We used publicly available expression data in six eukaryotic species: yeast (two sets 89), fruit fly (two sets 101112), worm (one set 13), rat (three sets 141516), mouse (five sets 17181920) and human (eleven sets 17, 2122232425262728) (for details see Table 1). Genes' chromosomal positions in yeast and worm were obtained from protein tables at GenBank ftp://ftp.ncbi.nih.gov/genbank/genomes/, and those in fruit fly and those in mouse, rat and human were obtained from FlyBase http://flybase.bio.indiana.edu/maps/lk/gnomap/ and from Resourcerer at TIGR http://pga.tigr.org/tigr-scripts/magic/r1.pl, respectively.

We investigated only the genes of which the chromosomal position was known. In each dataset, the genes were divided into n_chr subs ets, each of which consisted of genes/ORFs on the same chromosome (Here, n_chr denotes the number of the chromosomes in that species). The Pearson correlation coefficient, r, and chromosomal distance, CD, measured in base pairs (bp) were calculated for every possible pair in a subset. After this calculation was repeated for all subsets, all results were merged and the total number of the pairs, N, was counted. The N pairs were sorted according to their values of r (regardless of CD), and then the top 20 % of the N pairs were selected from the sorted data as highly correlated (HC) pairs. The pairs were sorted into bins of equal sized intervals of CD. Because the six species have different genome compactness, different widths were used: 20 kbp for the mammals (human, rat and mouse), 2.5 kbp for the worm and fruit fly data and 1 kbp for yeast. To investigate an effect of CD on co-expression, we defined a co-expression rate (CoER) in each bin:

When the CoERs of the six species were plotted in a graph, the first bin of the mammals was further divided so that the starting point of the curves were almost the same.

As control groups, we selected two more groups of 0.2 N pairs from the sorted data: the lowest 20 % of N, negatively correlated (NC) pairs, and the 20 % of N centered at the median, zero-correlation (ZC) pairs. The CoER was calculated for these groups, and the results were compared with the HC group.

Because there were large differences in the number of the gene-pairs and microarrays in the datasets, we sought some measure of the reliability of each dataset. To do so, we used the product of two factors which inform regarding the breadth of the sampling of the organism's transcriptome: the numbers of the total pairs and microarrays in each dataset. The averaged CoER in each species was calculated using weights derived from the products. We considered the dataset having the largest weight in each species the most reliable one. It was expected that the CoER would scatter around 0.2 if there was no distance (or any other) effect on co-expression. To verify this, we also calculated the standard deviation of the CoER using the weights.

When the six spec ies were compared a normalized distance (ND) was also used. The physical distance was normalized by the grand average of CD of all gene pairs next to each other in each species. The overall average was calculated as follows. First, the total length of a chromosome was divided by the number of genes on it. This was repeated for all chromosomes in a species and by averaging all values, we obtained the overall average in that species.

We also investigated Gene Ontology (GO) categories http://www.geneontology.org/ in the HC, NC and ZC groups in CD ranges between 0 and 20 kbp and between 980 and 1000 kbp. This analysis was carried out only for the most reliable dataset of yeast (Cho et al. 1998) and human (Diette, PGA Human CD4+Lymphocytes, http://microarray.cnmcresearch.org/pgadatatable.asp).

Because duplicated genes are likely to be co-expressed due to their common history, we investigated how many pairs in the HC group were duplicated ones. In each of the yeast, worm and mouse datasets, HC pairs were sorted according to the CD (in ascending order) and the top 10,000 were selected for a pair-wise, stand-alone protein BLAST analysis. Of the 10,000, the pairs in which the protein sequences of both genes were known were subject to analyze. We employed a criterion previously proposed for the identification of duplicated genes in vertebrates 34. Gene pairs having expected values (E) of less than 0.2 were deemed to be duplicated. Protein sequences were obtained from ExPASy Molecular Biology Server http://kr.expasy.org/ for mouse, from Wormpep.109 http://www.sanger.ac.uk/Projects/C_elegans/wormpep/ for worm and from Saccharomyces Genome Database http://www.yeastgenome.org/ for yeast.

To investigate intra- and inter-species differences, a multiple comparison of CoER was carried out using the Ryan procedure 29 at the significance level of α = 0.01. The underlying concept of this procedure is the incremental adjustment of the significance thresholds. Except for the significance thresholds, each of the tests was made in exactly the same manner as for a single pair. First, the highest and lowest CoERs were compared at the significance level of 2α / n(n-1), where n was the number of samples to be compared (in the inter-species comparison, n = 6). If the extremes differed significantly, we tested each of them against the CoER next to the other extreme at the significance level of 2α / n(n-2). If we found a significant difference in the previous step, we continued to test the highest CoER vs. the third lowest, the lowest vs. the third highest and the second highest vs. the second lowest using 2α / n(n-3). These steps were repeated until 2α / n(n-5). Because different bin widths were used in yeast, worm and fruit fly, the CoER was recalculated for the range between 0 and 20 kbp when the six species were compared. This comparison method was also employed to investigate intra-species differences in the eleven human datasets.

In all 24 datasets the distribution of Pearson correlation coefficient appeared to be a bell-shaped curve centered at approximately zero. In what follows, we will describe the results of the HC pairs unless otherwise noted. A higher CoER was obtained in the first bin than a long CD range between 980 k – 1000 kbp in all datasets.

In Fig. 1, the CoERs obtained from the eleven human datasets are plotted as a function of CD: Fig. 1(A),1(B) and 1(C) show the results of the HC, ZC and NC pairs, respectively. The CoERs from the HC pairs decreased as the CD increased although there were large swings in CoER in a CD range above 100 kbp. These swings were larger in smaller data sets because of stochastic effects and undersampling of the transcriptome. In contrast, in the CD range below 100 kbp, the CoERs from the ZC and NC groups were relatively flat (compare Fig. 1(A) with 1(B) and 1(C)).

The weighted average and standard deviation over the eleven curves in (A), (B) and (C) are shown in (D), (E) and (F), respectively. The average in (D) showed the same tendency of gradual decrease to 0.2, whereas the averages in (E) and (F) showed no distance effect. The weighted averages for all six species are given in Fig. 2. The phenomena shown in Fig. 1 were consistently observed in all species. These results strongly suggest that co-expression of neighboring genes is common in many eukaryotic species and also that the CD, especially a short CD below 10 kbp, is associated with increased frequency of co-expression.

The results of pair-wise analysis of GO category appeared to be different in the yeast and human datasets (Table 2). In yeast, only the HC pairs shared the same category and most of the pairs were not duplicates. Four pairs were found in a long CD range (980 – 1000 kbp). In the human data, more variety was obtained and pairs having the same category were found even in the NC group. A category, GO:5887 (integral to plasma membrane), was seen in the three groups while GO:6954 (inflammatory response) was seen in the HC and ZC. In the long CD range, eleven pairs were found. The results suggest the human genome involves more complicated functional relationships over a substantial CD.

Table 3 summarizes the BLAST results. In yeast, about 780 out of the 10,00 pairs were deemed to be duplicated pairs (E < 0.2). In the worm dataset, 8,370 pairs were available for the analysis and 2,658 (31.8 %) were regarded as duplicates. In the mouse datasets, out of about 3,500 analyzed pairs, 11.2 % were putative duplicates. However, in the three species, most pairs had expected values larger than 1. These results indicate that there are many non-duplicate pairs in the HC group, suggesting that the high CoERs in the HC group were due to not only effects of duplicated pairs but also non-duplicate effects. The distributions of the expected values in the five mouse datasets were almost the same (Table 3), suggesting that differences in microarrays were not significant.

In Fig. 1(D), the standard deviations for the first three bins are relatively large. For example, the CoERs in the first bin in the eleven datasets were in a range between 0.24 and 0.38. To investigate intra-species differences in humans, a multiple comparison with the Ryan procedure was carried out (α = 0.01). Forty-nine out of the 55 possible combinations were not significantly different. In the five mouse datasets, 12,778 HC pairs out of approximately 20,000 used for the BLAST analysis were commonly seen in two or more datasets. The distributions of the expected values in the five mouse datasets were almost the same (Table 3). This suggests that there was no significant intra-species difference. Accordingly, the noise in the microarray data and the differences in microarray design appear to have minor influences on our results.

The CoERs in the weighted averages of the six species were compared. The results of the intra- and inter-species comparisons indicate that there are significant differences (p < 0.01) in the CoER in a short CD range (0 – 20 kbp) between any pair among worm, mammal (human, rat and mouse), fruit fly and yeast except two pairs of (worm and rat), and (mouse and fruit fly) (Table 4). Although the rat CoERs in the first three bins are almost the same as those of the worm (Fig. 2(A)), the results using the normalized distance (Fig. 3) strongly suggest that the multicellular organisms except worm show similar CoERs. The CoERs of worm and yeast were much larger than the others for a ND range between 0.3 and 1. In yeast, which is a unic ellular eukaryote with a compact genome, the organization of coordinated gene regulation is probably different from the other species with more dispersed genomes. As previously reported 3, the worm genome involved much more duplicated pairs than the yeast and mouse (Table 3). According to Blumenthal et al. 30, the worm genome involves at least 1,000 operons, which correspond about 15 % of all C. elegans genes. After excluding the pairs in the duplicates and operons, the worm CoERs are similar to those of the other multicellular organisms (see worm2 in Fig. 2(A)), indicating that the duplicates and operons are the main reason for the larger CoERs in the worm. However, when the ND was used, the worm curves (both with and without duplicates and operons) were similar to the yeast data.

A comparison of Figs. 2(A) and 3 provides some information on mechanisms behind the distance effect. If the physical distance has the dominant effect (chromatin remodeling is a possible cause), the CoERs in Fig. 2(A) should be similar across the species. On the other hand, if the effect of ND is major, Fig. 3 should show similar curves. The actual results seem to be the former and suggest that the CD plays the dominant role. In the multicellular organisms, the CoERs were higher than 0.2 up to about 50 kbp whereas the yeast curve was flat above 10 kbp. The mechanism behind this difference is currently not clear, but there are some clues. For example, several factors have been identified as controlling localized gene transcription 31. These include the size of euchromatic chromosome territories and the spacing of chromatin "insulators" which provide impedance to non-specific enhancer activity upon neighboring genes 32. Variation across species of these factors could explain our findings although this has not been systematically studied to date. Further analysis is required to advance our understanding of the mechanisms.