GC Content Versus CompositionalHeterogeneity

To calculate the heterogeneity index from the genomic data, we compiled a dataset (Table ​(Table2)2) by selecting the longest continuous sequences from the most extensively sequenced eukaryotic genomes. In cases where a chromosome was almost completely sequenced and was deposited into databases as a set of consecutive contigs separated by gaps (e.g., human chromosomes 21 and 22) we selected the longest contig without attempting to concatenate all available data, as this may increase H_gc. Figure ​Figure1A1A compares the heterogeneity index values estimated for the sequences listed in Table ​Table22 using 50-kb and 100-kb windows. From Figure ​Figure1A1A we see that for every organism studied, GC-rich chromosomes have higher heterogeneity indices than do GC-poor ones. Additionally, sequences of taxonomically distant organisms are similar in terms of compositional heterogeneity if they have similar GC contents. For example, nematode chromosome V and Arabidopsis chromosome 2 both have a GC content of 36%, and in spite of the great taxonomic distance separating these two organisms, they have similar heterogeneity indices: 7.51 and 7.89 for 100-kb windows. Furthermore, human chromosome 21 has a GC content lower than that of Drosophila chromosome 2 (39% vs. 42%) and also has a lower compositional heterogeneity value (8.47 vs. 9.46). One exception is the extremely low compositional heterogeneity in the yeast sequences, despite the fact that their GC content is comparable to those of the nematode and Arabidopsis chromosomes. Overall, a strong correlation exists between GC content and compositional variation: For both window sizes the H_gc values correlate strongly with the GC levels of the sequences (r²=64%, P=0.002 and r²=74%, P<0.0001 for 50-kb and 100-kb windows, respectively).

Table 2

Genomic Sequences Used in OurStudy

Organism	Sequencea	Lengthb	Source
Saccharomyces cerevisiae	chr. IV	1.5	ftp://ncbi.nlm.nih.gov/genbank/genomes/S_cerevisiae/Chr04/
	chr. XV	1.1	ftp://ncbi.nlm.nih.gov/genbank/genomes/S_cerevisiae/Chr15/
Caenorhabditis elegans	chr. I	15.0	ftp://ncbi.nlm.nih.gov/genbank/genomes/C_elegans/CHR_I/
	chr. V	20.5	ftp://ncbi.nlm.nih.gov/genbank/genomes/C_elegans/CHR_V/
Arabidopsis thaliana	chr. 2	19.6	ftp://ncbi.nlm.nih.gov/genbank/genomes/A_thaliana/CHR_II/
	chr. 4	17.5	ftp://ncbi.nlm.nih.gov/genbank/genomes/A_thaliana/CHR_IV/
Drosophila melanogaster	chr. 2 arm L	21.6	http://www.fruitfly.org/
	chr. 3 arm R	27.5	http://www.fruitfly.org/
Homo sapiens	chr. 6, contig NT_001520	3.9	http://www.ncbi.nlm.gov/genome/seq/ctg.cgi?CTG=Hs6_1643&ORG=Hs
	chr. 21, contig NT_002836	28.5	http://www.ncbi.nlm.gov/genome/seq/ctg.cgi?CTG=Hs21_2980&ORG=Hs
	chr. 22, contig NT_001454	23.0	http://www.ncbi.nlm.gov/genome/seq/ctg.cgi?CTG=Hs22_1584&ORG=Hs

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For each organism we chose a pair of longest continuoussequences. 

^achr=chromosome 

^bLength is given in millions of base pairs. 

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Figure 1

Heterogeneity index values calculated for each chromosome in our dataset (Table ​(Table2)2) using adjacent windows (A) and windows separated by a 100-kb gap (B). The GC content of every sequence is indicated at the top of each graph. Asterisks signify sequences with all repetitive elements removed (masked). The broken line indicates the baseline H_gc value taken from Table ​Table11.

The longest continuous sequences available for human chromosomes 21 and 22 cover the majority of their lengths: 81% and 68%, respectively. The remaining 19% and 32% are represented by smaller contigs separated by gaps. As mentioned earlier, we excluded shorter sequences from analysis. We now look at the compositional properties of these two human chromosomes in their entirety. To do so we concatenate all contigs available for chromosomes 21 and 22 according to their physical location and calculated the H_gc (Table ​(Table3).3). In both cases the heterogeneity index values for concatenated sequences are slightly higher than for single longest contigs. It is especially evident in the case of chromosome 21 where H_gcfor the entire chromosome increased 18% over the single contig value when a window size of 100 kb is used. The increases can be attributed to two factors. First, sequencing gaps introduce discontinuities between some windows and so increase the overall compositional variation. Second, the telomeric region (e.g., 21q, contig NT_002835, 3,429,800 bp) is relatively GC-rich and therefore contributes to a higher H_gc.

Table 3

Comparison of H_gc Values for the Largest Continuous Fragments of Human Chromosomes 21 and 22 to the Values Obtained for All Sequences Available for the TwoChromosomes^a

Chromosomeb	Lengthc	Adjacent Windows		Windows 100-kb Apart
Win = 50 kbd	Win = 100 kb	Win = 50 kb	Win = 100 kb
21 contig	28.5	6.800	8.470	8.530	10.630
21 all	35.2	7.990	10.291	10.377	13.371
22 contig	23.0	12.817	10.291	18.479	21.445
22all	33.5	13.773	10.291	18.276	22.580

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^aIndividual contigs were concatenated according to their physical position. 

^bcontig = Longest contiguous fragment available for this chromosome; all = concatenated data. 

^cLength is given in millions of base pairs. 

^dWin = Window size for H_gc calculation. 

To understand how repetitive DNA affects the heterogeneity of nucleotide composition, we analyzed the sequences of human chromosomes 21 and 22 by excluding (masking) all repetitive DNA (interspersed and tandem repeats). Figure ​Figure11 shows that the compositional heterogeneity of masked sequences increases, whereas the GC content may go either up or down compared to the original, unmasked sequences. Thus, repetitive DNA actually tends to homogenize the GC content of a chromosome.

Compositional Continuity Within GenomicSequences

The isochore model predicts a certain degree of compositional continuity within human genomic sequences: Two adjacent DNA fragments (windows) should tend to be more similar in nucleotide composition than a pair of fragments separated by a distance. We used the heterogeneity index to investigate whether this is true, comparing windows separated by a 100-kb gap. Figure ​Figure1B1B shows the results of the calculation. In all organisms some compositional continuity is present as reflected by the fact that the heterogeneity indices for adjacent windows (Fig. ​(Fig.1A)1A) are smaller than those for windows separated by 100 kb (Fig. ​(Fig.1B).1B). The only exception is the yeast genome, which is highly uniform, so that the difference in GC content between two adjacent windows is similar to that between two windows separated by 100 kb. The correlation between the index values and GC levels of the sequences is stronger in Figure ​Figure1B1B than in Figure ​Figure1A1A (for Fig. ​Fig.1B,1B, r²=73%, P<0.0001 and r²=75%, P<0.0001 for 50-kb and 100-kb windows, respectively). The difference (ΔH_gc) between the H_gc value calculated using a gap and the value calculated using adjacent windows also correlates positively with the GC level of the sequences (P=0.002 and P=0.007 for 50-kb and 100-kb windows, respectively). Note that in Figure ​Figure1B,1B, the index values obtained using 50-kb windows do not lag behind the values calculated from 100-kb windows as dramatically as they do in Figure ​Figure1A.1A. Altogether, the compositional continuity is present in all sequences, but the scale at which it exists differs between yeast and the other eukaryotes in our dataset. Yeast chromosomes are homogeneous, so that the nucleotide composition does not change significantly across their entire span. For the purposes of this study we can consider each of the yeast chromosomes as a single uniform DNA segment. For the other eukaryotes in our dataset, which possess much larger chromosomes, compositional continuity is restricted to relatively small islands, so the chromosomes in their entirety are highly heterogeneous.

Compositionally Homogeneous SequenceSegments

As described above, although the genomes of multicellular eukaryotes are highly variable in GC content, they still exhibit some compositional continuity. Is it possible to find long compositionally homogeneous segments within each genome? To do so we developed a simple decomposition computer program based on the algorithm described in Methods. The program requires two parameters: the window length and the fluctuation limit. A careful choice of parameters is important. If the window is small, its GC content is subject to strong fluctuations, whereas if the window is large, it may conceal heterogeneity. If we assume that the GC content P_gc in a sequence of length L follows the binomial distribution B (L, p_gc), then the standard error of the GC content in a window of length l is

which attains the maximum value at P_gc=0.5. For P_gc=0.5 the standard errors for l=1 kb, 10 kb, and 100 kb are 2%, 0.5%, and 0.1%, respectively. In view of the high compositional heterogeneity in eukaryotic genomic sequences, the window size of 1 kb appears to be too small and vulnerable to random fluctuation effects (standard error=2%). Conversely, a window size of 100 kb is too large to uncover the underlying heterogeneity of genomic sequences (see below). We therefore choose the window size of 10 kb.

To see what a good fluctuation limit should be, we considered the yeast genome because it was shown to be highly uniform in both statistical and experimental studies (this paper; Macaya et al. 1976). An adequate fluctuation limit should allow us to consider the entire sequence of a yeast chromosome as a single uniform segment. Starting with the 3% limit, which is reasonable because it is much higher than the standard error of 0.5%, we applied the decomposition program to the sequence of chromosome IV, which is the largest yeast chromosome. This procedure was performed several times by incrementing the fluctuation limit value by 0.5% each time until the entire chromosome sequence became a single homogeneous segment (Fig. ​(Fig.2).2). As we see from Figure ​Figure2,2, when the fluctuation limit is 3% there are many relatively short homogeneous fragments. At the fluctuation limit of 5% chromosome IV can still be divided into seven segments. This suggests that this limit is still too low. For these seven segments the GC contents are within a small range, i.e., 37.6%–39.4%. So there are no segments that differ from each other by >5%. That is, these segments are separated from each other by sudden surges of GC content that may represent “background noise.” Only when the fluctuation limit reaches 7% is the noise completely filtered out. So, we propose to use this value as a standard to delimit compositionally homogeneous sequences within other eukaryotic chromosomes.

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Figure 2

Proportions of the total sequence length of yeast chromosome IV occupied by compositionally uniform sequence segments stratified into length classes using 20 kb as the bin size. The segments were identified using 10-kb window size and fluctuation limits indicated within gray boxes. The purpose of the analysis was to identify a fluctuation limit value at which the entire chromosome IV can be considered as a single uniform segment. This value is 7%.

To document the effects of the fluctuation limit on the identification of compositionally uniform segments, we applied the 5% and 7% limits to the genomes of multicellular organisms in our dataset (Table ​(Table2).2). Our goal was to determine the length distribution of homogeneous segments in these sequences. We used the decomposition algorithm to create a list of homogeneous segments for every chromosome using 10-kb window size and the two fluctuation limits. The segments were sorted by size and stratified into 32 classes. For every class we calculated the proportion of sequence length it occupies and plotted the obtained value. The results for selected sequences are given in Figures ​Figures3.3. Comparing Figure ​Figure3,3, A and B, we see that the higher fluctuation limit allows for longer uniform segments and increases overall the spread of distributions. In all organisms both fluctuation limits produced homogeneous segments that are skewed toward the lower end of the distribution, i.e., being shorter than 100 kb. A comparison of these results with the heterogeneity index calculations (Fig. ​(Fig.1)1) shows that in general the spread of the distribution for a sequence depends on the compositional heterogeneity of that sequence. In other words, the higher the compositional heterogeneity a chromosome displays, the more difficult it is to find homogeneous segments within this chromosome. For example, the nematode and Arabidopsis chromosomes studied exhibit a low compositional heterogeneity (Fig. ​(Fig.1A)1A) and possess many long homogeneous segments, whereas in the extremely variable sequence of human chromosome 22, most of the compositionally uniform fragments are within the 20–100 kb (Fig. ​(Fig.3B).3B).

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Figure 3

Proportions (y axis) of the total sequence length occupied by compositionally uniform sequence segments within chromosomes of multicellular eukaryotes stratified into length classes (x axis) using 20 kb as the bin size. Calculations were performed using 10-kb window size with 5% (A) and 7% (B) FL (fluctuation limits).

Because the 7% fluctuation limit was calibrated using the homogeneous yeast sequence, we consider the results in Figure ​Figure3B3B to be more realistic. Let us consider what homogeneous segments can be qualified as isochores. Note that according to the original description of isochores by Bernardi et al. (1985), isochores are longer than 300 kb. However, in Figure ​Figure33 we see very few homogeneous segments extending past the 300-kb limit. Therefore, we propose using 100 kb as the lower cutoff limit. How do individual isochores differ from each other in terms of average GC content? For each chromosome we calculated the GC content of every isochore. Based on these values we stratified the isochores into several GC level classes ranging from 30% to 60% using 5% as the bin size. Finally, we plotted the relative frequencies of isochores falling in each GC level class. The resulting graph is shown in Figure ​Figure4.4. Nematode chromosome V has the smallest number of classes, only two (35%–40%), whereas human chromosome 22 has the largest number, five (40%–60%). Note that based on our results, all examined eukaryotic genomes contain isochores. However, the diversity of isochores in terms of their GC content varies significantly among taxa.

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Figure 4

The relative frequencies of isochores falling into distinct GC content classes. To construct this figure, all isochores that are 100 kb and are homogeneous at 7% fluctuation level were ordered according to their GC content into seven classes using the 5% GC bin size. The broken line separates GC content classes that are unique for the human genome.

Eukaryotic Genomes AreMosaic

We see from Figure ​Figure33 that genomes of multicellular eukaryotes are composed of large numbers of short homogeneous segments. Therefore, they can be considered as mosaics made of homogeneous segments. If the heterogeneity of a sequence is small, then the “tiles” of the mosaic can be large (e.g., human chromosome 21 and nematode chromosome 5). If the variability is high, the tiles are usually small (e.g., human chromosome 22). In addition to size differences, homogeneous sequences within a genome also differ from each other in terms of mean GC content as illustrated in Figure ​Figure4.4. Using the mosaic analogy, we can refer to the differences in GC content as different colors of tiles used in the mosaic. In this case each color represents a distinct GC content category. Thus, sequences that exhibit low compositional variability are mosaics that have only a few colors (Nematode, Arabidopsis). On the other hand, highly variable sequences can be thought of as very colorful mosaics (human sequences). This analogy brings us to a conclusion that the organization of multicellular eukaryotic genomes is similar throughout the taxonomic levels: They are mosaics, but the size and color of components in these mosaics differ between taxa and depend primarily on the compositional heterogeneity of the genome.

Defining Isochores

Sufficiently long genomic fragments that are uniform in nucleotide composition can be called isochores. This term was coined by Bernardi et al. (1985) largely for the genomes of warm-blooded vertebrates (for review, see Bernardi 2000). These authors, however, did not explicitly define how much compositional heterogeneity is allowed within an isochore. In other words, it is not known what homogeneity criterion one should use to define isochores within a given genomic sequence. In this study we calibrated the homogeneity criterion using yeast sequences. The choice of yeast sequences is justifiable for three reasons: (1) Yeast DNA cannot be separated into separate components using gradient centrifugation (Macaya et al. 1976); (2) yeast chromosomes are sufficiently large, being close to the length requirement imposed by the original isochore model (300 kb; for review, see Bernardi 2000); and (3) the statistical analyses described earlier in this study support the notion about the uniformity of yeast sequences. Conversely, as we see from Figure ​Figure3B,3B, when the “yeast calibrated” homogeneity criterion is applied to the eukaryotic sequences, only a few homogeneous fragments can be identified that extend beyond 300 kb. Therefore, we propose a new definition of an isochore as any genomic fragment longer or equal to 100 kb such that when it is divided into a series of overlapping 10-kb windows, no two windows can differ by >7% GC. This definition is based on the use of the yeast sequences to find optimal window size and fluctuation limit values. Use of different parameters will change the length and number of isochores. Under this definition, isochores are on average much shorter than those originally described by the gradient centrifugation approach, which did not examine the compositional heterogeneity within a segment. Because the compositional heterogeneity is correlated with the overall GC content of a sequence, GC-rich isochores should tend to be shorter than GC-poor ones. Indeed, GC-rich sequences are more variable, so it is more difficult to find compositionally uniform regions within them. For example, in the case of chromosomes 21 and 22, there is a highly significant (P<0.0001) negative correlation between the length of the isochores and their GC content. Chromosome 21 is GC poor and contains 97 isochores with the average length of 170 kb, whereas chromosome 22 is GC rich and contains 47 isochores with the average size of 150 kb. Additionally, we expect isochores to occupy a smaller proportion of the total sequence length in GC-rich sequences than in the GC-poor ones. This is because the high variability of GC-rich sequences makes it difficult to find uniform regions that are sufficiently large to be considered isochores. For example, GC-rich chromosome 22 has ~30% of the total sequence length allocated to isochores, whereas GC-poor chromosome 21 has ~58%. The same is true for the other multicellular eukaryotes included in this study. These observations suggest that isochores are actually present in all eukaryotic genomes but the majority of isochores are relatively GC poor because GC-rich regions usually do not contain sufficiently long uniform segments. Moreover, the inability of the gradient centrifugation to reveal the high heterogeneity of the human genome is well illustrated in Figure ​Figure5,5, which indicates that the assignment of genome fragments into distinct GC content classes is oversimplified when the internal compositional heterogeneity is not taken into account. Each of the isochore classes described using the gradient centrifugation represents a pool of genomic DNA fragments with the mean GC content falling into one of the five classes (L1, L2, H1, H2, or H3). This, however, does not imply that they are homogeneous.

A caveat for the above discussion is that the definition of isochores that we propose relies solely on the use of the yeast sequences for calibrating the homogeneity criterion. Although we think this is appropriate for the above reasons, the use of different values for the window size and fluctuation limit will inevitably change what one might define as isochores. For example, an increase in window size would result in longer isochores because the fluctuation in the GC content will be smoothened out. Similarly, as Figure ​Figure22 suggests, an increase in the fluctuation limit allows for more variation to be tolerated and, hence, will lead to greater lengths of isochores. Although it is difficult to have a precise definition of isochores, the most important conclusion of our analyses is that regardless of the window size/fluctuation limit choice, all genomes of multicellular eukaryotes included in this study behave remarkably similar as indicated by the shape of distributions in Figure ​Figure3,3, A and B.

Compositional Heterogeneity Index

We developed a measure to quantify the compositional heterogeneity within a genomic sequence and to compare differences in heterogeneity between sequences. Let us consider a sequence with the GC content P that can be divided into n windows of length l. We first calculate the GC content of each window (e.g., GC₁, GC₂,…, GC_n) and then compute the average GC content difference between two adjacent windows:

1

Although equation 1 is useful for characterizing the compositional heterogeneity within a given sequence, it is not suitable for comparing heterogeneities between sequences because it is not normalized for the overall GC content p. For simplicity, let us assume that nucleotides are distributed randomly within a sequence. In this case we can consider each window as a simple random sample of the entire sequence with the standard error:

2

Now we can normalize the average difference (equation 1) by the standard error (equation 2) and obtain the following equation for the compositional heterogeneity index H_gc:

3

A PERL program for the H_gc calculation suitable for large genomic sequences will become available at http://nekrut.uchicago.edu.

We thank Satoshi Ota, Haidong Wang, Zhenglong Gu, Xuhua Xia, and two anonymous reviewers for their suggestions.Arian Smit provided the current version of the Repeat Masker software. The support by Richard Blocker proved to be vital in the UNIX/Linux system management. This study was supported by NIH grants GM 30998 and GM 55759.

The publication costs of this article were defrayed in part by payment of page charges. This article must therefore be hereby marked “advertisement” in accordance with 18 USC section 1734 solely to indicate this fact.