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Differential evolutionary rates of duplicated genes in protein interaction network
Gene 385 (2006) 57 – 63 www.elsevier.com/locate/gene
Differential evolutionary rates of duplicated genes in protein interaction network Takashi Makino, Yoshiyuki Suzuki, Takashi Gojobori ⁎ Center for Information Biology and DNA Data Bank of Japan, National Institute of Genetics, 1111 Yata, Mishima-shi, Shizuoka-ken 411-8540, Japan Received 21 February 2006; received in revised form 19 April 2006; accepted 23 June 2006 Available online 17 August 2006
Abstract In the network of protein–protein interactions (PPIs), a loss and gain of the partnering proteins can cause drastic changes of network formation during evolution. With the aim of examining the evolutionary effects of the loss and gain of the partnering proteins on PPIs, we examined a relationship between evolutionary rates and losses and/or gains of PPIs for duplicated gene pairs encoding proteins involved in the PPI network. For duplicated pairs, which provided us with a unique opportunity of making fair comparisons of the genes with the same initial condition, we found that the evolutionary rate of the protein with more PPI partners is much slower than that of the other with fewer PPI partners. Moreover, when the ratio of evolutionary rates (faster rate/slower rate) was computed for each of the duplicated pairs, the ratio for the duplicated pair sharing any PPI partners was significantly lower than that for the pair sharing no PPI partners. These results indicate that the duplicated gene pairs differentiate through the losses and/or gains of the PPI partners, resulting in a change in their evolutionary rates. In particular, we point out that the PPI losses for the duplicated gene products that are involved in the functional classes of ‘transcription’ and ‘protein fate’ have an impact on their evolutionary rates more than the PPI losses for others. © 2006 Elsevier B.V. All rights reserved. Keywords: Protein–protein interaction; Functional divergence; Gene duplication; Saccharomyces cerevisiae
1. Introduction Proteins interact with various molecules in order to manifest appropriate functions. In particular, protein–protein interactions (PPIs) are one of the most important components of biological networks. The amount of information about PPIs has grown rapidly due to the development of high-throughput two-hybrid systems (Uetz et al., 2000; Ito et al., 2000) and mass spectrometry of coimmunoprecipitated protein complexes (Gavin et al., 2002; Ho et al., 2002). It has become known that proteins with similar functions tend to interact with each other (Schwikowski et al., 2000; Ge et al., 2001). PPI networks have also been shown to consist of a small number of proteins with many PPI partners and a large number of proteins with a few partners (Jeong et al., 2001). The functional constraints of proteins involved in the PPI network are composed of several factors. The so-called fitness Abbreviations: PPIs, protein–protein interactions. ⁎ Corresponding author. Tel.: +81 55 981 6847; fax: +81 55 981 6848. E-mail address: [email protected] (T. Gojobori). 0378-1119/$ - see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.gene.2006.06.028
effects as well as the gene expression levels are typical factors, because they are known to be negatively correlated with the rate of amino acid substitution (Wilson et al., 1977; Hirsh and Fraser, 2001; Pal et al., 2001; Jordan et al., 2002). The number of PPIs for proteins is also an important factor for determining the evolutionary rate. It has been reported that the number of PPI partners for proteins is negatively correlated with the evolutionary rate (Fraser et al., 2002, 2003). Therefore, after gene duplication, the differentiation of PPIs through the PPI losses and/or PPI gains during evolution may affect the evolutionary rates of duplicated pair. For a duplicated gene pair, it has been shown that one copy usually has more PPI partners than the other (Wagner, 2002). Gene duplication is one of the major evolutionary mechanisms for generating novel genes (Ohno, 1970). After gene duplication, one of the pair may be redundant, such that functional constraint is relaxed to allow one or both to differentiate as long as the original function is retained as a whole. When a duplicated gene pair functionally differentiates, the evolutionary rate may be accelerated in one or both due to the relaxation of negative selection or the enhancement of positive selection (Li and
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Gojobori, 1983). In yeast, it has been proposed that the differentiation process is asymmetrical rather than symmetrical to minimize the risk of deleterious mutations (Wagner, 2002). It is therefore expected that the acceleration of evolutionary rate occurs mainly in one of the two copies after gene duplication. However, it is not yet known how the duplicated gene products affect their PPIs in evolution. After gene duplication, the accumulation of substitutions in the duplicated genes would be caused not only by the functional differentiation of gene products but also by the losses and/or gains of PPIs. Duplicated products often interact with the same proteins (Deane et al., 2002). One proposed model for the losses and/or gains of PPIs provides the reason why the products of a duplicated gene pair often share PPI partners (Wagner, 2001). In this model, although some duplicated pairs lose PPIs during the evolutionary process, many pairs retain some shared PPI partners. In a recent study, the magnitude of functional divergence for the duplicated gene pairs was measured by using the number of shared PPI partners between all pairs in the PPI networks (Baudot et al., 2004). To examine the relationship between the evolutionary rate and the functional differentiation of duplicated gene products, we focused on the shared PPI partners that were considered to reflect the functional differentiation of the duplicated gene products, because the products sharing PPI partners would not have largely diverged. The purpose of the present study is to understand how gene duplication influences the evolution of PPI networks. To study the relationship between gene duplication and the evolutionary rates of the gene products with PPI partners, we focused on the duplicated genes generated by genome duplication in Saccharomyces cerevisiae, which occurred about 100 million years ago (Wolfe and Shields, 1997; Kellis et al., 2004; Dietrich et al., 2004). We used the PPIs in S. cerevisiae that have well been documented based not only on hundreds of small-scale experiments but also on high-throughput methods. We set up and examined the hypothesis that the ratios of evolutionary rates (faster rate/slower rate) for the pairs sharing any PPI partners are lower than those for the pairs sharing no PPI partners. We then discuss the mechanisms of functional differentiation after gene duplication on the basis of the results obtained. 2. Materials and methods 2.1. Protein–protein interactions (PPIs) Among approximately 14,000 PPI data stored in DIP (the Database of Interacting Proteins, http://dip.doe-mbi.ucla.edu/), we used only the CORE data set, which contained 6205 PPIs, after the exclusion of proteins that interacted with themselves (self interactions). We further removed 231 PPIs from the CORE, because they were associated with the proteins derived from pseudogenes and erroneously predicted genes (Kellis et al., 2003). Thus, we used 5974 PPIs included in the CORE. The CORE contains the PPIs that satisfy one of the following three conditions. First, the interactions were determined by smallscale experiments. They are regarded as reliable PPIs, because they are derived from individual research papers. Second, each
interaction was identified by independent experiments at least twice. PPIs identified by high-throughput methods in the CORE have high correlation with respect to function and cellular location. Thus, the data quality in this feature is as reliable as that produced by small-scale experiments (Deane et al., 2002). Third, each interaction was confirmed by examining if paralogues interact with the same proteins or the paralogues themselves. If the proteins encoded by a duplicated gene pair share the same PPI partners, the PPIs between the duplicated pair and the shared partners are regarded as reliable. In fact, paralogues often interact with the same proteins (Deane et al., 2002). According to the third criterion, all of the shared PPIs between duplicated pairs in DIP should be included in the CORE. Scrutinizing approximately 14,000 PPIs stored in DIP, we identified 165 PPIs that satisfied the third criterion but were not included in the CORE. Therefore, we added these PPIs to the 5974 PPIs mentioned above, and a total of 6139 PPIs were used in this study. 2.2. Proteins encoded by duplicated genes in S. cerevisiae and their orthologues in Kluyveromyces waltii The genome duplication of S. cerevisiae took place about 100 million years ago (Wolfe and Shields, 1997). Four hundred and fifty duplicated gene pairs, each of which encodes a pair of proteins, were generated by genome duplication (Kellis et al., 2004). Removal of genes encoding ribosomal proteins is conventional in the study of duplicated genes, because they are known to have diverged after gene duplication so slowly that both copies tended to retain the original function (Pal et al., 2001; Gu et al., 2003). Therefore, we excluded 33 gene pairs encoding ribosomal proteins from this study. We further removed 153 pairs, because neither copy had a PPI partner. These left us with 261 pairs to analyze. We used the ORF sequences of the duplicated pairs to estimate the evolutionary rates (Saccharomyces Genome Database, http://www.yeastgenome.org/). To compare the evolutionary rates between a duplicated pair of S. cerevisiae, it was necessary to use an outgroup that was known to have diverged before the genome duplication. We used orthologues in K. waltii that were accurately determined by Kellis et al. (2004), because this species is known to have diverged from S. cerevisiae earlier than the genome duplication (Kellis et al., 2004). However, the speciation time does not appear to be much older than the genome duplication, because it has been reported that the genome duplication occurred in the S. cerevisiae lineage soon after speciation between K. waltii and S. cerevisiae (Wolfe, 2004). As a result, we obtained 261 sets of trios, each of which consisted of a duplicated pair from S. cerevisiae and one orthologue from K. waltii. 2.3. Comparison of evolutionary rates between duplicated gene products For each set of the 261 trios, a multiple alignment of amino acid sequences was made using CLUSTAL W (version 1.81; Thompson et al., 1994). Four sets of trios were removed from
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the study, because the sequences were too diverged to be aligned. To compare the rates of amino acid substitution between the duplicated gene products of S. cerevisiae, we estimated the number of amino acid substitutions after the genome duplication by constructing a phylogenetic tree for each trio. Each tree was constructed by the neighbor-joining method (Saitou and Nei, 1987) using the number of amino acid substitutions estimated by Kimura's method (1983), which were implemented in PHYLIP (version 3.573c). Note that Kimura's distance is known to be reliable as long as the proportion of difference (p) between amino acid sequences compared is smaller than 0.7 (Nei, 1987). For our data, multiple hits are considered to be corrected appropriately, because p rarely exceeded 0.7 (Supplementary Fig. 2). Three sets of trios were further removed from the analysis at this stage because the sum of two distances among the trio was shorter than the remaining one. Therefore, we used 254 sets of trios for the comparison of evolutionary rates. 2.4. Relative-rate test We compared several methods to conduct the relative-rate test between a pair of duplicated gene products for each of the 254 trios. For using a model-based relative-rate test, there were some problems. It required a substitution model (Wu and Li, 1985). Moreover, the substitution rates among the sites in a protein may vary (Jin and Nei, 1990). Therefore, we conducted the relative-rate test using the one degree of freedom method (Tajima, 1993), which was free from any model. 3. Results and discussion 3.1. Losses of PPIs for proteins encoded by duplicated genes Soon after gene duplication, the protein encoded by one copy should interact with the same set of proteins as the other, because these proteins are identical. It has been proposed that PPI partners of proteins encoded by duplicated genes change
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through PPI losses or PPI gains during evolution (Wagner, 2001). For duplicated gene pairs, it has been shown that one copy usually has more PPI partners than the other (Wagner, 2002). However, it was unclear which of the two mechanisms, namely PPI losses and PPI gains, is the major force of the evolution of PPIs. Proteins under strong functional constraints would be hard to change their PPI partners during evolution, because they are highly conserved. The PPI losses of the proteins may accelerate their evolutionary rates, because it has been reported that the evolutionary rate is negatively correlated with the number of PPIs (Fraser et al., 2002, 2003). If the PPI losses occur more often than the PPI gains for a duplicated pair, the protein encoded by one copy evolving at a slower rate would have more PPI partners than the other. To examine this possibility, we used 216 duplicated pairs, excluding 38 pairs where the pair had the same number of PPIs from the 254 pairs (we showed the statistics regarding the distribution of the number of PPIs for each duplicated pair in Supplementary Fig. 1). For each pair of gene products, we examined whether the protein with more PPI partners evolved more slowly than the other with less partners. We found that a protein with more PPI partners evolved at a slower rate in 134 (62%) out of the 216 pairs examined, which was significantly greater than expected (50%) under the null hypothesis of random association between the number of PPI partners and the evolutionary rate (P b 0.001; sign-test). Similar results were obtained when we focused only on the pairs with significant differences in the evolutionary rates between duplicated genes (Tajima, 1993). Out of the 254 duplicated gene pairs, 143 pairs showed statistically significant differences in the evolutionary rate. We analyzed 123 duplicated pairs, excluding 20 pairs where the pair had the same number of PPIs. It was found that a protein with more PPI partners evolved at a slower rate in 81 (66%) out of the 123 pairs examined, which was actually a 30% excess compared with the random expectation (50%), and highly significant (P b 0.001). For a duplicated pair of gene products, we showed that the one with more PPI partners evolves at a slower rate than the
Fig. 1. Schematic representations of F1, S1, F2, and S2. Closed circles and open circles respectively mean proteins encoded by duplicated gene pair sharing no PPI and sharing PPIs. F (light gray arrow) and S (gray arrow) respectively mean faster rate and slower rate, respectively, and subscripts 1 and 2 refer to the cases of sharing no PPI and sharing PPIs for duplicated pairs, respectively. The ratio of evolutionary rates for duplicated pairs after gene duplication was estimated by a faster evolutionary rate of one copy/a slower rate of another copy (F1/S1; F2/S2).
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T. Makino et al. / Gene 385 (2006) 57–63 Table 2 Functional classifications in the MIPS database a Functional class Metabolism Energy Cell cycle and DNA processing Transcription Protein synthesis Protein fate (folding, modification, destination) Cellular transport, transport facilitation and transport routes Cellular communication/signal transduction mechanism Cell rescue, defense and virulence Interaction with the cellular environment a
Modified from http://mips.gsf.de/genre/proj/yeast/index.jsp/.
genes under the same initial condition, we found that the protein encoded by one copy evolving at a slower rate had more PPI partners than the other copy. The results indicated that the PPI losses have occurred more often than the PPI gains for a copy evolving at a faster rate, under the assumption that PPIs of a copy evolving at a slower rate are conservative in the evolutionary process. 3.2. Functional divergence through changes in PPIs
Fig. 2. (a) Ratios of evolutionary rates for duplicated pairs sharing PPI partners and sharing no PPI partners. Open bars indicate duplicated pairs interacting to one another or sharing PPI partners, while closed bars indicate duplicated pairs sharing no PPI partners. (b) Only the duplicated pairs showing statistically significant differences in evolutionary rate were used.
other with less PPI partners. Although it has been shown that the evolutionary rate of the proteins has a negative correlation with the number of PPI partners (Fraser et al., 2002, 2003), these authors ignored noises such as differences in structural and functional features, and did not deal with functional divergence through the change of PPIs. For duplicated pairs that provided us with a unique opportunity of making fair comparisons of the Table 1 Results of the relative-rate test for duplicated pairs sharing PPI partners and sharing no PPI partners #Duplicated pairs #Duplicated pairs sharing PPI partners sharing no PPI partners Significant difference of rates 65 No significant difference 65 of rates
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After gene duplication, there are at least two possible pathways of PPI divergence for the proteins encoded by a duplicated gene pair. First, one of the proteins encoded by a duplicated pair keeps all the PPI partners, whereas the other loses them. The evolutionary rate of the former protein would be slower than that of the latter, because the former has to maintain the original function while the latter is free from it. In other words, they are likely to evolve at different rates. Second, both proteins share some of the PPI partners. In this case, both proteins may still have similar functions, and the sequences may not change as drastically as in the first case. The evolutionary rates of the gene products sharing PPI partners may not significantly differ from each other. Therefore, if the duplicated gene products lose the shared PPI partners, the ratio of evolutionary rates for the pair (faster rate/slower rate) may be higher than that for functionally similar pairs. To test this hypothesis, we examined whether F1/S1 were higher than F2/S2, where F and S denote faster rate and slower rate, respectively, and subscripts 1 and 2 refer to the cases of sharing no PPIs and sharing PPIs, respectively (Fig. 1). Here we defined duplicated pairs sharing PPIs as the pairs sharing at least one PPI partner. There were 124 duplicated pairs sharing no PPI partners and 130 duplicated pairs interacting to one another or sharing PPI partners. It was then found that F1/S1 was significantly higher than F2/S2 (Mann–Whitney U-test, P b 0.001; Fig. 2a). Even when we focused only on 143 duplicated pairs for which the evolutionary rates between the two copies were significantly different, F1/S1 for 78 pairs were significantly higher than F2/S2 for 65 pairs (Mann–Whitney U-test, P b 0.01; Fig. 2b). In addition, the proportion of duplicated pairs with significant differences in evolutionary rate among the pairs sharing no PPI partners was significantly greater than that
T. Makino et al. / Gene 385 (2006) 57–63 Table 3a Results of the relative-rate test for duplicated pairs having PPI partners and sharing no PPI partners in functional class ‘transcription’ #Duplicated pairs #Duplicated pairs sharing PPI partners sharing no PPI partners Significant difference of rates 10 No significant difference 13 of rates
19 7
Table 3c Results of the relative-rate test for duplicated pairs having PPI partners and sharing no PPI partners in the functional classes of ‘cellular communication/ signal transduction mechanism’, ‘cell rescue, defense and virulence’, and ‘interaction with cellular environment’ #Duplicated pairs #Duplicated pairs sharing PPI partners sharing no PPI partners Significant difference of rates 22 No significant difference 20 of rates
among the pairs sharing PPI partners (chi-square test for independence, P b 0.05; Table 1). Although we showed that PPI divergence is reflected in large ratios of the evolutionary rates of duplicated pairs, one might argue that the PPI divergence should be rather reflected in the evolutionary distance between a duplicated pair. When the evolutionary distance between a duplicated pair is very large because of the rapid evolutionary rates, they may not share PPI partners regardless of the ratio of evolutionary rates. Therefore, we examined whether the evolutionary distance between the duplicated pair sharing PPI partners was smaller than that between those sharing no PPI partners. However, the distances between the 96 pairs sharing PPI partners were not significantly shorter than those between the 67 pairs sharing no PPI partners. In addition, even when we removed 91 duplicated pairs with the evolutionary distance of N1.0 and compared F1/S1 with F2/S2, the former was still significantly higher than the latter (Mann– Whitney U-test, P b 0.05). These results strongly suggest that the change in PPI partners is primarily reflected in large ratios of the evolutionary rates for a duplicated pair. In addition, we also examined the relationship between the difference in the number of shared PPIs and the ratio of evolutionary rates. However, we did not find any statistically significant correlations between them. This may be because the magnitude of the difference in the number of PPIs for duplicated pairs is affected by the number of PPIs of a protein encoded by an ancient gene before gene duplication. Actually, it was difficult to investigate the gradual change in the number of shared PPIs for duplicated pairs during evolution, because the number of PPIs of the proteins encoded by ancient genes was unknown. For a duplicated gene pair, if the protein encoded by one copy evolving at a faster rate has not been silenced during evolution, it may have lost its PPI partners and had a chance of finding a new PPI partner under weak or no functional constraints. On the other hand, the PPIs for the protein encoded by one copy evolving at a slower rate may be conservative with relatively strong functional constraints. For duplicated pairs, the
Table 3b Result of the relative-rate test for duplicated pairs having PPI partners and sharing no PPI partners in functional class ‘protein fate’ #Duplicated pairs #Duplicated pairs sharing PPI partners sharing no PPI partners Significant difference of rates 2 No significant difference 10 of rates
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11 5
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gene product evolving at a faster rate will lose the shared PPI partners more frequently than the other. This implies that a pair of proteins encoded by a duplicated gene pair having few shared PPI partners evolves at different rates. In fact, the present study indicates that pairs sharing no PPI partners show a larger ratio of evolutionary rates than those sharing PPI partners, although it has been reported that a simple relationship between sequence divergence and their functional divergence revealed by the PPI network analysis could not be established (Baudot et al., 2004). When a duplicated pair shares no PPI partners, it is possible that they interact with different PPI partners with different functions. This means that gene duplication will lead to the functional differentiation of the duplicated gene products through the PPI losses and/or PPI gains, which will then cause a change in their evolutionary rates.
Fig. 3. Examples for the pairs of proteins encoded by duplicated gene pairs and their PPI partners. The circles and lines represent proteins and PPIs, respectively. The circles in gray are PPI partners. (a) The open circles represent proteins encoded by the duplicated gene pair (YDR480W and YPL049C), which are down-regulators of invasive growth and mating, respectively. (b) The closed circles represent proteins encoded by the duplicated gene pair (YNR023W and YCR052W), which are a subunit of SWI/SNF global transcription activator complex and a subunit of the RSC chromatin-remodeling complex, respectively.
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3.3. Tendency of PPI divergence for duplicated pair in different functional classes For investigating the functions of duplicated gene products, we used functional classification established by the MIPS database (Mewes et al., 2002; Table 2). In the functional class of ‘transcription’, there were significantly many duplicated pairs sharing no PPI partners and having a significant difference in evolutionary rates (chi-square test for independence, P b 0.05; Table 3a). There were also statistically significant differences in the rate between the two copies in the functional class of ‘protein fate’ (chi-square test for independence, P b 0.01; Table 3b). These results indicate that the PPIs of the proteins included in these functional classes do not tend to be conserved in the evolutionary process, resulting in a change in their evolutionary rates. Although the other functional classes showed no significant difference in ratio of evolutionary rates between duplicated pairs sharing PPI partners and those sharing no PPI partners, we found that there were relatively many duplicated pairs sharing PPI partners in the functional classes of ‘cellular communication/signal transduction mechanism’, ‘cell rescue, defense and virulence’, and ‘interaction with cellular environment’ (Table 3c). PPIs of the proteins included in these functional classes are likely to be conserved during the evolutionary process. The results showed that the impact of the PPI losses for the duplicated gene products on their evolutionary rates depends on their functions. We found many cases of duplicated gene pairs sharing PPI partners in the functional classes such as ‘cellular communication/signal transduction mechanism’, ‘cell rescue, defense and virulence’, and ‘interaction with cellular environment’. For example, YDR480W and YPL049C (a duplicated pair in ‘interaction with cellular environment’) share all PPI partners (Fig. 3a), and have no significant difference in evolutionary rate between them. It has also been shown that the pair shares a role in negatively regulating the invasive growth pathway (Cook et al., 1996). After gene duplication, the pair has shared the PPI partners and not diverged their functions in the evolutionary process, resulting in keeping similar evolutionary rates. We also found many cases of duplicated gene pairs sharing no PPI partners in the functional classes such as ‘transcription’ and ‘protein fate’. For example, YNR023W and YCR052W (a duplicated pair in ‘transcription’) do not share PPI partners, and have a significant difference in evolutionary rate. In addition, they are subunits in different protein complexes. YNR023W is a subunit of SWI/SNF global transcription activator complex, and YCR052W is a subunit of the RSC chromatin-remodeling complex (Fig. 3b; Cairns et al., 1996). We consider that the significant difference in evolutionary rate between them is caused by drastic changes in the PPI partners during evolution. Although the proteins encoded by these duplicated gene pairs should have interacted with the same PPI partners immediately after the gene duplication, one of the copies may have subsequently changed its PPI partners and diverged its functions. It is thus suggested that YCR052W, which evolves at a faster rate than YNR023W, obtained novel functions by changing PPI partners. Thus, the evolutionary comparison of the PPI partners
of one copy in a duplicated pair with those of the other is important for understanding their functional differentiations through PPI network divergence. Acknowledgements We are grateful to Yoshio Tateno, Kazuho Ikeo, Matthew Webster, two anonymous reviewers and all the members of the DNA Analysis Laboratory for valuable comments and discussion. This research was supported by Grants-in-Aid for Creative Basic Research from the Ministry of Education, Culture, Sports, Science and Technology, Japan (to T.G.). Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.gene.2006.06.028. References Baudot, A., Jacq, B., Brun, C., 2004. A scale of functional divergence for yeast duplicated genes revealed from analysis of the protein–protein interaction network. Genome Biol. 5, R76. Cairns, B.R., et al., 1996. RSC, an essential, abundant chromatin-remodeling complex. Cell 87, 1249–1260. Cook, J.G., Bardwell, L., Kron, S.J., Thorner, J., 1996. Two novel targets of the MAP kinase Kss1 are negative regulators of invasive growth in the yeast Saccharomyces cerevisiae. Genes Dev. 10, 2831–2848. Deane, C.M., Salwinski, L., Xenarios, I., Eisenberg, D., 2002. Protein interactions, two methods for assessment of the reliability of high throughput observations. Mol. Cell Proteomics 1, 349–356. Dietrich, F.S., et al., 2004. The Ashbya gossypii genome as a tool for mapping the ancient Saccharomyces cerevisiae genome. Science 304, 304–307. Fraser, H.B., Hirsh, A.E., Steinmetz, L.M., Scharfe, C., Feldman, M.W., 2002. Evolutionary rate in the protein interaction network. Science 296, 750–752. Fraser, H.B., Wall, D.P., Hirsh, A.E., 2003. A simple dependence between protein evolution rate and the number of protein–protein interactions. BMC Evol. Biol. 3, 11. Gavin, A.C., et al., 2002. Functional organization of the yeast proteome by systematic analysis of protein complexes. Nature 415, 141–147. Ge, H., Liu, Z., Church, G.M., Vidal, M., 2001. Correlation between transcriptome and interactome mapping data from Saccharomyces cerevisiae. Nat. Genet. 29, 482–486. Gu, Z., Steinmetz, L.M., Gu, X., Scharfe, C., Davis, R.W., Li, W.H., 2003. Role of duplicate genes in genetic robustness against null mutations. Nature 421, 63–66. Hirsh, A.E., Fraser, H.B., 2001. Protein dispensability and rate of evolution. Nature 411, 1046–1049. Ho, Y., et al., 2002. Systematic identification of protein complexes in Saccharomyces cerevisiae by mass spectrometry. Nature 415, 180–183. Ito, T., et al., 2000. Toward a protein–protein interaction map of the budding yeast, a comprehensive system to examine two-hybrid interactions in all possible combinations between the yeast proteins. Proc. Natl. Acad. Sci. U. S. A. 97, 1143–1147. Jeong, H., Mason, S.P., Barabasi, A.L., Oltvai, Z.N., 2001. Lethality and centrality in protein networks. Nature 411, 41–42. Jin, L., Nei, M., 1990. Limitations of the evolutionary parsimony method of phylogenetic analysis. Mol. Biol. Evol. 7, 82–102. Jordan, I.K., Rogozin, I.B., Wolf, Y.I., Koonin, E.V., 2002. Essential genes are more evolutionarily conserved than are nonessential genes in bacteria. Genome Res. 12, 962–968. Kellis, M., Patterson, N., Endrizzi, M., Birren, B., Lander, E.S., 2003. Sequencing and comparison of yeast species to identify genes and regulatory elements. Nature 423, 241–254.
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Differential evolutionary rates of duplicated genes in protein interaction network Takashi Makino, Yoshiyuki Suzuki, Takashi Gojobori ⁎ Center for Information Biology and DNA Data Bank of Japan, National Institute of Genetics, 1111 Yata, Mishima-shi, Shizuoka-ken 411-8540, Japan Received 21 February 2006; received in revised form 19 April 2006; accepted 23 June 2006 Available online 17 August 2006
Abstract In the network of protein–protein interactions (PPIs), a loss and gain of the partnering proteins can cause drastic changes of network formation during evolution. With the aim of examining the evolutionary effects of the loss and gain of the partnering proteins on PPIs, we examined a relationship between evolutionary rates and losses and/or gains of PPIs for duplicated gene pairs encoding proteins involved in the PPI network. For duplicated pairs, which provided us with a unique opportunity of making fair comparisons of the genes with the same initial condition, we found that the evolutionary rate of the protein with more PPI partners is much slower than that of the other with fewer PPI partners. Moreover, when the ratio of evolutionary rates (faster rate/slower rate) was computed for each of the duplicated pairs, the ratio for the duplicated pair sharing any PPI partners was significantly lower than that for the pair sharing no PPI partners. These results indicate that the duplicated gene pairs differentiate through the losses and/or gains of the PPI partners, resulting in a change in their evolutionary rates. In particular, we point out that the PPI losses for the duplicated gene products that are involved in the functional classes of ‘transcription’ and ‘protein fate’ have an impact on their evolutionary rates more than the PPI losses for others. © 2006 Elsevier B.V. All rights reserved. Keywords: Protein–protein interaction; Functional divergence; Gene duplication; Saccharomyces cerevisiae
1. Introduction Proteins interact with various molecules in order to manifest appropriate functions. In particular, protein–protein interactions (PPIs) are one of the most important components of biological networks. The amount of information about PPIs has grown rapidly due to the development of high-throughput two-hybrid systems (Uetz et al., 2000; Ito et al., 2000) and mass spectrometry of coimmunoprecipitated protein complexes (Gavin et al., 2002; Ho et al., 2002). It has become known that proteins with similar functions tend to interact with each other (Schwikowski et al., 2000; Ge et al., 2001). PPI networks have also been shown to consist of a small number of proteins with many PPI partners and a large number of proteins with a few partners (Jeong et al., 2001). The functional constraints of proteins involved in the PPI network are composed of several factors. The so-called fitness Abbreviations: PPIs, protein–protein interactions. ⁎ Corresponding author. Tel.: +81 55 981 6847; fax: +81 55 981 6848. E-mail address: [email protected] (T. Gojobori). 0378-1119/$ - see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.gene.2006.06.028
effects as well as the gene expression levels are typical factors, because they are known to be negatively correlated with the rate of amino acid substitution (Wilson et al., 1977; Hirsh and Fraser, 2001; Pal et al., 2001; Jordan et al., 2002). The number of PPIs for proteins is also an important factor for determining the evolutionary rate. It has been reported that the number of PPI partners for proteins is negatively correlated with the evolutionary rate (Fraser et al., 2002, 2003). Therefore, after gene duplication, the differentiation of PPIs through the PPI losses and/or PPI gains during evolution may affect the evolutionary rates of duplicated pair. For a duplicated gene pair, it has been shown that one copy usually has more PPI partners than the other (Wagner, 2002). Gene duplication is one of the major evolutionary mechanisms for generating novel genes (Ohno, 1970). After gene duplication, one of the pair may be redundant, such that functional constraint is relaxed to allow one or both to differentiate as long as the original function is retained as a whole. When a duplicated gene pair functionally differentiates, the evolutionary rate may be accelerated in one or both due to the relaxation of negative selection or the enhancement of positive selection (Li and
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Gojobori, 1983). In yeast, it has been proposed that the differentiation process is asymmetrical rather than symmetrical to minimize the risk of deleterious mutations (Wagner, 2002). It is therefore expected that the acceleration of evolutionary rate occurs mainly in one of the two copies after gene duplication. However, it is not yet known how the duplicated gene products affect their PPIs in evolution. After gene duplication, the accumulation of substitutions in the duplicated genes would be caused not only by the functional differentiation of gene products but also by the losses and/or gains of PPIs. Duplicated products often interact with the same proteins (Deane et al., 2002). One proposed model for the losses and/or gains of PPIs provides the reason why the products of a duplicated gene pair often share PPI partners (Wagner, 2001). In this model, although some duplicated pairs lose PPIs during the evolutionary process, many pairs retain some shared PPI partners. In a recent study, the magnitude of functional divergence for the duplicated gene pairs was measured by using the number of shared PPI partners between all pairs in the PPI networks (Baudot et al., 2004). To examine the relationship between the evolutionary rate and the functional differentiation of duplicated gene products, we focused on the shared PPI partners that were considered to reflect the functional differentiation of the duplicated gene products, because the products sharing PPI partners would not have largely diverged. The purpose of the present study is to understand how gene duplication influences the evolution of PPI networks. To study the relationship between gene duplication and the evolutionary rates of the gene products with PPI partners, we focused on the duplicated genes generated by genome duplication in Saccharomyces cerevisiae, which occurred about 100 million years ago (Wolfe and Shields, 1997; Kellis et al., 2004; Dietrich et al., 2004). We used the PPIs in S. cerevisiae that have well been documented based not only on hundreds of small-scale experiments but also on high-throughput methods. We set up and examined the hypothesis that the ratios of evolutionary rates (faster rate/slower rate) for the pairs sharing any PPI partners are lower than those for the pairs sharing no PPI partners. We then discuss the mechanisms of functional differentiation after gene duplication on the basis of the results obtained. 2. Materials and methods 2.1. Protein–protein interactions (PPIs) Among approximately 14,000 PPI data stored in DIP (the Database of Interacting Proteins, http://dip.doe-mbi.ucla.edu/), we used only the CORE data set, which contained 6205 PPIs, after the exclusion of proteins that interacted with themselves (self interactions). We further removed 231 PPIs from the CORE, because they were associated with the proteins derived from pseudogenes and erroneously predicted genes (Kellis et al., 2003). Thus, we used 5974 PPIs included in the CORE. The CORE contains the PPIs that satisfy one of the following three conditions. First, the interactions were determined by smallscale experiments. They are regarded as reliable PPIs, because they are derived from individual research papers. Second, each
interaction was identified by independent experiments at least twice. PPIs identified by high-throughput methods in the CORE have high correlation with respect to function and cellular location. Thus, the data quality in this feature is as reliable as that produced by small-scale experiments (Deane et al., 2002). Third, each interaction was confirmed by examining if paralogues interact with the same proteins or the paralogues themselves. If the proteins encoded by a duplicated gene pair share the same PPI partners, the PPIs between the duplicated pair and the shared partners are regarded as reliable. In fact, paralogues often interact with the same proteins (Deane et al., 2002). According to the third criterion, all of the shared PPIs between duplicated pairs in DIP should be included in the CORE. Scrutinizing approximately 14,000 PPIs stored in DIP, we identified 165 PPIs that satisfied the third criterion but were not included in the CORE. Therefore, we added these PPIs to the 5974 PPIs mentioned above, and a total of 6139 PPIs were used in this study. 2.2. Proteins encoded by duplicated genes in S. cerevisiae and their orthologues in Kluyveromyces waltii The genome duplication of S. cerevisiae took place about 100 million years ago (Wolfe and Shields, 1997). Four hundred and fifty duplicated gene pairs, each of which encodes a pair of proteins, were generated by genome duplication (Kellis et al., 2004). Removal of genes encoding ribosomal proteins is conventional in the study of duplicated genes, because they are known to have diverged after gene duplication so slowly that both copies tended to retain the original function (Pal et al., 2001; Gu et al., 2003). Therefore, we excluded 33 gene pairs encoding ribosomal proteins from this study. We further removed 153 pairs, because neither copy had a PPI partner. These left us with 261 pairs to analyze. We used the ORF sequences of the duplicated pairs to estimate the evolutionary rates (Saccharomyces Genome Database, http://www.yeastgenome.org/). To compare the evolutionary rates between a duplicated pair of S. cerevisiae, it was necessary to use an outgroup that was known to have diverged before the genome duplication. We used orthologues in K. waltii that were accurately determined by Kellis et al. (2004), because this species is known to have diverged from S. cerevisiae earlier than the genome duplication (Kellis et al., 2004). However, the speciation time does not appear to be much older than the genome duplication, because it has been reported that the genome duplication occurred in the S. cerevisiae lineage soon after speciation between K. waltii and S. cerevisiae (Wolfe, 2004). As a result, we obtained 261 sets of trios, each of which consisted of a duplicated pair from S. cerevisiae and one orthologue from K. waltii. 2.3. Comparison of evolutionary rates between duplicated gene products For each set of the 261 trios, a multiple alignment of amino acid sequences was made using CLUSTAL W (version 1.81; Thompson et al., 1994). Four sets of trios were removed from
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the study, because the sequences were too diverged to be aligned. To compare the rates of amino acid substitution between the duplicated gene products of S. cerevisiae, we estimated the number of amino acid substitutions after the genome duplication by constructing a phylogenetic tree for each trio. Each tree was constructed by the neighbor-joining method (Saitou and Nei, 1987) using the number of amino acid substitutions estimated by Kimura's method (1983), which were implemented in PHYLIP (version 3.573c). Note that Kimura's distance is known to be reliable as long as the proportion of difference (p) between amino acid sequences compared is smaller than 0.7 (Nei, 1987). For our data, multiple hits are considered to be corrected appropriately, because p rarely exceeded 0.7 (Supplementary Fig. 2). Three sets of trios were further removed from the analysis at this stage because the sum of two distances among the trio was shorter than the remaining one. Therefore, we used 254 sets of trios for the comparison of evolutionary rates. 2.4. Relative-rate test We compared several methods to conduct the relative-rate test between a pair of duplicated gene products for each of the 254 trios. For using a model-based relative-rate test, there were some problems. It required a substitution model (Wu and Li, 1985). Moreover, the substitution rates among the sites in a protein may vary (Jin and Nei, 1990). Therefore, we conducted the relative-rate test using the one degree of freedom method (Tajima, 1993), which was free from any model. 3. Results and discussion 3.1. Losses of PPIs for proteins encoded by duplicated genes Soon after gene duplication, the protein encoded by one copy should interact with the same set of proteins as the other, because these proteins are identical. It has been proposed that PPI partners of proteins encoded by duplicated genes change
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through PPI losses or PPI gains during evolution (Wagner, 2001). For duplicated gene pairs, it has been shown that one copy usually has more PPI partners than the other (Wagner, 2002). However, it was unclear which of the two mechanisms, namely PPI losses and PPI gains, is the major force of the evolution of PPIs. Proteins under strong functional constraints would be hard to change their PPI partners during evolution, because they are highly conserved. The PPI losses of the proteins may accelerate their evolutionary rates, because it has been reported that the evolutionary rate is negatively correlated with the number of PPIs (Fraser et al., 2002, 2003). If the PPI losses occur more often than the PPI gains for a duplicated pair, the protein encoded by one copy evolving at a slower rate would have more PPI partners than the other. To examine this possibility, we used 216 duplicated pairs, excluding 38 pairs where the pair had the same number of PPIs from the 254 pairs (we showed the statistics regarding the distribution of the number of PPIs for each duplicated pair in Supplementary Fig. 1). For each pair of gene products, we examined whether the protein with more PPI partners evolved more slowly than the other with less partners. We found that a protein with more PPI partners evolved at a slower rate in 134 (62%) out of the 216 pairs examined, which was significantly greater than expected (50%) under the null hypothesis of random association between the number of PPI partners and the evolutionary rate (P b 0.001; sign-test). Similar results were obtained when we focused only on the pairs with significant differences in the evolutionary rates between duplicated genes (Tajima, 1993). Out of the 254 duplicated gene pairs, 143 pairs showed statistically significant differences in the evolutionary rate. We analyzed 123 duplicated pairs, excluding 20 pairs where the pair had the same number of PPIs. It was found that a protein with more PPI partners evolved at a slower rate in 81 (66%) out of the 123 pairs examined, which was actually a 30% excess compared with the random expectation (50%), and highly significant (P b 0.001). For a duplicated pair of gene products, we showed that the one with more PPI partners evolves at a slower rate than the
Fig. 1. Schematic representations of F1, S1, F2, and S2. Closed circles and open circles respectively mean proteins encoded by duplicated gene pair sharing no PPI and sharing PPIs. F (light gray arrow) and S (gray arrow) respectively mean faster rate and slower rate, respectively, and subscripts 1 and 2 refer to the cases of sharing no PPI and sharing PPIs for duplicated pairs, respectively. The ratio of evolutionary rates for duplicated pairs after gene duplication was estimated by a faster evolutionary rate of one copy/a slower rate of another copy (F1/S1; F2/S2).
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T. Makino et al. / Gene 385 (2006) 57–63 Table 2 Functional classifications in the MIPS database a Functional class Metabolism Energy Cell cycle and DNA processing Transcription Protein synthesis Protein fate (folding, modification, destination) Cellular transport, transport facilitation and transport routes Cellular communication/signal transduction mechanism Cell rescue, defense and virulence Interaction with the cellular environment a
Modified from http://mips.gsf.de/genre/proj/yeast/index.jsp/.
genes under the same initial condition, we found that the protein encoded by one copy evolving at a slower rate had more PPI partners than the other copy. The results indicated that the PPI losses have occurred more often than the PPI gains for a copy evolving at a faster rate, under the assumption that PPIs of a copy evolving at a slower rate are conservative in the evolutionary process. 3.2. Functional divergence through changes in PPIs
Fig. 2. (a) Ratios of evolutionary rates for duplicated pairs sharing PPI partners and sharing no PPI partners. Open bars indicate duplicated pairs interacting to one another or sharing PPI partners, while closed bars indicate duplicated pairs sharing no PPI partners. (b) Only the duplicated pairs showing statistically significant differences in evolutionary rate were used.
other with less PPI partners. Although it has been shown that the evolutionary rate of the proteins has a negative correlation with the number of PPI partners (Fraser et al., 2002, 2003), these authors ignored noises such as differences in structural and functional features, and did not deal with functional divergence through the change of PPIs. For duplicated pairs that provided us with a unique opportunity of making fair comparisons of the Table 1 Results of the relative-rate test for duplicated pairs sharing PPI partners and sharing no PPI partners #Duplicated pairs #Duplicated pairs sharing PPI partners sharing no PPI partners Significant difference of rates 65 No significant difference 65 of rates
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After gene duplication, there are at least two possible pathways of PPI divergence for the proteins encoded by a duplicated gene pair. First, one of the proteins encoded by a duplicated pair keeps all the PPI partners, whereas the other loses them. The evolutionary rate of the former protein would be slower than that of the latter, because the former has to maintain the original function while the latter is free from it. In other words, they are likely to evolve at different rates. Second, both proteins share some of the PPI partners. In this case, both proteins may still have similar functions, and the sequences may not change as drastically as in the first case. The evolutionary rates of the gene products sharing PPI partners may not significantly differ from each other. Therefore, if the duplicated gene products lose the shared PPI partners, the ratio of evolutionary rates for the pair (faster rate/slower rate) may be higher than that for functionally similar pairs. To test this hypothesis, we examined whether F1/S1 were higher than F2/S2, where F and S denote faster rate and slower rate, respectively, and subscripts 1 and 2 refer to the cases of sharing no PPIs and sharing PPIs, respectively (Fig. 1). Here we defined duplicated pairs sharing PPIs as the pairs sharing at least one PPI partner. There were 124 duplicated pairs sharing no PPI partners and 130 duplicated pairs interacting to one another or sharing PPI partners. It was then found that F1/S1 was significantly higher than F2/S2 (Mann–Whitney U-test, P b 0.001; Fig. 2a). Even when we focused only on 143 duplicated pairs for which the evolutionary rates between the two copies were significantly different, F1/S1 for 78 pairs were significantly higher than F2/S2 for 65 pairs (Mann–Whitney U-test, P b 0.01; Fig. 2b). In addition, the proportion of duplicated pairs with significant differences in evolutionary rate among the pairs sharing no PPI partners was significantly greater than that
T. Makino et al. / Gene 385 (2006) 57–63 Table 3a Results of the relative-rate test for duplicated pairs having PPI partners and sharing no PPI partners in functional class ‘transcription’ #Duplicated pairs #Duplicated pairs sharing PPI partners sharing no PPI partners Significant difference of rates 10 No significant difference 13 of rates
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Table 3c Results of the relative-rate test for duplicated pairs having PPI partners and sharing no PPI partners in the functional classes of ‘cellular communication/ signal transduction mechanism’, ‘cell rescue, defense and virulence’, and ‘interaction with cellular environment’ #Duplicated pairs #Duplicated pairs sharing PPI partners sharing no PPI partners Significant difference of rates 22 No significant difference 20 of rates
among the pairs sharing PPI partners (chi-square test for independence, P b 0.05; Table 1). Although we showed that PPI divergence is reflected in large ratios of the evolutionary rates of duplicated pairs, one might argue that the PPI divergence should be rather reflected in the evolutionary distance between a duplicated pair. When the evolutionary distance between a duplicated pair is very large because of the rapid evolutionary rates, they may not share PPI partners regardless of the ratio of evolutionary rates. Therefore, we examined whether the evolutionary distance between the duplicated pair sharing PPI partners was smaller than that between those sharing no PPI partners. However, the distances between the 96 pairs sharing PPI partners were not significantly shorter than those between the 67 pairs sharing no PPI partners. In addition, even when we removed 91 duplicated pairs with the evolutionary distance of N1.0 and compared F1/S1 with F2/S2, the former was still significantly higher than the latter (Mann– Whitney U-test, P b 0.05). These results strongly suggest that the change in PPI partners is primarily reflected in large ratios of the evolutionary rates for a duplicated pair. In addition, we also examined the relationship between the difference in the number of shared PPIs and the ratio of evolutionary rates. However, we did not find any statistically significant correlations between them. This may be because the magnitude of the difference in the number of PPIs for duplicated pairs is affected by the number of PPIs of a protein encoded by an ancient gene before gene duplication. Actually, it was difficult to investigate the gradual change in the number of shared PPIs for duplicated pairs during evolution, because the number of PPIs of the proteins encoded by ancient genes was unknown. For a duplicated gene pair, if the protein encoded by one copy evolving at a faster rate has not been silenced during evolution, it may have lost its PPI partners and had a chance of finding a new PPI partner under weak or no functional constraints. On the other hand, the PPIs for the protein encoded by one copy evolving at a slower rate may be conservative with relatively strong functional constraints. For duplicated pairs, the
Table 3b Result of the relative-rate test for duplicated pairs having PPI partners and sharing no PPI partners in functional class ‘protein fate’ #Duplicated pairs #Duplicated pairs sharing PPI partners sharing no PPI partners Significant difference of rates 2 No significant difference 10 of rates
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11 5
11 5
gene product evolving at a faster rate will lose the shared PPI partners more frequently than the other. This implies that a pair of proteins encoded by a duplicated gene pair having few shared PPI partners evolves at different rates. In fact, the present study indicates that pairs sharing no PPI partners show a larger ratio of evolutionary rates than those sharing PPI partners, although it has been reported that a simple relationship between sequence divergence and their functional divergence revealed by the PPI network analysis could not be established (Baudot et al., 2004). When a duplicated pair shares no PPI partners, it is possible that they interact with different PPI partners with different functions. This means that gene duplication will lead to the functional differentiation of the duplicated gene products through the PPI losses and/or PPI gains, which will then cause a change in their evolutionary rates.
Fig. 3. Examples for the pairs of proteins encoded by duplicated gene pairs and their PPI partners. The circles and lines represent proteins and PPIs, respectively. The circles in gray are PPI partners. (a) The open circles represent proteins encoded by the duplicated gene pair (YDR480W and YPL049C), which are down-regulators of invasive growth and mating, respectively. (b) The closed circles represent proteins encoded by the duplicated gene pair (YNR023W and YCR052W), which are a subunit of SWI/SNF global transcription activator complex and a subunit of the RSC chromatin-remodeling complex, respectively.
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3.3. Tendency of PPI divergence for duplicated pair in different functional classes For investigating the functions of duplicated gene products, we used functional classification established by the MIPS database (Mewes et al., 2002; Table 2). In the functional class of ‘transcription’, there were significantly many duplicated pairs sharing no PPI partners and having a significant difference in evolutionary rates (chi-square test for independence, P b 0.05; Table 3a). There were also statistically significant differences in the rate between the two copies in the functional class of ‘protein fate’ (chi-square test for independence, P b 0.01; Table 3b). These results indicate that the PPIs of the proteins included in these functional classes do not tend to be conserved in the evolutionary process, resulting in a change in their evolutionary rates. Although the other functional classes showed no significant difference in ratio of evolutionary rates between duplicated pairs sharing PPI partners and those sharing no PPI partners, we found that there were relatively many duplicated pairs sharing PPI partners in the functional classes of ‘cellular communication/signal transduction mechanism’, ‘cell rescue, defense and virulence’, and ‘interaction with cellular environment’ (Table 3c). PPIs of the proteins included in these functional classes are likely to be conserved during the evolutionary process. The results showed that the impact of the PPI losses for the duplicated gene products on their evolutionary rates depends on their functions. We found many cases of duplicated gene pairs sharing PPI partners in the functional classes such as ‘cellular communication/signal transduction mechanism’, ‘cell rescue, defense and virulence’, and ‘interaction with cellular environment’. For example, YDR480W and YPL049C (a duplicated pair in ‘interaction with cellular environment’) share all PPI partners (Fig. 3a), and have no significant difference in evolutionary rate between them. It has also been shown that the pair shares a role in negatively regulating the invasive growth pathway (Cook et al., 1996). After gene duplication, the pair has shared the PPI partners and not diverged their functions in the evolutionary process, resulting in keeping similar evolutionary rates. We also found many cases of duplicated gene pairs sharing no PPI partners in the functional classes such as ‘transcription’ and ‘protein fate’. For example, YNR023W and YCR052W (a duplicated pair in ‘transcription’) do not share PPI partners, and have a significant difference in evolutionary rate. In addition, they are subunits in different protein complexes. YNR023W is a subunit of SWI/SNF global transcription activator complex, and YCR052W is a subunit of the RSC chromatin-remodeling complex (Fig. 3b; Cairns et al., 1996). We consider that the significant difference in evolutionary rate between them is caused by drastic changes in the PPI partners during evolution. Although the proteins encoded by these duplicated gene pairs should have interacted with the same PPI partners immediately after the gene duplication, one of the copies may have subsequently changed its PPI partners and diverged its functions. It is thus suggested that YCR052W, which evolves at a faster rate than YNR023W, obtained novel functions by changing PPI partners. Thus, the evolutionary comparison of the PPI partners
of one copy in a duplicated pair with those of the other is important for understanding their functional differentiations through PPI network divergence. Acknowledgements We are grateful to Yoshio Tateno, Kazuho Ikeo, Matthew Webster, two anonymous reviewers and all the members of the DNA Analysis Laboratory for valuable comments and discussion. This research was supported by Grants-in-Aid for Creative Basic Research from the Ministry of Education, Culture, Sports, Science and Technology, Japan (to T.G.). Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.gene.2006.06.028. References Baudot, A., Jacq, B., Brun, C., 2004. A scale of functional divergence for yeast duplicated genes revealed from analysis of the protein–protein interaction network. Genome Biol. 5, R76. Cairns, B.R., et al., 1996. RSC, an essential, abundant chromatin-remodeling complex. Cell 87, 1249–1260. Cook, J.G., Bardwell, L., Kron, S.J., Thorner, J., 1996. Two novel targets of the MAP kinase Kss1 are negative regulators of invasive growth in the yeast Saccharomyces cerevisiae. Genes Dev. 10, 2831–2848. Deane, C.M., Salwinski, L., Xenarios, I., Eisenberg, D., 2002. Protein interactions, two methods for assessment of the reliability of high throughput observations. Mol. Cell Proteomics 1, 349–356. Dietrich, F.S., et al., 2004. The Ashbya gossypii genome as a tool for mapping the ancient Saccharomyces cerevisiae genome. Science 304, 304–307. Fraser, H.B., Hirsh, A.E., Steinmetz, L.M., Scharfe, C., Feldman, M.W., 2002. Evolutionary rate in the protein interaction network. Science 296, 750–752. Fraser, H.B., Wall, D.P., Hirsh, A.E., 2003. A simple dependence between protein evolution rate and the number of protein–protein interactions. BMC Evol. Biol. 3, 11. Gavin, A.C., et al., 2002. Functional organization of the yeast proteome by systematic analysis of protein complexes. Nature 415, 141–147. Ge, H., Liu, Z., Church, G.M., Vidal, M., 2001. Correlation between transcriptome and interactome mapping data from Saccharomyces cerevisiae. Nat. Genet. 29, 482–486. Gu, Z., Steinmetz, L.M., Gu, X., Scharfe, C., Davis, R.W., Li, W.H., 2003. Role of duplicate genes in genetic robustness against null mutations. Nature 421, 63–66. Hirsh, A.E., Fraser, H.B., 2001. Protein dispensability and rate of evolution. Nature 411, 1046–1049. Ho, Y., et al., 2002. Systematic identification of protein complexes in Saccharomyces cerevisiae by mass spectrometry. Nature 415, 180–183. Ito, T., et al., 2000. Toward a protein–protein interaction map of the budding yeast, a comprehensive system to examine two-hybrid interactions in all possible combinations between the yeast proteins. Proc. Natl. Acad. Sci. U. S. A. 97, 1143–1147. Jeong, H., Mason, S.P., Barabasi, A.L., Oltvai, Z.N., 2001. Lethality and centrality in protein networks. Nature 411, 41–42. Jin, L., Nei, M., 1990. Limitations of the evolutionary parsimony method of phylogenetic analysis. Mol. Biol. Evol. 7, 82–102. Jordan, I.K., Rogozin, I.B., Wolf, Y.I., Koonin, E.V., 2002. Essential genes are more evolutionarily conserved than are nonessential genes in bacteria. Genome Res. 12, 962–968. Kellis, M., Patterson, N., Endrizzi, M., Birren, B., Lander, E.S., 2003. Sequencing and comparison of yeast species to identify genes and regulatory elements. Nature 423, 241–254.
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