Fig. 1. Schematic representation of the progressive addition of sequences into the clusters. Maximal cliques are searched during step 1 and may contain multidomain proteins. As a result, the sequence labeled 2 may also be a member of another clique. During step 2, any sequence (belonging or not to a clique) similar to a sequence within a clique is added to its content (sequences 3 and 4). Step 3 is optional and allows the further allocation of sequences not yet included in a cluster (addition of sequence 5). Then, the clusters sharing more than 80% of their sequences are merged (not shown here). A few sequences (such as sequence 6) may remain as singletons even if similar to other sequences in a cluster.

Fig. 2. Schematic representation showing how Cluster-C can break some clusters built by the transitive single link method. Depending on whether step 3 is run or not, Cluster-C will produce clusters 1b and 2b or 1c and 2b instead of one single cluster. In both cases, the final two clusters will share common sequences but will not be merged at step 4 since they share less than 80% of their elements.

Fig. 3. Number (as percent of the total) of subgraphs (triangles) and maximal cliques (squares) as a function of the number of links they contained. (A) Set of 52 bacterial proteomes; (B) A. thaliana proteome; (C) two yeasts proteomes. In (A) and (B), the subgraphs containing more than 100 000 and 10 000 connections, respectively, were grouped into one single point for the purpose of clarity. The majority of the subgraphs contained less than 100 links and the majority of the cliques were built from these small subgraphs.

Fig. 4. Distribution of the cluster sizes (by intervals of 100) for the bacterial set after steps 2 and 3 (inclusion of related sequences within the clusters) and after step 4 (merging of clusters sharing more than 80% of their sequences).

Fig. 5. Comparison of the distribution of clusters as obtained by the transitive method (triangles) and by Cluster-C (squares) for the bacterial set of sequences. Note that the huge cluster (>40 000 sequences) built by the transitive method has been broken by Cluster-C into smaller clusters.

Table 1. Some data pertaining to the massive protein sequence comparisons performed in this study with the LASSAP software (Glémet and Codani, 1997)

SW: Smith and Waterman alignment score. The parameters for the Smith and Waterman comparisons were the same as in Comet et al., 1999. Z-values calculations were performed only for those pairs of sequences showing a Smith–Waterman alignment score greater than 22. Arabidopsis thaliana: 27 288 proteins downloaded from TIGR (http://www.tigr.org/ release of July 2002). Saccharomyces cerevisiae and Schizosaccharomyces pombe: 11 279 sequences downloaded from EBI, July 2002 (http://www.ebi.ac.uk/proteome). Bacteria: 129 899 non redundant bacterial protein sequences downloaded from EBI (July 2002): Anabaena sp. strain PCC 7120, Aquifex aeolicus, Bacillus halodurans, Bacillus subtilis, Borrelia burgdorferi, Brucella melitensis, Buchnera aphidicola (subsp. Acyrthosiphon pisum), Campylobacter jejuni, Caulobacter crescentus, Chlamydia muridarum, Chlamydia pneumoniae strain CWL029, Chlamydia pneumoniae strain J138, Chlamydia trachomatis, Clostridium acetobutylicum, Clostridium perfringens, Escherichia coli O157:H7 strain EDL933, Escherichia coli O157:H7 substrain RIMD 0509952, Escherichia coli K-12, Deinococcus radiodurans, Haemophilus influenzae, Helicobacter pylori strain 26695, Helicobacter pylori strain J99, Lactococcus lactis (subsp. lactis) strain IL1403, Listeria innocua, Listeria monocytogenes, Mycoplasma genitalium, Mycobacterium leprae, Mycoplasma pneumoniae, Mycoplasma pulmonis, Mycobacterium tuberculosis strain H37Rv, Neisseria meningitidis strain MC58 (serogroup B), Neisseria meningitidis strain Z2491 (serogroup A), Pasteurella multocida, Pseudomonas aeruginosa, Ralstonia solanacearum, Rhizobium loti, Rhizobium meliloti, Rickettsia conorii, Rickettsia prowazekii, Salmonella typhimurium, Salmonella typhi, Staphylococcus aureus strain Mu50, Staphylococcus aureus strain N315, Streptococcus pneumoniae strain TIGR4, Streptococcus pyogenes strain SF370, Synechocystis sp. PCC 6803, Thermotoga maritima, Treponema pallidum, Ureaplasma parvum, Vibrio cholerae, Xylella fastidiosa, Yersinia pestis.

Table 2. Some data pertaining to the construction of clusters in four steps by Cluster-C (see the text), with a comparison to the results obtained through the transitive single link method

Those sequences with Z-values <14 were not included in the clusterization process (see Table 1). The last line shows the number of extra sequences that were not included in a cluster.