subgroup size of four, since Spearman correlation coefﬁcients begin to be signiﬁcant from n = 4 (for a one-tailed test). We did not use subgroups of more than four organisms, since as the number of organisms increases the number of positive pairs present in each group of organisms decreases. In many COGs, there exist paralogs for some of the organ- isms. Since these paralogs can have very different codon bias measures, we discarded a gene for a given organism in the case that its paralogs had very different scores. Therefore, in such a case, the organism was not considered as represented within this COG. Genes for an organism were discarded if the dif- ference between the highest and lowest CAI values of paralogs exceeded 0.1. For paralogs that were maintained, the score used for this organism within this COG was the average of the paralogs’ CAI values. After this step, only COGs having a score for each of the four organisms were kept. The CAI scores of each genome within these COGs were converted to Z-scores, in order to have a common range of values for the various genomes. The normalization was computed per genome by the mean and standard deviation of the proteins included in the analysis. Calculation of correlation between the predicted abundance profiles of proteins For each group of organisms, pairs of functionally related proteins (COGs) where both have representatives in each of the four organisms (after ﬁltering, as described in the previous section) were taken. Spearman correlation coefﬁcients were calculated between the normalized CAI measures for these pairs in the various organisms. Often, COGs include protein domains, and not necessarily entire proteins. This could potentially introduce a bias into the analysis, since a single protein, or a set of proteins, may appear in more than one COG. Since these proteins would have the same codon bias measure in both COGs, this would inevitably contribute to a correlation between these often functionally related COGs. Therefore, for each group of organisms, pairs of COGs with common proteins within this subgroup of organ- isms were not included. Analysis of significance In order to analyze signiﬁcance for each subgroup of four organisms, a negative set consisting of all possible pairs of proteins from the positive dataset was created (excluding the functionally related pairs). This negative set included only proteins from the positive dataset, since the interacting protein dataset (and to a much lesser extent, the pathway dataset) was found to be biased toward abundant proteins, and we wished to neutralize this bias. The median value of the correlation coef- ﬁcients in these negative sets was not equal to zero for many subgroups of organisms. This demonstrates that there is a bias in some of the combinations of organisms, which was part of the incentive for our approach of looking at groups of organ- isms separately (other reasons are detailed above). For some of the subgroups of genomes, relatively few pro- teins in the positive dataset had representatives in the four genomes. Therefore, only subgroups of genomes resulting in a negative set of at least 1000 pairs were kept for the ﬁnal analysis. Nucleic Acids Research, 2005, Vol. 33, No. 3 1053 For each group of four organisms, a one-sided Wilcoxon test was performed, comparing the correlation coefﬁcients of the positive group with the median of the correlation coefﬁcients of the generated negative set. For this calculation, we used the exactRankTests package (http://cran.r-project.org/doc/ packages/exactRankTests.pdf) written for the R project for Statistical Computing (35). This procedure allows for ties in the data, which are common when calculating the Spearman correlation coefﬁcient for n = 4. The hypothesis was that the correlations in the positive group are not greater than the median of the negative set. In order to calculate whether the overall results were sig- niﬁcant, the observed fraction of groups of organisms with signiﬁcant Wilcoxon P-values (<0.05) was compared with the expected fraction of 0.05 using the binomial test. RESULTS AND DISCUSSION General overview of the approach We tested whether the predicted protein levels of functionally associated proteins (as predicted by the CAI) change in a correlated fashion across different organisms (Figure 1). We looked at 48 bacterial, archaeal and fungal genomes (Supple- mentary Table 1), and extracted orthologous proteins within these organisms using the COG database (see Materials and Methods). We looked at two types of functional associations: interacting proteins and proteins that function in consecutive steps within metabolic pathways (we term these ‘neighboring proteins’). We refer to protein pairs extracted from these two datasets as ‘positive’ pairs. For these positive pairs, we cal- culated the correlation coefﬁcients between the codon bias values of the pair mates in different organisms, and analyzed the signiﬁcance of these correlations. Ideally, we would have liked to analyze all the positive pairs at once, for the 48 organisms. However, due to the nature of the data, we used a different approach that allowed us to minimize the loss of data and to analyze the signiﬁcance of the phenomenon. One characteristic of the data that led us to our approach is that many proteins occur in only a subset of the organisms (different proteins have different phylogenetic proﬁles). In such cases, the abundance proﬁles across all organisms will contain many values that may lead to erroneous correlations. Another characteristic is that for cer- tain combinations of organisms there is background noise, evident in the fact the codon bias values are distributed such that even within a random group of pairs of proteins, most are slightly correlated. Our approach consisted of looking at different subgroups of organisms, and analyzing the stat- istical signiﬁcance of the phenomenon within each subgroup separately. We took all subgroups of size four for our analysis (see Materials and Methods), which enabled us to include a large number of positive pairs in many subgroups. With our approach, we could analyze pairs of functionally related pro- teins even if their phylogenetic proﬁles across all organisms are very different, while taking background noise into account. An additional advantage of this approach is that it enabled us to look separately at different subgroups of organisms. The main steps of the analysis for each four-organism group are illustrated in Figure 2.