H4 acetylation levels in their upstream intergenic regions. Increasing H3K9 acetylation level enhances gene transcription (Table 2), regardless of the acetylation level at other sites. A similar but weaker pattern can be seen for H3K14 acetylation. In contrast, the increase of H4 acetylation level is associated with both elevated and reduced transcription rates. A possible explanation is that the regulatory effect of H4 acetylation is dependent on acetylation level at other sites, while another explanation is that the H4 acetylation effect is weak overall. These relationships are not sensitive to the cutoff threshold for removing ambiguous genes.

As a quantitative validation of the above observation, we re-examined the validity of equation 2 in modeling the regulatory role of histone acetylation. We observed that the inclusion of all quadratic interaction terms among the three histone acetylation covariates in the regression model does not improve the model fitting (that is, R² = 0.3262 and 0.3278, respectively, for intergenic regions, and R² = 0.3131 and 0.3132, respectively, for coding regions). The same conclusion also holds when we do not include the sequence motif information and nucleosome occupancy data as covariates (R2 = 0.1841 and 0.1925, respectively, for intergenic regions). These observations suggest that the combinatorial effect is, at best, undetectable from the current data and the simple cumulative model (equation 2) is sufficient. Similar results were obtained using the acetylation data in Kurdistani et al. 2 (Additional data file 1).

A statistical measure of the effect of an individual factor/covariate on the response variable is the partial correlation (Materials and methods), which roughly reflects the 'pure' relationship between two variables while controlling other factors. As shown in Table 3, partial correlations between transcription rates and intergenic H3K9 and H3K14 acetylation levels, while controlling the sequence information and H4 acetylation levels, are 0.25 and 0.21, respectively; whereas that between transcription rates and H4 acetylation effect is insignificant (-0.03). In addition, the difference between the effects of H3 and H4 acetylations is visually evident (Figure 2). The same phenomenon can be observed by comparing different regression models. As shown by Table 1, the R² (adjusted R-square) for the model without using the H4 acetylation information is comparable to the full model, whereas the performance of the model without H3 acetylation is significantly poorer. Interestingly, the transcription rate is negatively correlated with coding region H4 acetylation. These observations suggest that while H3 acetylation plays an important role in global gene activation, H4 acetylation in the intergenic region has little global effect. Similar results were also obtained for the acetylation data in Kurdistani et al. (Additional data file 1).

Gcn5 is the catalytic component of the SAGA complex and preferentially acetylates H3 lysines, including K9, K14, and K18. Esa1 is the catalytic component of the NuA4 complex and preferentially acetylates H4 lysines. Based on the above analysis, we predicted that the global gene expression was significantly affected by the abundance of Gcn5 but not of Esa1. Genome-wide occupancy of Gcn5 and Esa1 has been measured previously 4. Both enzymes were found to be globally associated with active genes, and the Pearson correlation between the occupancy levels of the two is as high as 0.7890, probably because they share a common component, Tra1, for recognizing targets 28. We modified equation 2 to estimate the association between Pol II occupancy 4 and these two HATs. In this case, the response variable y_i is the log-ratio of Pol II binding, whereas the x_ij (j = 1,2) are the log-transformed binding ratios of Gcn5 and Esa1, respectively. Fitting the model using both Gcn5 and Esa1 data yields an R² of 0.2365. If we remove Gcn5 from the model, the R² is reduced to 0.1808. However, removing Esa1 causes little change in model performance (R² = 0.2366). In addition, the partial correlation between the occupancy levels of Pol II and Gcn5 while controlling Esa1 occupancy is 0.2690, whereas the number is reduced to only 0.0154 if the order of Gcn5 and Esa1 is reversed. Taken together, these results show that, indeed, Esa1 only marginally affects the global association with Pol II binding.

Datasets analyzed in this study include those for histone acetylation, nucleosome occupancy, gene expression, and genome sequence. In two recently published papers, genome-wide histone acetylation levels at eleven 2 and three sites 8 in yeast were measured using CHIP-chip. A major difference in experimental procedure between these two studies is that the acetylated DNA was hybridized against nucleosomal DNA on microarrays in Pokholok et al.'s study 8, but was hybridized against the genomic DNA in Kurdistani et al.'s study 2. Since in the latter dataset histone acetylation was confounded with nucleosome occupancy, our discussion in the main text is focused on analyzing Pokholok et al.'s data. To compare the results from the two experiments, we repeated our analysis procedure on a normalized version of Kurdistani et al.'s data after removing its dependency on nucleosome occupancy. We found that the main conclusions remain the same. Detailed analysis of Kurdistani et al.'s data is presented in Additional data file 1.

In addition, several groups have measured genome-wide nucleosome occupancy in yeast 138. We chose to utilize Pokholok et al.'s nucleosome occupancy data in our analysis as well, since nucleosome occupancy has a clear effect on gene regulation 6. We used Bernstein et al.'s transcription rate data 1 as the response variable in our study of the relationship between gene transcription and histone acetylation. These transcription rates were estimated by dividing the transcription levels by half-life time 16. Due to concern that measured microarray data may vary significantly among different microarray platforms or research groups 323334, we repeated our analysis using an independent dataset 15. The results obtained from the two gene transcription data are similar (Additional data file 1).

After removing genes (with their corresponding intergenic and coding regions) that have missing data in any of the above datasets, we merged all the data into a single dataset, which contains 3,049 intergenic and 3,384 coding regions. The genomic sequence of S. cerevisiae was downloaded from the Saccharomyces Genome Database 14. The promoter sequences (up to 800 base pairs (bp) upstream of the translation start site of each gene) were extracted for cis regulatory signal analysis.

Transcription factors regulate genes by binding to transcription factor binding sites (TFBSs), which are short sequence segments (approximately 10 bp) located near genes' transcription start sites (TSSs). In yeast, these binding sites are mostly within 500 bp upstream of each gene's TSS. It has been shown that a gene's expression pattern can be predicted to a great extent by its upstream sequence information 26. We took two different approaches to accommodate sequence information in our analysis of the histone acetylation effect.

In our first approach, we conducted de novo TFBS predictions using MDscan 24 among the upstream sequences of the genes that were transcribed at high rates 1. In particular, this algorithm searched for enriched sequence motifs of widths 5 to 15 in the promoter sequences, resulting in 580 statistically significant, possibly overlapping, candidate TFBMs (p value < 0.05). We then used these motif patterns to scan all promoter regions for matches so as to compute a motif score for each TFBM at each promoter 24. To avoid overfitting, we selected a subset of 33 functional motifs based on the association of the motif score of a promoter with the transcription rate of the corresponding gene. In particular, we used both a linear regression procedure, Motif Regressor 25, and a model-free method, regularized sliced inverse regression (RSIR) 35, as explained below.

Our second approach to account for the cis regulatory information was to directly use the 666 transcription factor binding motifs reported by Beer and Tavazoie 26, which is a combination of computational predictions using AlignACE 22 and 51 experimentally derived ones 3637. Since these motifs have been shown to have a high predictive power for gene expression patterns, they may also be informative for predicting transcription rate. Out of these 666 motifs, our linear regression and RSIR procedures (see below) found 15 that are highly relevant to predicting gene transcription rates.

RSIR 35 is a statistical method for dimension reduction and variable selection. It assumes that gene i's transcription rate y_i and its sequence motif scores x_i = (x_i1,...,x_iM)^T are related as:

y i = f ( β 1 T x i , β 2 T x i , ... , β k T x i ε i ) ,       ( equation  3 ) MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbhv2BYDwAHbqedmvETj2BSbqee0evGueE0jxyaibaiKI8=vI8tuQ8FMI8Gi=hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciGacaGaaeqabaqadeqadaaakeaacaWG5bWaaSbaaSqaaiaadMgaaeqaaOGaeyypa0JaamOzaiaacIcaiiqacqWFYoGydaqhaaWcbaGaaGymaaqaaiaadsfaaaacbeGccaGF4bWaaSbaaSqaaiaadMgaaeqaaOGaaiilaiab=j7aInaaDaaaleaacaaIYaaabaGaamivaaaakiaa+HhadaWgaaWcbaGaamyAaaqabaGccaGGSaGaaiOlaiaac6cacaGGUaGaaiilaiab=j7aInaaDaaaleaacaWGRbaabaGaamivaaaakiaa+HhadaWgaaWcbaGaamyAaaqabaGccqaH1oqzdaWgaaWcbaGaamyAaaqabaGccaGGPaGaaiilaiaaxMaacaWLjaWaaeWaceaacaqGLbGaaeyCaiaabwhacaqGHbGaaeiDaiaabMgacaqGVbGaaeOBaiaabccacaaIZaaacaGLOaGaayzkaaaaaa@5CBB@

where f() is an unknown (and possibly nonlinear) function, β_l = (β_l1,...,β_lM)^T, (l = 1,...,k), are vectors of linear coefficients, and ε_i represents the noise. The number k is called the dimension of the model. A linear regression model is a special one-dimensional case of equation 3. RSIR estimates both k and the β_l values without estimating f(). Since many entries of the β_lj values are close to zero, which implies that the corresponding motif scores contribute very little in equation 2, we retain only those motifs whose coefficient β_lj is significantly nonzero.

We applied RSIR to the 580 candidate motifs selected by MDscan and the 666 motifs from 26, with the transcription rate as the response variable. In both cases, k was estimated as 1, and f() showed a strong linear pattern. We found 104 and 69 motifs, respectively, that have significantly nonzero coefficients in our RSIR model.

Previous application suggests that RSIR is conservative in selecting variables 35. We applied the stepwise regression algorithm (which is a recursive method commonly used for variable selection; see page 347 of 27) to further reduce the number of motifs. In the end, a total of 33 motifs from MDscan and 15 motifs from 26 were retained for further use. These motifs represent our summary of sequence-specific information on gene transcription rates.

To assess the significance of our model for controlling the confounding effects due to sequence information, we randomly permuted the transcription rates data 50 times and repeated the same statistical procedures: identifying motif candidates using MDscan, selecting the most significant motifs using RSIR, and fitting the linear regression model. The distribution of R² obtained for these randomized data was used as a baseline to evaluate the significance of our statistical procedure.

We also performed a five-fold cross validation procedure to test whether equation 2 overfit data. In particular, the full set of genes (seethe Data sources section above) was randomly partitioned into five subsets of equal sizes. Each subset was used for testing in turn with the rest used for training. For each training subset, the sequence motifs were inferred using MDscan, RSIR, and stepwise regression methods. We fit the model equation 2 using the training data and then evaluated out-of-sample error by applying to the testing data. The in-sample and out-of-sample root mean square errors were then compared.

Let X and Y represent two random variables and Z = (Z₁,Z₂,...,Z_p) be a set of control random variables. The linear relationship between X and Z can be estimated via a linear regression model X = α_X + Zβ_X + ε_X, similarly for that between Y and Z. The residues ε_X and ε _Y contain the information left unexplained by Z. The partial correlation between X and Y while controlling Z is defined as the Pearson correlation between ε_X and ε_Y.