A New Database (GCD) on Genome Composition for Eukaryote and Prokaryote Genome Sequences and Their Initial Analyses

Abstract

Eukaryote genomes contain many noncoding regions, and they are quite complex. To understand these complexities, we constructed a database, Genome Composition Database, for the whole genome composition statistics for 101 eukaryote genome data, as well as more than 1,000 prokaryote genomes. Frequencies of all possible one to ten oligonucleotides were counted for each genome, and these observed values were compared with expected values computed under observed oligonucleotide frequencies of length 1–4. Deviations from expected values were much larger for eukaryotes than prokaryotes, except for fungal genomes. Mammalian genomes showed the largest deviation among animals. The results of comparison are available online at http://esper.lab.nig.ac.jp/genome-composition-database/.

Introduction

Noncoding regions are the major part of eukaryote genomes, and most of them are believed to evolve neutrally (Kimura 1983). Under this assumption, we expect that the frequency of a particular short oligonucleotide, or DNA word, of 10 bp or shorter should be primarily determined through accumulation of neutral mutations, and the total set of frequencies of all DNA words of certain length should follow some simple statistical rules. Oligonucleotide frequencies of one genome can provide a useful mechanism of genome comparison (Karlin 2005), including phylogeny reconstruction (Takahashi et al. 2009). Most frequently, such comparisons are based on a dinucleotide composition model (Karlin and Mrazek 1997; Gentles and Karlin 2001) or on self-organizing maps (Abe et al. 2003). It may be better to examine longer oligonucleotide compositions. We created a series of statistical models predicting the frequencies of word of up to 4 nt in a genome. We retrieved all available complete eukaryote and prokaryote genomes, constructed such models for them, and compared the actual word frequencies with those predicted by the models to determine the discrepancy.

Here, we present a database, called Genome Composition Database (GCD), which shows how accurately each genome can be approximated by a model. The GCD also provides the sequences of over- and underrepresented DNA words. The unique point of this database is that it allows to compare compositional complexity of genomes and to analyze over- or underrepresentation of particular oligonucleotides.

Materials and Methods

Available complete genomes were collected from NCBI (http://www.ncbi.nlm.nih.gov/; Wheeler et al. 2007), Ensembl (http://uswest.ensembl.org/; Flicek et al. 2012), University of California–Santa Cruz (http://genome.ucsc.edu/; Fujita et al. 2011), FlyBase (http://flybase.org/; McQuilton et al. 2012), and WormBase (http://www.wormbase.org/; Harris 2010). Genome sequences of a total of 1,228 species (101 eukaryotes, 1,043 eubacteria, and 84 archaea, as of June 2010) were used to construct the database. For every genome, we created a series of five composition models: uniform (composition of A, C, G, and T are set to be all 25%), mononucleotide, dinucleotide, trinucleotide, and tetranucleotide. Each composition model is based on the total size and word frequencies of an actual genome.

The uniform composition model has just one parameter—genome size. The mononucleotide model has two parameters—genome size and GC content. We use both DNA strands to perform the word counting, so the number of G bases is always same with number of C, same for A and T, and each DNA word has the same frequency with its reversed complementary counterpart. Among the 16 dinucleotides, there are 12 that differ from their reversed complementary dinucleotide and 4 that are identical to their reversed complementary one (CG, GC, AT, and TA). Therefore, the first group of dinucleotides can be described with six frequencies (12/2) and the second—with four. Subtracting one, and adding the genome size, we obtain ten parameters for the dinucleotide model. In case of trinucleotide frequencies, none of the trinucleotides are identical to their reversed complementary counterpart, so the model has 4³/2 = 32 parameters. In tetranucleotide case, there are 16 tetranucleotides that are identical to their reversed complementary counterparts, so the tetranucleotide model has (4⁴ − 16)/2 + 16 = 136 parameters.

For a genome G of total length M and a DNA word w, a composition model can be used to compute p(w), which is the probability of observing w at any particular position in the genome. For example, the uniform composition model gives

(1)

where L is the length of w. The mononucleotide composition model predicts

(2)

where w_i is the ith nucleotide of w, F(x) is the observed frequency of x in the genome sequence, and C(x) is the complementary sequence to x. Using the same principle, p(w) from dinucleotide, trinucleotide, and tetranucleotide composition models can be computed.

The model expectation of the frequency of word w in both strands of the modeled genome is then given as follows:

(3)

Then, we can define the deviation of the observed frequency from the expected frequency:

(4)

Because each of the composition models assumes independence of different genome positions from each other, E(w) follows the binomial distribution, and its variance can be computed as follows:

(5)

The standard deviation of E(w) is its square root.

We then can define the relative abundance of w, under this particular model, as follows:

(6)

This r(w) is 0 for DNA words, occurring in the genome with exactly the same frequency, as predicted by the composition model. r(w) is positive when the actual frequency is larger than expected by the model. In such cases, we describe that w is overrepresented in the genome, according to this model. When the actual frequency is smaller than expected by the model, r(w) is negative, and w is underrepresented.

Now we can summarize the overall magnitude of over- or underrepresentation of all DNA words of length L in the genome (using a particular composition model of choice) as follows:

(7)

where W is the set of all DNA words of length L and

Because R is the standard deviation of a sample of all r(w) for a particular word length L, the unit of R is the same with that of r(w), which is σ_E(w) (standard deviation of the word frequency, predicted by the model). For each w, Rσ_E(w) gives the relative number of occurrences of w, which would make w averagely rare or abundant.

R is computed for a particular genome, composition model, and L and summarizes the ability of the composition model to predict the frequencies of words of length L in the genome. Large R implies that many w's have large absolute values of r(w), which means that their actual frequencies are far from those expected by the model. Thus, a large value of R signifies that the model's ability to describe the actual genome is poor.

A good composition model has small value of R, with R being 0 for the perfect model. An example of such perfect model is the L-bp composition model used to predict the frequencies of words of the same length L bp or shorter. For instance, the dinucleotide composition model has the exact information about dinucleotide frequencies, so it gives perfect predictions for 1-bp or 2-bp word frequencies, resulting in R value of 0.

For the longer words, R is typically much larger than 0 for nonrandom sequences. On the other hand, when a random sequence is modeled using any composition model, the actual variances of the word frequencies are the same with the variances predicted by the model; therefore, R is close to 1 in this case (approaching 1 as the sequence becomes longer).

This is also the case for semirandom sequences, where the deviation from uniform randomness is at most as complex (controlled by at most as many parameters) as the model used to analyze the sequence. For example, a semirandom GC-biased sequence can be accurately modeled by the nucleotide composition model, or any more complex model, but not by the uniform composition model. The R values obtained with the uniform composition model for such sequence are much larger than 1, whereas other models still produce R close to 1. Thus, the R values directly reflect compositional complexity of the sequence.

Figure 1 illustrates this by showing the example histograms of relative abundances for all words of length 8 in the human genome, using five different models. The strange bimodal-looking shape of the uniform model histogram results from the extreme depletion of CpG dinucleotide in mammalian (including human) genomes. Any 8-bp word containing CpG will appear as strongly underrepresented when comparing the actual frequencies with those predicted by the uniform model. So, all such words contribute to the left peak on the histogram, whereas words without CpG form the other peak, in agreement with the model.

FIG. 1.—

Histograms of relative abundances of all oligonucleotides of 8 bp in human genome, according to the five composition models. The R value computed for each model is used as a horizontal scaling factor. The vertical red line corresponds to the expected frequency. The words placed to the left of the line are underrepresented and to the right—overrepresented.

We computed R for all five composition models for available complete genomes, both eukaryotes and prokaryotes. Table 1 shows R values for seven representative species. We then extracted unusually rare and unusually abundant words, which we define as those having |r(w)| > R. These DNA words, together with the corresponding statistics, are available for viewing and downloading at the GCD online.

Table 1.

R Value Comparison for Selected Species

	Model
	Uniform	Mono	Di	Tri	Tetra
Escherichia coli E24377A	9.5	9.4	7.6	5.3	3.2
Saccharomyces cerevisiae (baker's yeast)	18.7	9.0	6.2	5.0	3.4
Arabidopsis thaliana (thale cress)	72.7	33.6	23.7	18.6	13.9
Drosophila melanogaster (fruit fly)	59.7	41.3	29.9	23.1	19.3
Oryzias latipes (medaka)	165.9	115.8	71.2	49.5	37.3
Anolis carolinensis (lizard)	251.1	188.9	130.4	110.0	92.1
Mus musculus (mouse)	343.9	309.0	219.0	145.1	122.8

Note.—This table compares the R values of E. coli, yeast, plant, fruit fly, fish, lizard, and mouse, respectively, for each of the five models we used, based on words of 8 bp.

Next, we analyzed the spacing patterns of individual DNA words in complete genomes. Looking at all occurrences of a particular DNA word in the genome, we can extract the distances between the genomic locations of every two neighboring occurrences and use this set of distances as a spacing data set for this particular word. Sample parameters (mean, standard deviation, skewness, and kurtosis) are computed for such data set. What would be the physical meaning of those parameters? The mean distance approximately equals to the genome size divided by total number of occurrences, so it correlates with the reciprocal of the word frequency. Standard deviation shows how evenly is a particular word distributed in the genome. Skewness shows whether extremely unusual spacing values for this word tend to be large or small. Kurtosis shows if the word tends to form clusters and the density of those clusters relative to the distance between them.

Taking a particular parameter for all words of length L, we get a sample of 4^L values. The nature of this sample would characterize the genome as a whole. Furthermore, selecting only subset of DNA words with parameters falling into particular ranges, we can extract interesting DNA words.

In order to verify the models and better understand the parameters, we constructed a range or semirandom sequences using a random sequence generator (Kryukov K, unpublished data). Each semirandom sequence was based on particular real genome used as template (e.g., the human genome): It had the same size with the template genome, and it imitated N-bp composition of the template genome, with N ranging from 1 to 4. Thus, we constructed four semirandom genomes based on a single actual genome sequence. We used genomes of five species as templates: human, Anolis carolinensis (lizard), Xenopus tropicalis (frog), Oryzias latipes (fish), and Drosophila melanogaster (fruit fly). The resulting 20 semirandom genomes were added into the GCD.

Results

Figure 2 shows the comparison of R values for 101 eukaryote genomes used in this study, as well as representative prokaryote genomes, computed for 5 bp oligonucleotides. Such R values represent how well different composition models can predict 5-bp composition of the genome. Panel A shows all eukaryote genomes and panel B shows representative prokaryote genomes. Supplementary figure 1 (Supplementary Material online) shows comparison of all prokaryote genomes included in this study. R values of five composition models are displayed as differently colored areas. As can be seen, R varies greatly among species and groups of species. Mammals are compositionally more complex than nonmammal vertebrates, land vertebrates are more complex than fishes, and fishes are more complex than most invertebrates and plants, which are still more complex than fungi and protists. Compositional genome complexity of prokaryotes, represented by R values, is comparable with that of fungi.

FIG. 2.—

Comparison of R values based on oligonucleotides of 5 bp and all five composition models. (A) Eukaryote genomes (all available in public databases by October 2010). (B) Representative prokaryote (both eubacteria and archaea) genomes.

Figure 3 shows the average R values for different groups of organisms, with standard deviation. Under all five composition models, statistically significant difference is observed between the R values of mammals and nonmammal vertebrates (Mann–Whitney P < 0.001, see supplementary table 1, Supplementary Material online for test results). Statistically significant difference is also observed between nonmammal vertebrates and invertebrates. Interestingly, R values of invertebrates are close to those of plants and significantly higher than those of fungi, protists, or prokaryotes (archaea and eubacteria). In terms of R values, fungi genomes are more similar to those of prokaryotes than those of other eukaryotes.

FIG. 3.—

Average R values for different groups of organisms, with standard deviations, using five different composition models. Standard deviation for each value is displayed.

Significantly, over- and underrepresented DNA words may be biologically important. Tables 2 and 3 show the partial lists of under- and overrepresented words of 10 bp in human genome, using tetranucleotide composition model. The complete lists of under- and overrepresented words, for every of the included genomes, for each of the five composition models, and for DNA words of up to 10 bp for eukaryotes and 8 bp for prokaryotes, are available at the GCD online. Both the actual and the expected frequency are given for both DNA strands combined, so each word's frequency is identical with that of its reversed complementary counterpart (given in parentheses).

Table 2.

Underrepresented Oligonucleotides of 10 bp, Example from Human Genome

Rank	Oligonucleotide	Actual Observed Frequency	Frequency Predicted by the Model	Deviation from the Expected Frequency, in Model's Standard Deviations
1	tataaaaaaa (tttttttata)	45,933	115,110	−203.9
2	aaattttttc (gaaaaaattt)	29,389	89,480	−200.9
3	tttttttggg (cccaaaaaaa)	19,774	72,956	−196.9
4	aaaaattttt	103,832	185,936	−190.4
5	ttttttggga (tcccaaaaaa)	14,119	60,161	−187.7
6	aaaatttttc (gaaaaatttt)	33,460	89,480	−187.3
7	aaaaaaatat (atattttttt)	80,964	153,706	−185.6
8	aaaaaatttc (gaaatttttt)	34,571	89,480	−183.6
9	aaaaattttg (caaaattttt)	33,265	87,274	−182.8
10	aaaaaatttg (caaatttttt)	33,454	87,274	−182.2

NOTE.—Showing ten most underrepresented oligonucleotides, according to the tetranucleotide composition model. Both the actual and the expected frequency are given for both DNA strands combined, so each word's frequency is identical with that of its reversed complementary counterpart (given in parentheses).

Table 3.

Overrepresented Oligonucleotides of 10 bp, Example from Human Genome

Rank	Oligonucleotide	Actual Observed Frequency	Frequency Predicted by the Model	Deviation from the Expected Frequency, in Model's Standard Deviations
1	acacacacac (gtgtgtgtgt)	1,161,477	9,207	12008.1
2	tgtgtgtgtg (cacacacaca)	1,169,668	12,946	10166.1
3	cctgtaatcc (ggattacagg)	835,133	6,999	9898.3
4	ctgtaatccc (gggattacag)	825,499	7,235	9619.4
5	aaaaaaaaaa (tttttttttt)	5,951,413	380,529	9031.2
6	ctgggattac (gtaatcccag)	802,262	7,934	8917.5
7	tgtaatccca (tgggattaca)	856,563	11,024	8053.0
8	taatcccagc (gctgggatta)	839,950	10,726	8006.5
9	gattacaggc (gcctgtaatc)	628,774	7,004	7429.1
10	tgcagtgagc (gctcactgca)	580,240	7,705	6522.3

NOTE.—Showing ten most overrepresented oligonucleotides, according to the tetranucleotide composition model.

Other than the reporting the general compositional complexity, the GCD can be used to compute the distances between the composition vectors of various complete genomes and submitted sequences (similar to the method taken by Takahashi et al. 2009). We used this tool to analyze three classes of human sequences: random sample from the human genome, conserved sequences of unknown function, and conserved functionally important sequences. Although sequences from these three classes are all found in the human genome, they have different nature and evolutionary history, allowing interesting comparison. The UCE data set (human–mouse–rat ultraconserved elements, 481 sequence, 126 kbp in total, Bejerano et al. 2004) was used as the data set of conserved sequences of unknown function. Human microRNA (miRNA) seed sequences (1,100 sequences from miRBase, 7.7 kbp in total, Kozomara and Griffiths-Jones 2011) were used as functionally important conserved sequences.

Figure 4A shows the average Euclidean distances between the composition vectors obtained from randomly sampled human sequence and composition vectors of complete vertebrate genomes. Each sample was chosen to have the same number of sequences and average sequence length with the UCE data set: 481 sequences, 262 bp each. One thousand such samples were produced. Di-, tri-, and tetranucleotide composition vectors are used for comparison. As expected, primate genomes are the closest to human sample, and more diverged species show progressively larger distances, with some fluctuations.

FIG. 4.—

Euclidean distances between composition vectors (oligonucleotide frequencies) of sample data sets and complete vertebrate genomes for three composition models (dinucleotide, trinucleotide, and tetranucleotide). (A) When sampled data set is human genome. One thousand samples were used, where each sample consisted of 481 sequences of 262 bp each (for a total size of each sample same with the UCE data set), taken from the random locations in the complete human genome. Also, panel (A) shows the standard deviations of the distances. (B) The composition of the UCE data set is compared with that of complete vertebrate genomes. (C) The composition of human miRNA seed sequences is compared with that of complete vertebrate genomes.

Figure 4B shows the comparison for human–mouse–rat ultraconserved elements. The compositional distances between the UCE and the complete vertebrate genomes appear to be relatively uniform among vertebrates and much larger than those for the random human sample. Interestingly, these sequences appear to be compositionally close to lizard, fish, and frog.

Figure 4C shows the compositional distances between human miRNA sequence data set and complete vertebrate genomes. Again the distances are uniformly large. Platypus and the fishes are compositionally the closest to this data set.

To further investigate the differences between these three data sets, we computed the average distances by combining the genomes into four groups (fig. 5). The distances show a steep increase in case of random human sample (fig. 5A), while much more uniformity can be seen for UCE and miRNA seed data sets (fig. 5B and C).

FIG. 5.—

Average compositional distance (Euclidean distances between the composition vectors) between sample data sets and complete genomes grouped into four groups. Panels (A, B, and C) correspond to panels (A, B, and C) of figure 4. Standard deviations of the distances are shown for all cases.

Figure 6 shows the plots for the pairs of spacing parameters, taken for 8 bp oligonucleotides for six species—human, lizard, fish, fruit fly, yeast, and Escherichia coli. Although the interpretation is difficult, more structure can be seen in the plots of more complex organisms.

FIG. 6.—

Plots of the spacing distribution parameters for six species, based on oligonucleotides of 8 bp. Each row represents one genome. Different columns show plots for different pairs of parameters, from left to right: mean spacing (x axis) versus standard deviation (y axis), mean (x) versus skewness (y), mean (x) versus log(kurtosis) (y), standard deviation (x) versus skewness (y), standard deviation (x) versus log(kurtosis) (y), and skewness (x) versus log(kurtosis) (y). Each dot in the plot represents a particular 8 bp DNA word, so 48 words constitute the data set in each case.

Figure 7 shows spacing plots for four random genomes (generated using human genome as a template), the complete actual human genome and the repeat-masked version of the human genome. Repeat-masked is included because complexity is often associated with repetitive sequences. In case of the “Hs Random 1” sequence, discrete elements appear in the figure. Those elements correspond to the groups of DNA words containing different number of GC. With GC contents being the only parameter for constructing the sequence, DNA words with the same number of GC will have exactly same compositional properties, blurred only by randomness of the sequence. In case of “Hs Random 2” similar grouping happens, this time depending on number of CpG each particular word may contain. Going into more complex semirandom sequence, the discreteness becomes less clear, and the plots are getting closer to that for the real human genome. Still significant difference remains between the plots of semirandom and real sequences and very little difference between the plots of repeat-masked and the complete human genome.

FIG. 7.—

Plot of the spacing distribution parameters for semirandom sequences, compared with the real human genome, as well as repeat-masked one. Based on oligonucleotides of 10 bp. Semirandom genomes 1, 2, 3, and 4 are constructed using 1-, 2-, 3-, and 4-bp composition of the actual human genome.

Discussion

The GCD provides a convenient measure of relative complexity of various genomes from statistical point of view. A genome is compositionally simple if its composition can be accurately described by a simple model. A set of R values for various word length and models can tell us how complex a particular genome is?

As figure 2 shows, R values become smaller with the increase of model complexity—as expected, a more complex model can describe genome composition more accurately, which results in smaller discrepancy. We observe that, generally speaking, R values are related to the general complexity of the organism. Remarkably, even tetranucleotide compositional models are unable to give good predictions of 5-bp composition in case of complex genomes, particularly for mammals and land vertebrates.

Figure 3 confirms that compositional complexity of a genome is in good correlation with general complexity of the organism. Mammalian genomes are significantly more compositionally complex than genomes of any other organisms. Compositional discrepancy R computed with different composition models seems to be useful as a measure of compositional complexity of the genome.

The extremely rare and extremely abundant sequences, as shown in tables 2 and 3, suggest the possible mechanisms of creating compositional complexity. The most underrepresented 10 bp DNA words (using tetranucleotide composition model) seem to be found on the boundary of mononucleotide repeats, particularly poly-A to poly-T boundary (words 1, 2, 4, 6, 7, 8, 9, 10 in table 2) also poly-A to poly-C (words 3 and 5 in table 2). This means that such boundary is much less common, than suggested by the 4-bp composition.

Among the top overrepresented words, there are poly-A (word 5 in table 3), dinucleotide repeats (words 1 and 2 in table 3), as well as fragments of sequence “gcctgtaatcccagc” (words 3, 4, 6, 7, 8, 9 in table 3), which has about 800,000 occurrences in the human genome compared with the expected number of about 7,000–10,000. This sequence being unusual is already reported by Valle (1993); however, no explanation for the cause was given.

Figure 4 shows the compositional distances between three sequence data sets (human sample, UCE, and miRNA seeds) and vertebrate genomes. Figure 5 summarizes the distances for organism groups, including invertebrates. Although in all three cases, the sequences are contained in the human genome, the compositional distances of those sequences to various genomes show very different pictures. The random sample behaves as expected—the compositional distance is increasing with the increase of divergence from human. However, UCE and miRNA seed data sets show more or less uniform compositional distances from various vertebrate genomes. This suggests that those sequences became conserved before the emergence of mammals. In case of miRNA seed sequences, the composition distances to all vertebrate genomes are more or less uniform, suggesting those sequences were fixed much earlier than the emergence of vertebrates. Composition of the UCE and miRNA seed sequences is frozen and represents the composition of the ancestoral genome, at the time where the fixation occurred. The compositional distance from the current day vertebrates is larger for miRNA seed data set because the miRNA fixation occurred much earlier, so larger compositional distance exists between the ancestoral genome and current day genomes. Thus, this allows us to discuss the composition of premammal vertebrate genome (in case of UCE data set) and early animal genome (in case of miRNA seeds).

Oligonucleotide spacing patterns, summarized as sample parameters and displayed as scatterplots (figs. 6 and 7), provide a further interesting view into the compositional complexity. It is apparent that the human genome is very different from the semirandom sequences that imitate only some compositional properties of the actual genome. Often we attribute complexity to the abundant repetitive elements in the vertebrate genome. However, the spacing scatterplots for the repeat-masked human genome looks similar to those of the complete genome and different from those based on the semirandom sequences. It remains to be seen whether the apparent complexity results from the isochore structure of the mammalian genomes (Bernardi et al. 1985), from decaying ancient repeats, or from some other mechanism.

The online GCD provides the means of comparing the compositional complexity of various complete genome and extracting unusual DNA words. The composition parameters computed using five models, as well as histograms, are available. Also spacing patterns, summarized as parameter histograms and 2D scatterplots, are included. In addition that database features a facility for submitting a sequence data set and performing composition analysis and comparison with various complete genomes.

Compositional models that we used in this study only utilize the word frequencies as parameters. The natural next challenge is to design an integrated composition model, which would be based on both frequencies and spacing patterns. Such model would better approximate the genome and thus would allow focusing more closely on the real source of complexity.

Supplementary Material

Supplementary figure 1 and table 1 are available at Genome Biology and Evolution online (http://www.gbe.oxfordjournals.org/).