Modular organization in the reductive evolution of protein-protein interaction networks
Genome Biology volume 8, Article number: R94 (2007)
The variation in the sizes of the genomes of distinct life forms remains somewhat puzzling. The organization of proteins into domains and the different mechanisms that regulate gene expression are two factors that potentially increase the capacity of genomes to create more complex systems. High-throughput protein interaction data now make it possible to examine the additional complexity generated by the way that protein interactions are organized.
We have studied the reduction in genome size of Buchnera compared to its close relative Escherichia coli. In this well defined evolutionary scenario, we found that among all the properties of the protein interaction networks, it is the organization of networks into modules that seems to be directly related to the evolutionary process of genome reduction.
In Buchnera, the apparently non-random reduction of the modular structure of the networks and the retention of essential characteristics of the interaction network indicate that the roles of proteins within the interaction network are important in the reductive process.
Bacterial endosymbionts of insects, such as Buchnera aphidicola [1, 2], Blochmannia floridanus  and Wigglesworthia glossinidia , are paradigms of reductive evolution. These bacteria live in a stable and isolated environment, the bacteriocyte of insects, where the host provides most of their nutritional requirements. As a consequence, the genomes of these bacteria have undergone a process of reduction, losing around 90% of their ancestral genes. These endosymbionts also fail to acquire new genes due to their incapacity to incorporate DNA via lateral gene transfer and their isolated environment. Nevertheless, although their genomes represent a subset of the genome of their ancestors, these gamma-proteobacteria remain closely related to Escherichia coli (98% of the genes in Buchnera have clear orthologues in E. coli). Accordingly, the process of genome shrinkage that these species have undergone has been well documented in terms of the evolution of the corresponding protein families [1, 2].
Recent research indicates that the capacity of an organism for adaptation depends not only on the properties of its individual molecular components, but also on the structure and organization of its underlying network of molecular interactions. Indeed, it was recently proposed that the modular organization of the network of interactions is necessary to adapt to changing environments . In such a modular system, the compartmentalization of a set of interactions that are both closely interconnected and remain weakly connected to other components in the artificial environment increases. Accordingly, the organization into so-called modules is favored by constant changes in environmental conditions, highlighting the direct causal relationship between such changes and the increase in network modularity. Nevertheless, this proposal awaits a direct assessment in a real biological system.
Studies on the organization and properties of protein networks have flourished recently thanks to data from high-throughput experiments, for example, two-hybrid screens, pull-down experiments and ChIP-on-chip studies [6–10]. Despite limitations in terms of the extent and quality of the datasets, the results produced have been fundamental in enabling the first studies of network structure to be carried out [7, 11]. Such studies have involved the comparison of networks from different origins  and the construction of the first models of network behavior and evolution [13, 14].
Taking advantage of the two recently published high-throughput protein interaction maps of E. coli [9, 15], we have performed a study in which we focused on the reductive evolution of the Buchnera genome. The comparison between the E. coli and Buchnera interaction networks was based on the assumed low rate of protein interaction turnover  and the weak probability that new interactions would be generated in the restricted conditions in which Buchnera lives. Accordingly, it can be assumed that when proteins are conserved between E. coli and Buchnera, the protein interactions are also likely to be maintained . Therefore, the direct relationship between the genomes, the clear conservation of proteins and the probable similarity of their interactions provides a perfect scenario to assess the consequences of adaptation to a stable and nutrient-rich environment.
E. coli is a free-living bacteria known to be capable of adapting to very different environments [18–20]. In contrast, Buchnera is an endosymbiotic bacteria living in a very stable medium. As a result, we would expect the E. coli network to be more modular than that of Buchnera. Hence, reductive evolution might be responsible not only for decreasing the gene repertoire of Buchnera, but also for reducing its network modularity. This hypothesis can be tested by comparing the organization of the protein-protein interaction networks of these two species.
Results and discussion
Modular structure of the E. colinetwork
Modules are set of components (proteins) with a clear imbalance in favor of internal versus external connections. Therefore, the modularity of a network can be quantified by comparing the number of connections within and between modules. Consequently, the main problem when defining modules is the search for the optimal division of the network that maximizes the ratio between intra- and inter-module connectivities. Several algorithms have been proposed to carry out the task of decomposing networks into their modular components [21–24]. We have used two recently proposed algorithms [23, 24] that have been shown to produce optimal decomposition of biological networks. Since both algorithms are based on different approaches, and two different maps of protein-protein interactions of E. coli are available [9, 15], the validity of the conclusions is relatively independent of the method and the data source. It is important to realize that the values of the modularity coefficients have to be normalized/corrected with respect to the modularity expected in equivalent random networks of the same connectivity, thereby eliminating the effect that the pattern of connections in the network could have on the calculation of its modularity (see Materials and methods).
The results of analyzing the structure of the E. coli network show that it is most modular at any level, irrespective of the clustering methods used (see Table S3 in Additional data file 1 for descriptions and results obtained using other clustering approaches for determining modularity). The optimal decompositions render between 10 and 15 modules (Table 1), most of them significant from a functional point of view (see Materials and methods). Some of the modules are quite homogeneous and contain easily discernible functions, that is, protein synthesis (including ribosomal proteins), transcription (RNA polymerase), cell division, DNA synthesis (DNA polymerase), or DNA maintenance, corresponding well to the empirical analysis of the original dataset established by Butland et al. . These modules account for more than half of the modularity in the network (Table S1 in Additional data file 1). Other modules contribute less to the global modularity and are composed of proteins with more diverse functions. The overall structure of the network indicates the existence of a central core that is clearly organized into modules of protein interactions, while many other functions or activities associated with this core display less modular structure.
The potential Buchnera protein interaction network was obtained by maintaining the connections between the orthologous proteins in E. coli. The modular decomposition of the resulting network shows that the Buchnera network was always significantly less modular than that of E. coli (Table 1). The decrease in the modularity coefficient implies that the network obtained for Buchnera is much harder to separate into isolated components than that of E. coli. Therefore, we concluded that the process of reducing the genome size (reductive evolution) creates a less compartmentalized network with a smaller degree of modularity.
An alternative approach is to study the process of module reduction maintaining the modular structure obtained for E. coli but deleting the proteins that do not have orthologues in Buchnera. In this way, the reduction of the modules originally defined in E. coli can be assessed. We found that the ensuing 'constrained' decomposition of the Buchnera network is also less modular than that of E. coli. Indeed, the modularity observed is similar to that observed when the Buchnera network was decomposed independently (Table 1). Furthermore, with the exception of the module containing ribosomal proteins, the modules in the 'constrained' network are significantly smaller than those in E. coli. The deletion involves between 70% and 91% of the nodes and, interestingly, the set of conserved nodes often consists of those involved in the connection between modules (Figure 1).
Nevertheless, the coefficients are low in all cases. In E. coli, they are around 0.1, indicating little modularity (high modularity is achieved when the coefficient reaches values around 0.3). The coefficients are close to zero in all Buchnera networks, indicating that modularity has been almost completely lost in these networks.
The role of the nodes in the reduction of the modular structure of the network
The connections between modules in the E. coli network are dominated by non-hub connectors, that is, nodes with an average number of links within their module but that are well connected to other modules . These nodes account for more than 80% of the connections between modules. The remaining connections are made by connector hubs with strong links both within and between modules but that are, in turn, weakly connected between themselves (examples of connector hubs are peptidyl-prolyl cis/trans isomerase tig and pyruvate dehydrogenase aceE). This is characteristic of a feature known as dissortativity , which has been documented in several other biological networks. There is extensive communication between modules in the E. coli network and this is mainly based on the links provided by non-hub connectors.
In the constrained reduced Buchnera network, it is apparent that the number of peripheral nodes has diminished. While there was less than average loss of non-hub connectors, connector hubs were almost completely preserved (Figure 2). Therefore, connector hubs appear to create a highly preserved backbone of interactions. This emphasizes the crucial importance of connector hubs in maintaining the integrity of the protein network, in contrast to the findings from studies of metabolic networks .
The reduction of network modularity and of the overall properties of the network
Reduction of modularity affects certain topological aspects of the network. For simplicity, we restrict our analysis to the results for the Butland dataset, since the results for the Arifuzzaman  dataset are very similar. The analysis of connectivity shows that the E. coli and Buchnera networks follow a power-law distribution with exponents (γ) of 2.25 for E. coli and 2.03 for Buchnera. The smaller exponent in Buchnera indicates that hubs are more prevalent in the network, since they are in contact with a larger proportion of nodes. This highlights the relevance of connector hubs, which produce a more compact network in Buchnera, as reflected by the average number of links per node (6.07 link per node in Buchnera versus 4.16 in E. coli) and the smaller diameter of the Buchnera network (2.821 versus 3.607 for E. coli). Both networks are almost completely connected, which means that there are very few nodes in islands not linked to the main component. In both networks, isolated nodes constitute just 2% of the total number of nodes. Additionally, the length of the paths crossing the network remains unaltered, and only 60 of a possible 37,408 paths were longer in Buchnera than in E. coli, with a difference of just one node. Therefore, rather than fragmenting the network, the removal of nodes and links in the Buchnera network maintains the global topology of the network, preserving the main interaction backbone. The preferential deletion of connections between peripheral nodes that lie outside of the core of the network creates an apparent enrichment of densely connected motifs in Buchnera, particularly when the relative proportions are considered (Table S1 in Additional data file 1).
When nodes were randomly removed from the E. coli network until it reached a size equivalent to that of Buchnera, the organization of the network was completely lost. The resulting network is fragmented into a myriad of small components (islands), each with few isolated nodes. This is an important indication of how node deletion during reductive evolution has been accomplished in a controlled manner that preserves the network organization and the cross-talk between the remaining processes.
We compare the structure of two independent sets of experimentally derived interactions for E. coli with the deduced structure of interactions for the closely related Buchnera genome. Thus, the reductive evolution followed by Buchnera, whereby more than 90% of the ancestral genes have been lost, is correlated with the loss of modularity of the protein interaction network. Nevertheless, the rest of the characteristics of the network in Buchnera essentially remain unchanged. These observations provide an initial model to understand reductive evolution, adaptation to environments and network organization. As in previous analyses of network structure, it is clear that, in this early phase, the models will benefit greatly from additional information from other genomes, and from an overall improvement in the quality of the proteomic experiments. Nevertheless, even bearing these limitations in mind, it is possible to see how the reduced modularity in the Buchnera genome is caused by the partial deletion of nodes in regions that are connected to dense clusters of essential functions in the E. coli protein interaction network. This is demonstrated by measuring the modularity in the reduced network. In contrast to what would be expected if the preferentially deleted genes were those participating in a non-modular part of the E. coli network, the modularity decreased with respect to the E. coli network.
The E. coli network is apparently composed of a modular core and a mostly non-modular peripheral region. This could imply that, at this level, modular structures are not determinant for the evolution of the network. Reduction of modularity is not achieved by the removal of entire modules (which could even produce an increase in the modularity coefficient), but rather by selective deletion of nodes in the modular parts of the network (Figure 3). In other words, the process of genome reduction apparently involves deleting peripheral regions of the network and the selective loss of proteins forming part of densely packed clusters that are separated into modules. However, it affects the proteins directly implicated in maintaining the connections between modules to a much smaller extent (Figure 2). The result is a very compact network with a smaller diameter, a conserved backbone and an increase in the proportion of densely connected motifs, as well as the preservation of characteristics such as path length and network topology. The way to maintain or increase modularity in reduced networks would be to remove connections between modules and, therefore, communication between processes, which could be highly deleterious. Our conclusion is that the loss of modularity in Buchnera networks seems to be mainly related to the conservation of the network backbone, rather than resulting from the loss of adaptability to environmental conditions.
These results might be important in the context of the evolutionary implications of network structure. It has been suggested that the organization of biological networks (interaction and control networks) is a direct product of the simple process of gene duplication and deletion, and that it is not directly subjected to natural selection . The apparently non-random reduction of the modular structure of the networks and the retention of essential characteristics of the interaction network indicate that the roles of proteins within the interaction network are important in the reductive process. Accordingly, the importance of the roles of the proteins must be taken into consideration when discussing the effect of the natural selection on the organization of protein networks.
Materials and methods
The first study  is based on yeast-based tandem affinity purification (TAP) adapted to E. coli. In this procedure, 1,000 E. coli open reading frames were tagged (22% of the genome) and their interactions with other proteins within this set were determined. It was possible to determine 5,254 protein-protein interactions, involving 1,264 proteins (Butland dataset). To our knowledge, this was the first set of E. coli protein-protein interaction data determined by high-throughput procedures.
The second study  was based on producing His-tagged bait proteins; after co-purifying the interacting bait and prey proteins on a Ni2+-NTA column, they were identified by mass spectrometry. There were 4,339 E. coli proteins tested, for which 11,511 interactions were determined. The authors provided a reliable set of 8,893 of these interactions, involving 2,821 proteins, which were reproducible in the original study (Arifuzzaman dataset). The reliable set was the one used by us in this study.
While both datasets share 983 proteins, only 168 interactions are present in both sources, a situation similar to that observed in yeast .
For E. coli proteins, orthologues in B. aphidicola strain APS (RefSeq NC_002528) were identified by perfoming BLASTP homology searches. To correctly identify orthologues, both proteins must fulfill the following criteria: one is the best hit of the other (best bi-directional hits); the BLASTP E-value must be above 1e-15; and the alignment must span at least 80% of the residues in both proteins. Considering complete genomes, we were able to identify E. coli orthologues for 98% of Buchnera proteins, while around 90% of E. coli protein-coding genes have been deleted from the Buchnera genome (E. coli strain K-12 contains 4,243 genes; Buchnera has 564 genes). For the two sources of data (1,264 E. coli proteins in the Butland dataset and 2,821 in the Arifuzzaman dataset), we identified 278 and 260 orthologues in the proteome of Buchnera, respectively.
The protein-protein interaction network in Buchnera was generated by mapping E. coli interactions between conserved proteins in Buchnera. The removal of nodes (proteins) implies the removal of all links attached to them. This creates a network of 1,638 interaction pairs for the Butland dataset and 549 for the Arifuzzaman dataset, implying that the latter is enriched in interactions between proteins that are not conserved in Buchnera.
We also created a third network based on data from the STRING database [26, 27]. STRING contains known and inferred relationships between E. coli proteins derived using diverse methods. The version of STRING used in this work involves 3,868 proteins implicated in 33,733 relationships, and it does not include the data from the other two sources. Thus, it comprises an independent set of interactions that can be used to validate the modular decomposition of the networks.
For the networks, the node degree was measured as the number of links for each node. Links were non-directional and corresponded to protein-protein interactions. Protein motifs were identified as described previously . The path length (l) between all pairs of nodes was calculated using a standard Dijstra algorithm.
A module is defined as a part of the network with abundant connections between the nodes within it, and less connected to nodes outside the module. The ratio between these two measures (connections within the module and with other modules) defines the modularity coefficient Q. The modularity coefficient was calculated as the fraction of edges in the network that connect the nodes in a module minus the expected value of the same quantity in a network, with the same assignment of nodes in modules but with random connections between nodes [5, 22, 23]:
where K is the number of modules, L is the number of edges in the network, l s is the number of edges between nodes in modules, and d5 is the sum of the degrees of the nodes in module s. Since modularity is possibly affected by the different size or connectivity of the networks, it is advisable to normalize this measure with respect to the modularity of random networks with the same connectivity. These random networks are generated by swapping the connections between pairs of nodes. For instance, if the real network contains the interactions A-B and C-D, the randomized network will contain A-D and B-C. In this way, the random network maintains node degrees and connectivity.
Several algorithms have been proposed to extract modules from networks. To test the validity of our conclusions, we used two different methods to calculate modules and modularity coefficients. The algorithm of Guimerá and Nunes-Amaral  is based on a simulated annealing procedure, and it has been successfully used to decompose metabolic networks. Newman's algorithm  is based on the spectral decomposition of the eigenvectors of a modularity matrix derived from the interactions between nodes. Both methods claim to obtain optimal decomposition of the networks, and the results using both algorithms are very similar (Table 1). Guimerá's algorithm achieves slightly higher modularities, while Newman's algorithm is considerably faster, especially when dealing with big networks. The analysis of the resulting modules shows that both decompositions are similar, with 70% of the interactions belonging to the same modules. The normalized modularity coefficients are very close, regardless of the algorithm or the data source used, indicating that they are robust and not influenced by such factors.
Since we wanted to inspect the conservation of modularity when the network is reduced, the modularity of Buchnera's networks was calculated either by generating a new modular decomposition for Buchnera, or using the same modular decomposition obtained for E. coli such that the modules were maintained while the nodes and interactions not present in Buchnera were removed. In this way, we are able to study the way in which original modules are reduced.
To check the quality and functional relevance of modules, we used data from the STRING database [26, 27]. Modules with functional significance would be expected to be enriched in these interactions. Therefore, we calculated the total number of interactions per pair of proteins in STRING and, accordingly, the number of interactions per pair that would be expected within each of the modules in the network based on the size of the module. We consider that the module is validated if it is significantly enriched in STRING interactions (p value < 0.1).
The networks were plotted with the Cytoscape software . The evaluation of functions over-represented in each of the modules (using Gene Ontology  'biological process' category) was performed using the BiNGO plug-in 
Additional data files
The following additional data are available with the online version of this paper. Additional data file 1 includes supplementary tables: Table S1 lists the composition of the main modules in E. coli, for the modular decomposition of the Butland dataset using Guimerá's algorithm; Table S2 shows the different motifs with three or four nodes found in the real networks and randomized networks; Table S3 shows the results of the modular decomposition of the Butland dataset by means of a k-means clustering algorithm, as an additional confirmation of the validity of the results; Table S4 lists the main conserved hubs in Buchnera, and their functions in the Butland dataset. Additional data file 2 shows the relationship between the connectivity of the nodes and their deletion in Buchnera's network (Butland dataset), and the probability of the deletion of nodes as a function of the probable number of connections. Additional data file 3 illustrates three examples of hub deletion in Buchnera.
van Ham RC, Kamerbeek J, Palacios C, Rausell C, Abascal F, Bastolla U, Fernandez JM, Jimenez L, Postigo M, Silva FJ, et al: Reductive genome evolution in Buchnera aphidicola. Proc Natl Acad Sci USA. 2003, 100: 581-586. 10.1073/pnas.0235981100.
Shigenobu S, Watanabe H, Hattori M, Sakaki Y, Ishikawa H: Genome sequence of the endocellular bacterial symbiont of aphids Buchnera sp. APS. Nature. 2000, 407: 81-86. 10.1038/35024074.
Gil R, Silva FJ, Zientz E, Delmotte F, Gonzalez-Candelas F, Latorre A, Rausell C, Kamerbeek J, Gadau J, Holldobler B, et al: The genome sequence of Blochmannia floridanus : comparative analysis of reduced genomes. Proc Natl Acad Sci USA. 2003, 100: 9388-9393. 10.1073/pnas.1533499100.
Akman L, Yamashita A, Watanabe H, Oshima K, Shiba T, Hattori M, Aksoy S: Genome sequence of the endocellular obligate symbiont of tsetse flies, Wigglesworthia glossinidia. Nat Genet. 2002, 32: 402-407. 10.1038/ng986.
Kashtan N, Alon U: Spontaneous evolution of modularity and network motifs. Proc Natl Acad Sci USA. 2005, 102: 13773-13778. 10.1073/pnas.0503610102.
Ito T, Chiba T, Ozawa R, Yoshida M, Hattori M, Sakaki Y: A comprehensive two-hybrid analysis to explore the yeast protein interactome. Proc Natl Acad Sci USA. 2001, 98: 4569-4574. 10.1073/pnas.061034498.
Lee TI, Rinaldi NJ, Robert F, Odom DT, Bar-Joseph Z, Gerber GK, Hannett NM, Harbison CT, Thompson CM, Simon I, et al: Transcriptional regulatory networks in Saccharomyces cerevisiae. Science. 2002, 298: 799-804. 10.1126/science.1075090.
Giot L, Bader JS, Brouwer C, Chaudhuri A, Kuang B, Li Y, Hao YL, Ooi CE, Godwin B, Vitols E, et al: A protein interaction map of Drosophila melanogaster. Science. 2003, 302: 1727-1736. 10.1126/science.1090289.
Butland G, Peregrin-Alvarez JM, Li J, Yang W, Yang X, Canadien V, Starostine A, Richards D, Beattie B, Krogan N, et al: Interaction network containing conserved and essential protein complexes in Escherichia coli. Nature. 2005, 433: 531-537. 10.1038/nature03239.
Gavin AC, Aloy P, Grandi P, Krause R, Boesche M, Marzioch M, Rau C, Jensen LJ, Bastuck S, Dumpelfeld B, et al: Proteome survey reveals modularity of the yeast cell machinery. Nature. 2006, 440: 631-636. 10.1038/nature04532.
Barabasi AL, Oltvai ZN: Network biology: understanding the cell's functional organization. Nat Rev Genet. 2004, 5: 101-113. 10.1038/nrg1272.
Milo R, Shen-Orr S, Itzkovitz S, Kashtan N, Chklovskii D, Alon U: Network motifs: simple building blocks of complex networks. Science. 2002, 298: 824-827. 10.1126/science.298.5594.824.
Guelzim N, Bottani S, Bourgine P, Kepes F: Topological and causal structure of the yeast transcriptional regulatory network. Nat Genet. 2002, 31: 60-63. 10.1038/ng873.
Luscombe NM, Babu MM, Yu H, Snyder M, Teichmann SA, Gerstein M: Genomic analysis of regulatory network dynamics reveals large topological changes. Nature. 2004, 431: 308-312. 10.1038/nature02782.
Arifuzzaman M, Maeda M, Itoh A, Nishikata K, Takita C, Saito R, Ara T, Nakahigashi K, Huang HC, Hirai A, et al: Large-scale identification of protein-protein interaction of Escherichia coli K-12. Genome Res. 2006, 16: 686-691. 10.1101/gr.4527806.
Wagner A: How the global structure of protein interaction networks evolves. Proc Biol Sci. 2003, 270: 457-466. 10.1098/rspb.2002.2269.
Pal C, Papp B, Lercher MJ, Csermely P, Oliver SG, Hurst LD: Chance and necessity in the evolution of minimal metabolic networks. Nature. 2006, 440: 667-670. 10.1038/nature04568.
Blattner FR, Plunkett G, Bloch CA, Perna NT, Burland V, Riley M, Collado-Vides J, Glasner JD, Rode CK, Mayhew GF, et al: The complete genome sequence of Escherichia coli K-12. Science. 1997, 277: 1453-1474. 10.1126/science.277.5331.1453.
Hayashi T, Makino K, Ohnishi M, Kurokawa K, Ishii K, Yokoyama K, Han CG, Ohtsubo E, Nakayama K, Murata T, et al: Complete genome sequence of enterohemorrhagic Escherichia coli O157:H7 and genomic comparison with a laboratory strain K-12. DNA Res. 2001, 8: 11-22. 10.1093/dnares/8.1.11.
Chen SL, Hung CS, Xu J, Reigstad CS, Magrini V, Sabo A, Blasiar D, Bieri T, Meyer RR, Ozersky P, et al: Identification of genes subject to positive selection in uropathogenic strains of Escherichia coli : a comparative genomics approach. Proc Natl Acad Sci USA. 2006, 103: 5977-5982. 10.1073/pnas.0600938103.
Rives AW, Galitski T: Modular organization of cellular networks. Proc Natl Acad Sci USA. 2003, 100: 1128-1133. 10.1073/pnas.0237338100.
Newman ME, Girvan M: Finding and evaluating community structure in networks. Phys Rev E Stat Nonlin Soft Matter Phys. 2004, 69: 026113-
Guimerá R, Nunes-Amaral LA: Functional cartography of complex metabolic networks. Nature. 2005, 433: 895-900. 10.1038/nature03288.
Newman ME: Modularity and community structure in networks. Proc Natl Acad Sci USA. 2006, 103: 8577-8582. 10.1073/pnas.0601602103.
Mrowka R, Patzak A, Herzel H: Is there a bias in proteome research?. Genome Res. 2001, 11: 1971-1973. 10.1101/gr.206701.
von Mering C, Jensen LJ, Snel B, Hooper SD, Krupp M, Foglierini M, Jouffre N, Huynen MA, Bork P: STRING: known and predicted protein-protein associations, integrated and transferred across organisms. Nucleic Acids Res. 2005, 33: D433-437. 10.1093/nar/gki005.
STRING Database. [http://string.embl-heidelberg.de]
Harris MA, Clark J, Ireland A, Lomax J, Ashburner M, Foulger R, Eilbeck K, Lewis S, Marshall B, Mungall C, et al: The Gene Ontology (GO) database and informatics resource. Nucleic Acids Res. 2004, 32: D258-261. 10.1093/nar/gkh066.
Maere S, Heymans K, Kuiper M: BiNGO: a Cytoscape plugin to assess overrepresentation of gene ontology categories in biological networks. Bioinformatics. 2005, 21: 3448-3449. 10.1093/bioinformatics/bti551.
JT wishes to acknowledge Roger Guimerá and Mark Newman. JT is the recipient of a contract from the FIS programme, ISCIII, Ministerio de Sanidad y Consumo (Spain). This work has been supported by grant BMC2003-00305 from Ministerio de Educación y Ciencia (Spain), to A.M., and EU grants DIAMONDS: LSHG-CT-2004-512143 and EMERGENCE, to A.V.
Electronic supplementary material
Additional data file 1: Table S1 lists the composition of the main modules in E. coli, for the modular decomposition of the Butland dataset using Guimerá's algorithm. Table S2 shows the different motifs with three or four nodes found in the real networks and randomized networks. Table S3 shows the results of the modular decomposition of the Butland dataset by means of a k-means clustering algorithm, as an additional confirmation of the validity of the results. Table S4 lists the main conserved hubs in Buchnera, and their functions in the Butland dataset. (DOC 118 KB)
Additional data file 2: Relationship between the connectivity of the nodes and their deletion in Buchnera's network (Butland dataset), and the probability of the deletion of nodes as a function of the probable number of connections. (PPT 184 KB)
About this article
Cite this article
Tamames, J., Moya, A. & Valencia, A. Modular organization in the reductive evolution of protein-protein interaction networks. Genome Biol 8, R94 (2007). https://doi.org/10.1186/gb-2007-8-5-r94