In order to study the coexpression of proximate genes, we analyzed 100 expression datasets derived from Affymetrix microarray experiments. We use the Pearson correlation coefficient (R) of two genes to measure the level of their coexpression. The mean R of all the neighbouring gene pairs in our dataset is 0.07468 (with standard error 0.00424). This mean value is statistically significant (with p-value 0.0001) as it is +11.4 standard deviations from the mean R in a randomized genome. In a randomized genome with the same genes and expression values, the mean R is only 0.03086 (with standard deviation 0.00384) (Figure 1A). Tandem duplicated genes have identical functions and hence are often highly coexpressed. To eliminate the effects of tandem duplicates on this coexpression study, we removed all members except one in each tandem gene cluster and redid the analysis. After removal of tandem duplicates, the mean R became 0.06844 (with standard error 0.00426). It is slightly smaller than the value when all genes are included in the analysis, but still significant (with p-value 0.0001, +9.7 standard deviations from the random mean) (Figure 1B).

Surprisingly, the mean R is almost identical for zebrafish and Arabidopsis genomes 15 when the gene order is randomized, which is about 0.03 with standard deviation 0.004). The underlying cause behind this is unclear. The positive mean value rather than zero could be an effect of the coexpression of the housekeeping genes as suggested in Williams and Bowles 15 . The reason for the identical mean R when these two genomes are randomized is probably either that the housekeeping genes show common patterns of expression in different genomes, dominating the mean R value, or alternatively, that there is a constant bias or weak autocorrection between all genes in each microarray dataset (see Additional file 1 for detailed discussion and also 11 ).

To further explore the coexpression of proximate genes, we partitioned the genes into non-overlapping blocks of k (3 ≤ k ≤ 20) physically adjacent genes according to their start position. For each gene block, we calculated a mean R of the coexpression values; then the mean of all the mean Rs is calculated and plotted in Figure 2. The degree of coexpression first decreases and then becomes stable when the block size k increases from 3 to 20. To verify the significance of the coexpression degree of the genes for each block size, we compared them to what would have been obtained if the genes had been rearranged in each of the following three ways: (1) randomly permuting the gene order over the entire genome; (2) randomly permuting the order of genes within each chromosome; and (3) randomly permuting the order of non-overlapping blocks of 3 consecutive genes. The last rearrangement is used to examine whether the coexpression degree in the larger blocks are dominated mainly by genes that are separated by only one or two genes. The analyses show that there is a significant difference in degree of coexpression between actual and randomized genome (Figure 2). Finally, we remark that the start point for partitioning the genes into non-overlapping blocks has little effect on the analysis presented above because of the way we calculate the mean coexpression value of genes within a block.

Genes are classified into different classes according to the biological processes they are involved in the GO database 22 . We evaluated the mean R of the coexpression value of a pair of genes within a GO class that contains 20 or less genes. There are 853 such GO classes. The mean R is higher than 0.13, 0.30 and 0.50 in 50%, 25% and 10% of these classes, respectively (see Additional file 2). Thus, genes within a GO class are highly coexpressed as reported in other genomes.

In this analysis, the genes within 50 kilo-base pairs (kbp) from each other are collected, mean R values calculated, and the distance between them rounded to the nearest number in 0, 2000, 4000..., 50000. Figure 3 plots the mean of these R values against their intergenic distance. There is a clear negative correlation between intergenic distance and degree of coexpression in both the full dataset (regression line R ² = 0.50) or after removal of tandem duplicates (regression line R ² = 0.46). The correlation is most significant for the gene pairs of distances between 10 kbp to 40 kbp (R ² = 0.79, p < 0.005 for the full dataset, R ² = 0.83, p < 0.005 for the dataset without tandem duplicates). Outside of this range, this correlation seems to be absent.

Genes can be transcripted in two directions, denoted by (→) and (←). Thus, two genes can have: divergent transcription (← →), convergent transcription (→ ←), or parallel transcription (← ← or → →) orientation. We partitioned all the gene pairs into three groups according to transcription orientation. For each orientation class of gene pairs, we calculated the mean R value. Regardless of whether tandem duplicates are removed or not, gene pairs with parallel orientation showed the highest degree of coexpression, in both average as well as median values, while gene pairs with convergent orientation showed the lowest degree of coexpression (Table 1). Kruskal-Wallis tests confirmed this effect of orientation (p = 0.0267) for the entire dataset, but the effect is insignificant after the removal of tandem duplicates (p = 0.2894). This is presumably because most tandem gene pairs have parallel orientation.

We have seen from the analyses that a correlation exists between intergenic distance and degree of coexpression. To further the study in this direction, we examined coexpression among the genes in a positional cluster. We adopted the neighbourhood model to identify positional gene clusters and evaluated positional clustering using a method proposed by Li, Lee and Zhang 19 . In the neighbourhood model, two genes are in a cluster if and only if there is a series of genes between them such that the distance between two adjacent genes in the series is less than a specified distance (D).

The significance of a positional cluster depends on the value of D, the number of genes it contains, and the gene density of its vicinity. In this study, we set D to be 25K, which is one-eighth of the average distance between genes (206K for the full dataset, 213K after removal of tandem duplicates. c.f. Table 1). These clusters are described in Additional file 3.

Neighbouring genes within the clusters we identified tend to show a higher degree of coexpression than neighbouring pairs that are not. This observation is consistent with the observation that is mentioned above: a pair of genes within shorter intergenic distance tends to be more coexpressed. Table 2 shows that with only one exception, the mean R values for clusters of all sizes are higher than 0.07468, the value of mean R of all neighbouring gene pairs in the whole dataset.

Among the identified positional clusters, there are ten highly significant clusters containing eight or more genes, listed in Table 3. They include hox gene clusters hoxba on Chr3 and hoxca on Chr23 23 , olfactory receptor gene cluster or1 on Chr15, cytochrome P450 aromatase gene cluster cyp2j on Chr20, and major histocompatibility complex (Mhc) gene cluster on Chr19 24 25 . The other five clusters contain a mix of genes from different GO classes. Although these genes have not yet been investigated, they are likely structurally and functionally unrelated. In each of the gene clusters except for three eight-gene clusters on Chr4, Chr19 and Chr20, genes have high level of coexpression.

It is proposed that evolutionary selection organizes genes according to their biological function so that their expression can be co-ordinately regulated. To test this hypothesis, we use the GO database 22 as a source of annotations of biological processes. The number of clusters formed by genes in some GO class is listed in Table 4 (see Additional file 4 for details). The number is very much reduced when compared to the total number of clusters for each size. Thus, most positional gene clusters we observe are likely not composed of genes with similar biological functions. As suggested by Spellman and Rubin 10 , the above hypothesis is not supported.

Finally, we investigated whether there is a correlation between the mean R of gene pairs and p-value for a positional cluster. With D = 25K, we considered all the pairs of the neighbouring genes in the same cluster. We divided the gene pairs into seven categories according to the p-value of the clusters to which the gene pairs belong. These seven categories correspond one-to-one to the following intervals of p-values: 0~10^-6, 10^-6~10^-5, 10^-5~10^-4, 10^-4~10^-3, 10^-3~10^-2, 10^-2~10^-1, 10^-1~1. To simplify presentation we consider (base 10 logarithm) -lg p-value instead of p-value, and use the intervals: 0~1, 1~2, 2~3, 3~4, 4~5, 5~6, > 6. We calculated the mean R of the neighbouring gene pairs in each category and observed a significant correlation between -lg p-value and the degree of coexpression of neighbouring gene pairs, either using the complete dataset (Figure 4) or the dataset after tandem duplicates are removed (Figure 5). This correlation is extremely significant for gene pairs that are transcripted in the parallel orientation. The mean R value is as high as 0.5088 (with standard error 0.0642) for the complete dataset and 0.3228 (with standard error 0.1330) even after tandem duplicates are removed. We also observed that at low p-value (high -lg p-value), more gene pairs in the identified clusters are transcribed in the parallel orientation, even with tandem duplicates (Table 5). We examined a correlation between -lg p-value and neighbouring gene distance to find if such a high correlation can be explained with intergenic distance. No such correlation was found (Figure 6).

Our gene-expression datasets are compiled from several previous studies with the Affymetrix GeneChip^® Zebrafish Genome Array (GeneChip 430), which contains 39,000 Danio rerio transcripts. These microarray data were used to study the transcriptional changes of genes in embryonic development and divided into the following four groups:

(i) Nine expression datasets based on experiments on zebrafish embryonic fibroblast cell lines ZF4 and PAC2 (with accession id E-MEXP-736 in ArrayExpress) 28 . They are the gene expression profiles of these two cell lines in cultures with and without the presence of serum.

(ii) Two expression datasets (id E-MEXP-737) derived from experiments on the 24-hour embryos from the Tuebingen cell line 28 .

(iii) Forty-two expression datasets (id E-MEXP-758) from analysis of the transcriptional response to TCDD at different stages 29 . They were used to identify the gene expression changes in the heart and other tissues of zebrafish larvae at 1 h, 2 h, 4 h and 12 h after exposure to TCDD beginning at 72 h fertilization, and

(iv) Forty-one expression datasets collected at the Lab of Functional Genomics, the Institute of Molecular and Cell Biology, Singapore 30 31 32 . The microarray data in 30 were collected in the experiments with RNA extracted from wild type AB and def ^hi429 mutant embryos after 5-day fertilization. In 31 , microarray gene expression profiles of the liver and the remaining liver-free body of adult zebrafish (wild type AB strain) were used to study the regulation mechanism of liver-enriched genes. In 32 , microarray data were obtained from the experiments with RNA samples extracted from five embryos for gene expression profiling of the 18-somite zebrafish cloche mutant, in which development of hematopoietic lineage is severely impaired.

Microarray experiment database ArrayExpress is available at EMBL-EBI 33 . These available datasets were preprocessed by using the invariant set normalization method 34 .

Expressed genes were identified using the Ensembl database. The clone sequences in Affymetrix Zebrafish Genome Array were aligned back to the zebrafish genomic sequence (available from 35 ) using BLAST program. This results in 6802 expressed zebrafish genes. The positional information of these genes was then extracted to arrange the genes for analysis.

The zebrafish GO terms are obtained along with the genomic sequences from the Ensembl database 35 . It annotates the 6802 genes into 1722 GO classes. The correspondence between gene IDs and Affymetrix Zebrafish DB IDs is obtained similarly.

We used the same criterion to remove tandem duplicates as in 3 . Two genes are considered as tandem duplicate if they are within 100 genes from each other and aligned by BLAST with E-value less than 0.2. After a tandem gene cluster was detected, we removed all but one gene from the analysis. After removal of 215 tandem genes, 6587 genes remained for further analysis.

Pearson's correlation coefficient (R) is used to measure the level of coexpression between two genes. For two genes X and Y with expression values (x ₁, x ₂,... x _n ) and (y ₁, y ₂,..., y _n ) in n microarray experiments respectively, R(X, Y) is computed as

∑ i ( x i − x ¯ ) ( y i − y ¯ ) ∑ i ( x i − x ¯ ) 2 ∑ i ( y i − y ¯ ) 2 MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xI8qiVKYPFjYdHaVhbbf9v8qqaqFr0xc9vqFj0dXdbba91qpepeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaqcfa4aaSaaaeaadaaeqaqaaiabcIcaOiabdIha4naaBaaabaGaemyAaKgabeaacqGHsislcuWG4baEgaqeaiabcMcaPiabcIcaOiabdMha5naaBaaabaGaemyAaKgabeaacqGHsislcuWG5bqEgaqeaiabcMcaPaqaaiabdMgaPbqabiabggHiLdaabaWaaOaaaeaadaaeqaqaaiabcIcaOiabdIha4naaBaaabaGaemyAaKgabeaacqGHsislcuWG4baEgaqeaiabcMcaPmaaCaaabeqaaiabikdaYaaaaeaacqWGPbqAaeqacqGHris5amaaqababaGaeiikaGIaemyEaK3aaSbaaeaacqWGPbqAaeqaaiabgkHiTiqbdMha5zaaraGaeiykaKYaaWbaaeqabaGaeGOmaidaaaqaaiabdMgaPbqabiabggHiLdaabeaaaaaaaa@5507@

where x ¯ MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGafmiEaGNbaebaaaa@2D66@ and y ¯ MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGafmyEaKNbaebaaaa@2D68@ are the mean expression value of X and Y in an experiment respectively.

The significance of mean R calculated from the real data was estimated by comparing it with the mean Rs for 10000 random genomes. In each random genome, genes were rearranged though a series of transposes.

To analyze the level of coexpression among the multiple proximate genes, we divided the genes in the Zebrafish genome into non-overlapping blocks, each of k consecutive genes, where k is a fixed integer from 3 to 20. For a block of k genes, there are k(k - 1)/2 pairs of genes; the mean R of these pairs is used to measure the degree of coexpression among the genes in the block, called the block R. The mean block R was compared with mean block Rs calculated from the randomized genome.

We examined positional gene clusters in the neighbourhood model. In the neighbourhood model, two genes x and y are in a cluster if and only if the distance between any two adjacent genes locating between x and y is less than a fixed threshold (D). For a cluster of n genes, its p-value is equal to (1 - e ^-αD ) ⁿ , where α is the gene density in a considered region 19 . Since gene density varies in the zebrafish genome, we set α to be the gene density in the 2 Mbp region around the gene cluster.

This formula is derived under the assumption that the (start) position of a gene is uniformly distributed. This assumption is obviously invalid in a whole chromosome since there are gene dense and sparse regions in a genome. Thus, we focus on the 2 Mbp region centred on the gene cluster to be analyzed.