Combinatorial analysis of chromatin marks

We investigated relationships between the genome-wide distributions of eight histone modifications, one histone variant and four DNA binding proteins in the immature myeloid human cell line K562 (Materials and Methods) at the 100 kb resolution of corresponding MRT data [61], [80]. As a first step, we computed the Spearman correlation coefficient of each mark with each other. We next represented the resulting matrix as a heat map after having reorganized rows and columns with a hierarchical clustering based on the Spearman correlation distance (Equation 1, Fig. 1). This preliminary analysis was very promising as regards to the possibility of reducing combinatorial complexity. All the epigenetic marks that are known to be involved in transcription positive regulation, namely H4K20me1, H3K9me1, H3K4me3, H3K27ac, RNAPII, CBX3, H2AZ, H3K79me2, H3K36me3, together with the transcription factors CTCF and Sin3A, form a block in the correlation matrix, meaning that they are all correlated with each other. The maximum correlation is actually obtained between the two active promoter marks H3K4me3 and H3K27ac. As suggested in Refs [27], [105], all these active marks are likely to occupy similar regions in the genome. In fact, two lines are clearly apart on the hierarchical clustering dendrogram (Fig. 1). They correspond to the repressive chromatin marks H3K27me3 and H3K9me3 that are respectively associated with the so-called facultative and constituve heterochromatins [105], [106]. These two marks are recognized by the chromodomains of polycomb (Pc) proteins and heterochromatin protein 1 (HP1), respectively, components of distinct gene silencing mechanisms which likely explains that they are strongly anticorrelated with each other. While H3K9me3 behaves quite independently with respect to most of the active chromatin marks, H3K27me3 correlates to some of them and especially to H4K20me1, H3K9me1 and CTCF. When further investigating the correlations between the thirteen considered chromatin marks and the MRT (Fig. 1), we found, consistently with previous works [56], [59], [61], [64], [65], a strong correlation for the transcriptionally active marks with early replication. Some moderate correlation was obtained for the Pc associated repressive marks H3K27me3 which contrasts with the significant anticorrelation observed for the constitutive heterochromatin mark H3K9me3 with late replication.

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Figure 1. Spearman correlation matrix between epigenetics marks and mean replication timing (MRT).

For each pair of variables we computed the Spearman correlation over all 100-overlapping windows with a valid score. Spearman correlation value is color coded using the color map shown on the right. A white line separates the MRT from epigenetics marks. Correlations with MRT (from late to early) are placed at the top and the right of the matrix. Lines for the thirteen epigenetic marks were reorganized by a hierarchical clustering using Spearman correlation distances (Equation 1) as illustrated by the dendrogram on the left of the graph. This ordering implies that highly correlated epigenetic marks are close to each other.

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In a second step, to objectively identify the prevalent combinatorial patterns of the thirteen chromatin marks, we performed a PCA [107] to reduce the dimensionality of the data (Materials and Methods). We then concentrated on the first three principal components, which together account for 76% of the total data set variance (Supplementary Fig. S1). By projecting the 100 kb genomic loci on the (PC1, PC2) plane (Fig. 2A) and the (PC3, PC2) plane (Fig. 2B), we noticed that four areas contain most of the population. On the (PC1, PC2) plane, a large area of medium density comes out from a plane of much higher density. As viewed on the (PC3, PC2) plane, in this very dense plane, loci mainly lie along two straight lines with a very high density of loci concentrated at the intersection of these lines. This led us to use the Clara clustering algorithm [88], which is very similar to k-means, with the number of clusters fixed to four (Materials and Methods). When labeling each of the four main chromatin states with a color, we obtained four domains in the 3D scatter plot (Fig. 3A) that have common boundaries as evidenced on the three orthogonal projections on the planes (PC1, PC2) (Fig. 3B), (PC1, PC3) (Fig. 3C) and (PC3, PC2) (Fig. 3D). To improve the quality of our clustering procedure, we filtered out poorly clustered data points that are closer to another cluster than to the one they belong to (black dots in Fig. 3), where the distance between a data point and a cluster is defined as the mean of the distances of this point to all the points in the cluster. Removing those points is exactly equivalent as removing points with a negative silhouette [108] (Materials and Methods).

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Figure 2. Principal Component Analysis (PCA).

Two-dimensional (2D) projections of the data on (A) the plane defined by the first (PC1) and second (PC2) principal components, and (B) the plane defined by the second (PC2) and the third (PC3) principal components. The densities were computed by a kernel density estimation. The density values are indicated by a color (white: high density, yellow: moderate density, green: low density) and a contour plot.

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Figure 3. Defining the four prevalent chromatin states.

(A) Scatterplot of the data points onto the first three principal components. Color dots indicate the four chromatin states as found by our clustering procedure (pink: transcriptionally active chromatin, orange: chromatin repressed by polycomb, green: silent unmarked chromatin, blue: HP1 heterochromatin). Points in dark grey are not classified in any chromatin state (see Materials and Methods). (B) Within-cluster sum of squares (Eq. 2) with respect to the number of clusters (see Materials and Methods). (C) Gap statistics (Eq. 4) with respect to the number of clusters (see Materials and Methods).

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To determine the number of clusters, we used two statistical criteria (Materials and Methods). Four is the optimal choice according to the within-cluster sum of squares that clearly displays an elbow (abrupt slowing down of the decay) at the cluster number equal to four (Fig. 3B). The gap statistic [109] indicates that two or four clusters are good solutions (Fig. 3C). Our choice of four main chromatin states (Fig. 3A) can thus be seen as an attempt to test the limits of the classical dichotomic picture [65], [74], [75] of two chromatin states, one open (euchromatin) and another one closed (heterochromatin) (Supplementary Fig. S2A).

Epigenetic content of the four prevalent chromatin states

The four prevalent chromatin states so identified and further labeled C1, C2, C3 and C4, were respectively found in 6572 (23.8%), 5312 (19.2%), 6603 (23.9%) and 6758 (24.4%) among the 27656 100 kb loci with a defined MRT (Materials and Methods). Indeed, we removed from the analysis the 2411 (8.7%) loci that were not properly classified in any chromatin state. More than 90% of the loci in C1 are associated (positive enrichment) with the histone modifications H3K36me3, H3K4me3, H3K27ac and H3K79me2, the hallmarks of transcriptionally active chromatin (Fig. 4) [2], [6], [105], as well as of the loci associated with RNA Polymerase II (Fig. 5) and the RPD3-interacting protein SIN3A (Fig. 5) as previously found in active euchromatin in Drosophila [22]. The majority of C1 loci are marked by H3k9me1 loci consistently with the observation of higher H3K9me1 levels in active promoters [105], and also contains the histone variant H2AZ whose binding level was shown to correlate with gene activity in human [105] (Fig. 4). C2 is notably associated with the histone modification H3K27me3 (Fig. 4), hence corresponds to a Polycomb repressed facultative heterochromatin state [105], [106]. Out of the four main chromatin states, C3 corresponds to 100 kb loci that are not enriched for any available marks. C3 can be compared to the “null” or “black” silent heterochromatin regions previously found in Drosophila [21], [22] and Arabidopsis [19] as covering a significant portion of the genome. C4 corresponds to the classic HP1-associated heterochromatin state with all of the 6603 C4 100-kb-loci containing the H3K9me3 mark and almost only that repressive mark (Fig. 4) [105], [106].

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Figure 4. Repartition of histone marks in the four chromatin states.

Boxplots of the decimal logarithm of histone mark ChiP-seq read density in 100 kb non-overlapping windows per chromatin state. Same color coding as in Fig. 3A.

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Figure 5. Repartition of transcription factors in the four chromatin states.

Boxplots of the decimal logarithm of transcription factor ChiP-seq read density in 100 kb non-overlapping windows per chromatin state. Same color coding as in Fig. 3A.

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Methylation of H3K9 is well known to be implicated in heterochromatin formation and gene silencing [2]. The fact that H3K9me1 is found almost equally in C1 and C2 and not in C4 (Fig. 4), confirms that this epigenetic modification may also be associated with transcriptional activation [105]. H3K9me3 is found in all C4 100-kb-loci as the probable signature of its ability to anchor the heterochromatin protein HP1 at the origin of the establishment of heterochromatin. But H3K9me3 is not exclusively found in C4 loci; indeed 75% of C1 loci and 50% of C2 loci contain some H3K9me3 marks (Fig. 4). In the transcriptionally active state C1, H3K9me3 is present in combination with all active marks which might conduct in the anchoring of the isoform of the HP1 protein [110]–[113], also called CBX3 (Fig. 5), which was recently shown to help the splicing of multiexonic genes [114], [115].

The insulator-binding protein CTCF is known to establish chromatin boundaries to prevent the spreading of heterochromatin into transcriptionally active regions [116], [117]. Consistent with the idea that CTCF-bound insulators prevent heterochromatin to invade genic regions, we found in good agreement with previous observation in Drosophila [21], [22] that CTCF is contained in C1 loci and to a slightly less extent in C2 loci (Fig. 5).

Despite the original association of H4K20 methylation with repressive chromatin [2], H4K20me1 was recently shown to strongly correlate with gene activation [105]. In particular when combined with H3K36me3 and H2BK5me1, this mark was found at highly expressed exons near human gene 5′-ends [118]. The high level of H4K20me1 found in C1 (Fig. 4) is quite consistent with these observations. However, we observed the same level of H4K20me1 in C2 which is silent. This suggests that this mark is not uniquely linked to transcription activation. Interestingly, recent works have confirmed that PR-Set7 involved in the deposition of H4K20me1 plays an important role in the control of replication origin firing in mammalian cells [119]–[121].

To assess the generality of the four prevalent chromatin states, we ran the same clustering procedure on the lymphoblastoid cell line GM12878 and on a third blood cell line (Monocyte CD14, Monocd14ro1746). The same four main chromatin states emerged in the three cell lines (Supplementary Figs S7, S9, S10, S11). Hence the chromatin organization in four chromatin states is shared by at least several somatic human cell lines.

Chromatin states are replicated at different times during S phase

This classification into four main chromatin states of the human genome shows strong similarities with those recently reported in Arabidopsis [19] and Drosophila [21], [22] suggesting the possible existence of some simple principles of epigenetic compartimentalization of eukaryotic genomes. However, what our study reveals with respect to previous works, is a strong correlation between these chromatin states and MRT (Fig. 6). C1, C2, C3 and C4 actually have significantly different MRT probability distribution functions (Fig. 6A) with a clear shift from early to late replicating as evidenced by the cumulative distribution functions (Fig. 6B). By applying a wilcoxon test to each pairs of chromatin states, we did verify that the p-value was infinitesimal. The transcriptionally active euchromatin state C1 replicates early in S phase consistent with previous analysis of open chromatin marks in human and mouse [56], [59], [61], [62], [64], [65]. The Pc-repressed facultative heterochromatin state C2 is replicated slightly later in mid-S phase which corroborates the recent finding of an association of H3K27me3 with mid-replicating chromosomal domains in human fibroblast [106]. This rather clear observation contrasts with previous contradictory results concerning the existence of high correlation between late replication and this repressive chromatin mark [65], [122]. The silent unmarked chromatin state C3 replicates later than C2 but before the HP1-associated heterochromatin state C4 that replicates very late almost at the end of S phase (Fig. 6). As previously reported in Drosophila [22], [63], these results confirm the existence of a strong link between epigenetic chromatin states and MRT in human. They further suggest that the epigenetically controlled chromatin structure has some impact on the normal progression of S-phase.

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Figure 6. MRT in the four chromatin states.

(A) Boxplots of MRT computed in 100 kb non-overlapping windows per chromatin state. (B) Empirical cumulative distribution function (c.d.f.) of MRT in the four chromatin states. Same color coding as in Fig. 3A.

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Chromatin states are different functionally

To address the question of the gene content of these four prevalent chromatin states, we used a data set of 23818 genes that are spatially distinct (Materials and Methods). Some of these genes (3001) were not taken into account in our analysis because their promoter don't belong to any chromatin state. The mean density of the 20817 genes that belong to one of the four chromatin states is 8.24 promoters per Mb. The only chromatin state that is highly enriched in gene promoters is the early replicating euchromatin state C1 that harbours 62.0% of gene promoters even though it represents about 25% of the total genome coverage by the four chromatin states (Table 1 and 2). The mid S facultative heterochromatin state C2 also contains a non negligible percentage (19.6%) of gene promoters that indeed corresponds to a modest density 7.7 promoters/Mb as compared to 19.1 promoter/Mb found in C1. The late replicating unmarked and constitutive heterochromatin states C3 and C4 are genuinely gene deserts with very low gene densities 4.1 promoters/Mb and 1.8 promoter/Mb respectively. The mean gene length increases gradually from C1 to C4 going from 42.5 kb to 133.1 kb (Table 1). This discrepancy in gene length explains why the gene coverage decreases less abruptly than the promoter density, with C1 mainly genic (62.9%), C2 modestly genic (49.8%) and C3 (39.5%) and C4 (29.3%) mostly intergenic.

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Table 1. Gene content in the four chromatin states.

https://doi.org/10.1371/journal.pcbi.1003233.t001

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Table 2. Domain organization of chromatin states.

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To investigate gene expression in chromatin states, we used a data set of 17872 genes with a valid expression value in K562 (Materials and Methods). Of those genes, 15869 belong to one of the chromatin states. We found that a vast majority of expressed genes with a (Equation 7) are in the early replicating euchromatin state C1 (Fig. 7B), which confirms the link between MRT and expressed gene density previously reported in mammals [55], [58], [59], [61]. As expected, most of the genes in the facultative Pc repressed heterochromatin state C2 are non expressed. Interestingly, we found that the density of non expressed genes in C1 is equivalent to the one in C2, indicating that it is more the predominance of active genes that characterizes early replicating regions than the absence of repressed genes. This explains why the correlation between MRT and gene expression is stronger if one considers the expressed gene density (, )) than the mean expresssion (, ) as previously observed in Drosophila [54]. Indeed in C1 the mean gene expression level is lowered by the presence of a non negligible set of non-expressed genes. The few genes in the heterochromatin states C3 and C4 are silent except a minority of them.

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Figure 7. Gene expression in the four chromatin states.

(A) c.d.f. of gene expression (measured in , see Materials and Methods) in the four chromatin states. (B) Density of promoters in the 4 chromatin states as a function of gene expression (genes were grouped into bins of width 0.05 in unit). Same color coding as in Fig. 3A.

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We assessed gene function on the basis of gene ontology [123]. We analyzed the genes in each chromatin states according to their biological process (Supplementary Fig. S3), component (Supplementary Fig. S4) and function (Supplementary Fig. S5) using GO SLIM annotation (Materials and Methods). We computed the enrichment p-value using the Hypergeometric distribution and used the odd ratio value to determine if the deviation from expected number of genes for the considered GO terms was an enrichment () or a depletion (). As previously observed for gene expression, these GO terms provide some clear discrimination between genes in the early replicating transcriptionally active euchromatin C1 and genes in the repressed heterochromatin states C2, C3 and C4. Genes enriched in C1 are almost systematically depleted in C2, C3 and C4, whereas on the opposite, genes that are depleted in C1 are enriched in at least one if not all the heterochromatin states C2, C3 and C4. We found C1 to be enriched mainly in housekeeping genes. The highest enrichments were obtained for the following process categories: mRNA processing, translation, ribosome biogenesis, DNA metabolic process, chromosome organization and segregation, cell cycle and cell division and for the corresponding component categories: ribosome, chromosome, nucleolus, nucleoplasm, nuclear envelope, mitochondrion and microtubule organizing center. The highly depleted process categories in C1 correspond to tissue specific genes that are not expressed in the immature myeloid K562 cell line as for example neurological system process, extracellular matrix organization, cell adhesion and cell motility, or that are defficient in these cancer cells like circulating system process [124], [125].

Compositional content of chromatin states

Along the line of the isochore model [126], GC-rich and GC-poor regions were shown to match the cytogenic R and G bands and to correlate well with early and late replicating domains in mammals [8], [127], [128]. GC-rich regions correspond to regions of very high density of genes including the housekeeping genes and associated CpG islands. This also correspond to regions enriched in short inter-dispersed repetitive DNA elements (SINEs, Alu) [8]. In contrast, GC-poor regions are definitely poor in genes, predominantly tissue-specific genes containing rather large introns, but are relatively rich in long inter-disperse repetitive DNA elements (LINES) [8] that are significantly more abundant in these regions. Consistently, we found that the early replicating euchromatin state C1 has a GC content distribution shifted to higher values as compared to the unmarked and constitutive heterochromatin states C3 and C4 respectively (Fig. 8A). C1 is definitely GC-rich with an mean value that is significantly higher than the genome average (). On the opposite C3 and C4 are GC-poor with and 36.7%, respectively. Surprisingly, the Pc repressed facultative heterochromatin state C2 has a GC content distribution similar to the one obtained for C1 (Fig. 8) with . This means that if a high density of early replicating and highly expressed genes implies a high GC content, the reciprocal is not true. For example, C2 loci corresponding to 18% of the genome are GC-rich (Fig. 8A) but gene poor (Table 1) and most of these C2 genes are silenced by Pc proteins.

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Figure 8. Sequence composition in the four chromatin states.

(A) Boxplots of GC content computed in 100 kb non-overlapping windows per chromatin state. (B) Boxplots of CpG o/e computed in 100 kb non-overlapping windows per chromatin states. Same color coding as in Fig. 3A.

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Cytosine DNA methylation is a mediator of gene silencing in repressed heterochromatin regions, while in potentially active open chromatin regions DNA is essentially unmethylated [129], [130]. Methyl-cytosines being hypermutable, prone to deamination to thymines, CpG o/e ratio (Materials and Methods) is commonly used as an estimator of DNA methylation, the higher this ratio, the lower the methylation [101], [131]. When computing CpG o/e after removing the CpG islands (CGIs) that are short unmethylated regions rich in CpG, in the four chromatin states, we found a significant shift of the CpG o/e pdf to smaller values when going from C1 () to C2 (), C3 () and C4 () (Fig. 8). Thus relative to the genome average value , the early replicating transcriptionally active euchromatin state C1 is clearly hypomethylated. The mid-S repressed facultative heterochromatin state C2 is also, but at a lesser extent, less methylated than the entire genome. As expected the late replicating unmarked and constitutive heterochromatin states C3 and C4 are definitely methylated, the later being significantly more methylated than the entire genome. Thus the differences in CpG o/e (Fig. 8B) and MRT (Fig. 6A) observed in the four chromatin states C1, C2, C3 and C4, explain the significant correlation observed genome wide between methylation and replication timing (, )) [101].

Note that chromatin state compositional content in Monocd14ro1746 is quite the same as in K562 (Supplementary Fig. S11). In constrast, C3 and C4 in GM12878 have exchanged their GC and CpGo/e distributions (Supplementary Fig. S9). Interestingly, this phenomenon is paired with C3 becoming more late in GM12878 than C4 (Supplementary Fig. S9). This observation suggests that the genomic regions that replicate late in S phase are more likely specified by sequence features than by epigenetic features. However, the GC content cannot be the primary determinant of MRT for C1 and C2 states. Indeed the GC distributions in C1 and C2 are nearly the same (Fig. 8A, Supplementary Fig. S9A and S11A) whereas a great discrepancy is observed in the MRT distributions (Fig. 6, Supplementary Fig. S8 and MRT data non available).

Repartition of chromatin states along human chromosomes

Once mapped on the genome (Fig. 9A,B), the four prevalent chromatin states differ not so much in the genome coverage but mainly in their number and length distribution of domains or blocks of adjacent 100-kb-loci in the same chromatin state (Table 2 and Fig. 9C). C1 and C2 chromatin blocks are more numerous but they are shorter with a mean length kb and 228 kb respectively. Their length pdfs do not reveal many domains larger than 1 Mb. C3 chromatin blocks are slightly less numerous and also mostly short, the larger mean length kb resulting from the existence of a few large C3 streches of several Mb length. The C4 block length pdf definitely differs from the previous ones by the presence of a fat tail. Not only the mean length kb is about three times the ones of C1, C2 blocks, but most of the C4 domains exceed 1 Mb up to 5 Mb and more, hence they are less numerous (Fig. 9C). This observation is quite consistent with the HP1-associated classical heterochromatin spreading mechanism and its possible association with the nuclear envelope [3], [6].

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Figure 9. Genome-wide spatial distribution of the four chromatin states.

(A) MRT profile along a 20 Mb long fragment of human chromosome 1. Below the MRT profile, gene positions are indicated by a segment (blue: not expressed, orange: expressed). At the bottom of the plot, the chromatin state of each 100 kb window is represented using the same color coding as in Fig. 3A. (B) Same as (A) for the following 20 Mb fragment of the human chromosome 1. (C) Histogram of chromatin state block length in a logarithmic representation (see Materials and Methods). (D) Same as (C) for chromatin state blocks formed by states 1 and 2 (1+2, light red) or by states 3 and 4 (3+4, light blue). (E) MRT in chromatin state blocks (1+2) with respect to their length. Each 100 kb window in a chromatin state block is represented by a blue dot. The mean profile was obtained by (i) ordering data points according to their block length, (ii) grouping them in classes of equal number of data points and (iii) computing the average length and MRT over each class. Vertical bars represent the standard deviation. Horizontal bars represent the range of length over each class. (F) Same as (E) for chromatin state blocks (3+4).

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When looking at the distribution of chromatin states along human chromosomes (Fig. 9A,B), there is a clear evidence that C1, C2, C3 and C4 blocks are not distributed independently. In large regions with MRT ≲ 0.4, short C1 and C2 blocks intersperse with each other, the C1s being the earliest ones (e.g from 158 to 161 Mb in Fig. 9A). In a few 100 kb wide regions of MRT0.6, C3 blocks are observed with a repressive effect (e.g around 156 Mb in Fig. 9A where chromosome 1 contains a lot of olfactory receptor genes). C4 lies in very late regions MRT and form large uninterrupted blocks of several Mb size (e.g from 185 to 190 Mb in Fig. 9A). This MRT dependent spatial organization of chromatin states prompted us to investigate neighborhood dependency between 100 kb loci. The obtained transition matrix (Table 3) confirms that C4 loci have by far the highest probability (0.85) to have a C4 neighbor consistent with C4 blocks being much longer than the other chromatin state blocks (Table 2 and Fig. 9C). It also quantifies the fact that C1 loci (and in turn blocks) have a much higher probability to have a neighbor that is a C2 locus (block) than a C3 or C4 locus (block) and vice-versa. This is consistent with the fact that C1 and C2 are likely to be replicated one after each other in early and mid S phase whereas C3 and C4 are replicated much later (Fig. 6). Consistently C4 loci (blocks) have a highest probability to have a neighbor that is a C3 locus (block) whereas C3 loci (blocks) have apparently no special preference. The spatial organization of chromatin blocks suggests that we can associate C1+C2 on one side and C3+C4 on the other side (Supplementary Fig. S2B) resulting in large-scale blocks of surprisingly very similar length distributions (Fig. 9D) with fat tails and respective means 779 kb and 808 kb. These mega-base long C1+C2 and C3+C4 chromatin blocks would on average be replicated rather early (Fig. 9E) and late (Fig. 9F), respectively. Importantly, fixing the number of chromatin states to two in our PCA and cluster analysis does not result in the same dichotomic picture (Supplementary Fig. S2A). Instead we discriminate the active chromatin state C1 from a composite silent state C2+C3+C4 (Supplementary Fig. S2B)

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Table 3. Transition matrix between chromatin states.

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Note that when using the so-computed transition matrix between chromatin states (Table 3) to generate randomly synthetic chromosomes, we obtained very good predictions for the four chromatin state block mean lengths (Table 2). However the corresponding sample standard deviations so predicted are significantly smaller than the ones computed for the genuine human chromosomes which is an indication that the succession of chromatin states along human chromosomes is probably governed by a more global and elaborated underlying segmentation process.

Distribution of chromatin states inside replication timing U-domains

When concentrating our study on the 876 replication timing U-domains previously identified in K562 cells [80], we revealed some remarkable organization of the four prevalent chromatin states (Fig. 10A). The highly expressed gene rich euchromatin state C1 is found to be confined in a closed () neighborhood of the “master” replication origins that border each individual U-domains (Fig. 10A). As confirmed on the mean occupation profiles obtained for four U-domains size categories (Fig. 10 E, F, G, H), this confinement is independent of the U-domains size and consistent with the previous observation [80], [101] that U/N-domain borders are significantly enriched in DNase I hypersensitive sites and in insulator-binding proteins CTCF. C1 can thus be seen as specifying the early initiation zones that border U-domains and that were further shown [80] to delimit topological domains on genome-wide (Hi-C) chromatin state conformation data. The Pc repressed heterochromatin state C2 is mostly found at finite distance (∼200–300 kb) from U-domain borders as clearly seen on the largest U-domains whose centers are drastically devoided of C2 loci (Fig. 10B,H). In small U-domains (), C2 occupies in majority their centers (Fig. 10E,F) that are replicated in mid-S phase. U-domain borders are also significantly depleted in unmarked and constitutive heterochromatin states C3 (Fig. 10C) and C4 (Fig. 10D), respectively. C3 is already present in the center of small U-domains (Fig. 10E,F) and homogeneously occupies large U-domain centers (Fig. 10G,H). C4 is significantly found in the center of U-domains that are larger than 1 Mb; C4 spreads and becomes predominant when increasing the size of U-domains beyond 1.8 Mb (Fig. 10G,H). These results show that the replication “wave” starting from the early initiation zones at U-domain borders and propagating inside U-domains during S-phase with the progressive activation of secondary replication origins [79], actually corresponds to a directional path through the four prevalent chromatin states C1, C2, C3 and ultimately C4 in the largest U-domains. This gradient of chromatin structure, from active openess at U-domain borders to closeness at U-domain centers via intermediate Pc repressed and unmarked heterochromatins is likely to be a key ingredient in the long-range chromatin control of the spatio-temporal replication program that underlies the megabase-sized replication fork polarity gradients observed in about 50% of the human genome [79], [80].

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Figure 10. Distribution of the four chromatin states inside replication timing U-domains.

(A) The 876 K562 U-domains were centered and ordered vertically from the smallest (top) to the largest (bottom). All transcriptionally active chromatin state C1 100-kb-windows were represented by an horizontal segment of the corresponding length. (B) Same as (A) for the Pc repressed by chromatin state C2. (C) Same as (A) for the silent unmarked chromatin state C3. (D) Same as (A) for the HP1 heterochromatin state C4. (E) Mean coverage of chromatin state with respect to the distance to the closest U-domain border for U-domains smaller than 0.8 Mb. Error bars represent the standard deviation of the mean. (F) Same as (E) for U-domains of size between 0.8 Mb and 1.2 Mb. (G) Same as (E) for U-domains of size between 1.2 Mb and 1.8 Mb. (H) Same as (E) for U-domains of size between 1.8 Mb and 3.0 Mb. Same color coding as in Fig. 3A.

https://doi.org/10.1371/journal.pcbi.1003233.g010

Conclusion/perspectives

In summary, this integrative analysis of epigenetic mark maps in the immature myeloid human cell line K562 has shown that the combinatorial complexity of these epigenetic data can be reduced to four prevalent chromatin states, one transcriptionally active open euchromatin state C1 and three distinct and silent heterochromatin states, namely a Pc repressed state C2, a unmarked silent state C3 and a HP1-associated constitutive state C4. By performing this statistical study at the (low) resolution 100 kb of available genome-wide MRT data, we have found that these chromatin states actually replicate at distinct periods of the S-phase, C1 replicates early, C2 is a mid-S phase phase state whereas C3 replicates later than C2 but before C4 that replicates very late, almost at the end of S-phase. In the Supplementary Data are reported, for comparison, the results of a similar integrative analysis of epigenomic data in the lymphoblastoid cell line GM12878 (Supplementary Figs S6, S7, S8 and S9) and in the blood cell line Monocd14ro1746 (Supplementary Figs S10, S11), which confirm that the classification of the human epigenome in four main chromatin states likely summarizes the data in different cell types. Interestingly, these four main chromatin states display remarkable similarities with that found in different cell types in Drosophila [21] and Arabidopsis [19] at the resolution ∼1 kb of gene expression data, suggesting the existence of simple principles of organization in metazoans as well as in plants [19]–[22]. When mapping these four chromatin states along the human chromosomes, our study reveals that the human genome can be segmented into megabase-sized domains of three different types with distinct spatio-temporal replication programs. In 50% of the human genome that are covered by the replication U-domains [80], the U-shape of the replication timing profile indicates that the effective replication velocity (which equals the inverse of the replication timing derivative [80], [98]) increases from U-domain borders to centers [79] as the signature of an increasing origin firing frequency during S-phase [132]. Our results (Fig. 10) show that this acceleration of the replication wave is actually observed along a directional path through the four main chromatin states, the open euchromatin state C1 at U-domain borders successively followed by the heterochromatin states C2, C3 and C4 at the U-domain centers. To which extent this chromatin gradient influences fork progression from the “master” early initiation zones at U-domain borders and secondary origins activation inside U-domains is a key issue of current modeling [79], [133]–[135] of the spatio-temporal replication program in human and more generally in mammals. The complete analysis of the other half of the human genome that is complementary to U-domains is more in agreement with the traditional dichotomic picture proposed in early studies of the mouse [55]–[57] and human [59], [65], [75] genomes, where early and late replicating regions occur in separated compartments of open and close chromatin, respectively. About 25% of the human genome are covered by megabase sized GC-rich (C1+C2) chromatin blocks that on average replicate early by multiple almost synchronous origins with equal proportion of forks coming from both directions (Table 4). This absence of well-positioned origins explains that the skew has not accumulated in these gene-rich regions that were shown to be devoided of skew N-domains [90]–[93]. The last 25% of the human genome corresponds to megabase sized GC-poor domains of interspersed (C3+C4) heterochromatin states or of long C4 domains that on average replicate late by again multiple almost coordinated origins (Table 4). These gene-poor regions are also devoided of skew N-domains and can be seen as the late replicating counter-part of the gene-rich (C1+C2) regions.

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Table 4. Distribution of chromatin states outside replication timing U-domains.

https://doi.org/10.1371/journal.pcbi.1003233.t004

Extending this study to different cell types including ES, somatic and cancer cells looks very promising. By performing our integrative analysis at low (100 kb) and high (1 kb) resolutions in parallel, we should be in position to investigate the global reorganization of replication domains during differentiation (or disease) in relation to coordinated changes in chromatin state and gene expression. For example, this multivariate approach should shed a new light on the so-called replication domain “consolidation” phenomenon [56] that corresponds to the disappearance (EtoL transition) or appearance (LtoE transition) of a U-domain border during differentiation [80].The probable coordinated change in chromatin state at 100 kb resolution and the possible change at 1 kb resolution are likely to explain the possible change in gene expression. This opens new perspectives in the study of chromatin-mediated epigenetic regulation of transcription and replication in mammalian genomes in both health and disease.

Mean replication timing data and replication U-domain coordinates

Timing profiles for the immature myeloid cell line K562 and the lymphoblastoid cell line GM06990 were obtained from the authors [80]. The mean replication timing (MRT) is given for 27656 100 kb non-overlapping windows in hg18 coordinates. We also retrieved the coordinates of the 876 U-domains in K562 and 882 U-domains in GM06990 from the authors [80].

Histone marks, H2AZ, CTCF, RNAP II, Sin3A and CBX3 ChIP-seq data

For all ChIP-seq data, we downloaded data in the Encode standard format “broadpeaks” (http://genome.ucsc.edu/FAQ/FAQformat.html). Broadpeaks format is a table of significantly enriched genomic intervals. Most of the data correspond to the release 3 (August 2012) of the Broad histone track. We downloaded the tables from: http://hgdownload.cse.ucsc.edu/goldenPath/hg19/encodeDCC/wgEncodeBroadHistone/. The CBX3 and Sin3A data corresponds to the release 3 (September 2012) of the HAIB TFBS track. Tables were downloaded from the UCSC from: http://hgdownload.cse.ucsc.edu/goldenPath/hg19/encodeDCC/wgEncodeHaibTfbs/

For the K562 cell line, we downloaded the broadpeak tables for the following antibodies: CTCF, H3K27ac, H3K27me3, H3K36me3, H3K4me3, H3K9me3, RNAP ll, H2AZ, H3K79me2, H3K9me1, H4K20me1, CBX3, Sin3A. For the GM12878 cell line, we downloaded: CTCF, H3K27ac, H3K27me3, H3K36me3, H3K4me3, H3K9me3. For the Monocd14ro1746 cell line we downloaded: CTCF, H2AZ, H3K27ac, H3K27me3, H3K36me3, H3K4me3, H3K79me2, H3K9ac, H3K9me3. Genomic intervals were then mapped back to hg18 using LiftOver.

Epigenetic profile computation at 100 kb resolution

For each ChIP-seq data, we computed a profile at the 100 kb resolution for the 27656 non-overlapping windows for which MRT is defined. The read density for one antibody in a window is the number of reads in this window that fall in significantly enriched intervals normalized by the window length.

Rank transformation and Spearman correlation matrix

All statistical computations were performed using the R software (http://www.r-project.org/).

In order to compute the Spearman correlation matrix, the epigenetic profiles at 100 kb resolution were transformed with the R function rank with option ties.method = max. Then we computed the Pearson correlation matrix on the transformed dataset. To reorder the matrix in Fig. 1, we computed the Spearman correlation distance as:(1)where is the spearman correlation. Then, a dendrogram was computed using the R function hclust with option method = average and with as dissimilarity.

Principal component analysis

Principal component analysis was performed on the rank transformed dataset using the function dudi.pca from the R package ade4 (see http://pbil.univ-lyon1.fr/ADE-4 and Ref. [107]) with the option scale = TRUE (i.e. each variable is centered and normalized before the PCA computation). The first three components were retained which accounts for of the dataset variance (see Supplementary Fig. S1), and clustering was performed in this 3D space.

Clustering strategy

We used Clara algorithm [88] which is an optimization of k-means for large data set. We used the clara function implemented in the R package cluster. The options were set to: stand = FALSE, sampsize = 500, samples = 20, metric = euclidean.

To assess the number of clusters, we used the pooled within-cluster sum of squares around the cluster mean. Suppose that the data set of size is divided in k clusters . Let d(x,y) be the euclidean distance between the points x and y. Let be the mean of the cluster, then the within-cluster sum of squares for this cluster is:(2)

The pooled within-sum of squares for the k clusters is:(3)

The pooled within-cluster sum of squares necessarily decreases with the number of clusters. A good choice for the number of clusters is the critical point where some clear crossover is observed from a fast decrease of at small k values to a weak decrease of at large k values. This means that, after this critical point, no much information is gained by adding a new cluster. In our analysis this crossover occurs for k = 4 clusters (see Fig. 3B).

We also used the Gap statistic [109] which is defined by :(4)

is the expected value of for a sample of size drawn from a proper reference distribution. We choose, as a reference, a uniform distribution over the range of the observed data. A good choice for the number of clusters is a value of k so that is much smaller than the expected from a random distribution (i.e. a high value of ). Four clusters is also a reasonable choice according to the gap statistic index computed with R package clusterSim (see Fig. 3C).

Poorly clustered data points were removed from the set of chromatin states. The silhouette value [108] is a way to quantify how well a point is clustered.

Definition 1. Given a particular clustering, , of the data in k clusters, let i be a data point and the average distance of the data point i to the members of the cluster . Let i be a member of cluster and(5)The silhouette value of the data point i is defined as:(6)

A silhouette value below 0 means that the data point is actually closer in average to the points from another cluster than to the one it has been assigned to. Points with a negative silhouette value are border line allocations. We decided to remove those points from the set of identified chromatin states. Hence chromatin states are groups (clusters) with homogeneous epigenetic features. 91% of all 100 kb non-overlapping windows of the human genome were assigned to one of the four chromatin states C1, C2, C3 or C4.

Markov transition matrix estimation

The number of transitions from i to j, , is the number of 100 kb windows of state i contiguous to a window of state j (the sense or antisense orientation is not taken in account). Let be the number of windows in chromatin state i. The conditional probability of a transition from i to j given i is .

Annotation and expression data

As human gene coordinates, we used the UCSC Known Genes table. When several genes presenting the same orientation overlapped, they were merged into one gene whose coordinates corresponded to the union of all the overlapping gene coordinates, resulting in 23818 distinct genes.

Expression data were retrieved from the Genome Browser of the University of California Santa Cruz (UCSC). To construct our expression data set, we used RefSeq Genes track as human gene coordinates. Genes with alternative splicing were merged into one transcript by taking the union of exons. Hence the TSS was placed at the beginning of the first exon. We obtained a table of 23329 genes. We downloaded expression valuess from the release 2 of Caltech RNA-seq track (ENCODE project at UCSC: http://hgdownload.cse.ucsc.edu/goldenPath/hg18/encodeDCC/wgEncodeCaltechRnaSeq/).

Expression for one transcript is given in reads per kilobase of exon model per million mapped reads (RPKM) [136]. RPKM is defined as:(7)where C is the number of mappable reads that fall into gene exons (union of exons for genes with alternative splicing), N is the total number of mappable reads in the experiment, and L is the total length of the exons in base pairs. We associated 17872 genes with a valid RPKM value in K562.

CpG o/e computation and GC content

CpG observed/expected ratio (CpG o/e) was computed as , where , and are the numbers of C, G and dinucleotides CG, respectively, counted along the sequence, L is the number of nonmasked nucleotides and l is the number of masked nucleotide gaps plus one, i.e. L-l is the number of dinucleotide sites. The CpG o/e was computed over the sequence after masking annotated CGIs. The GC content was computed on the native sequence.

Chromatin state blocks

We detected contiguous windows of the same chromatin state (C1 to C4). We then kept the coordinates of the blocks of contiguous windows. To form chromatin state blocks of states (1+2), we merely detected contiguous windows of state 1 or 2. The same procedure was applied to define chromatin blocks of states (3+4). For chromatin blocks (1+2) and (3+4), we authorized the inclusion of isolated windows which don't belong to any chromatin state so to not disrupt very long blocks.

GO term enrichment

Each gene name of our annotation dataset was associated to several GO terms from GO SLIM (high level GO terms) using the online mapper: http://go.princeton.edu/cgi-bin/GOTermMapper. Then for each chromatin state (C1 to C4), the number of occurrences of each GO term was determined by the number of promoters belonging to that state and associated to this GO term. The enrichment for each GO term in each cluster was tested using Fisher's exact test. We applied a procedure to control the false discovery rate (FDR) as described in [137]. The upper limit of the FDR was fixed to 20%. After detecting significant deviation from a random repartition of GO term occurrences, we used the odd ratio value to determine if the deviation was an enrichment () or a depletion ().