For the genome quintet of photosynthetic organisms that we initially analyzed in 5, both the posterior probability map and the bootstrap support map show that a plurality of datasets support three tree topologies: numbers 5, 10, and 15 (see Figures 2 and 3). The extended datasets (Figure 3) provide a more realistic illustration of the reliability of the individual analyses than the map based on the ML-mapping approach (Figure 2). While the plurality consensus is still discernable in Figure 3, many datasets do not map close to any of the vertices, suggesting that these sets of orthologous proteins cannot discriminate between at least some of the possible phylogenies. One might be tempted to conclude that not much phylogenetic information survived and that the apparent conflicts 5 were due to a lack of resolution only 13. However, each five-taxon tree has two internal branches, that is, two bipartitions that contain phylogenetic information. The smallest quantum of phylogenetic information is the individual bipartition, not the resolved tree topology. In the five-taxon case a bipartition can be viewed as a partially unresolved tree where two taxa are grouped together, while the relationship among the other three taxa remains unresolved. An analysis of the possible bipartitions is a better way to gauge the extent of surviving phylogenetic information and the conflict between the individual datasets than dekapentagonal maps. We summarize the support for the 10 possible bipartitions in the form of a histogram (Figure 4). The bipartition corresponding to the plurality consensus signal for trees 5, 10 and 15 is labeled as bipartition A. This bipartition has plurality support. Xiong et al.14 reported that enzymes involved in (bacterio)chlorophyll biosynthesis are supporting the topology that in the dekapentagonal map is labeled as topology 13. Topology 13 corresponds to two bipartitions labeled as E and G in Figure 4. In our set of 188 QuintOPs, only a few members of the chlorophyll biosynthesis pathway are present: bchB/chlB, bchL/chlL and chlM. The other members of the chlorophyll biosynthesis pathway were not picked up because of the strict requirements imposed on the QuintOP assembly, that is, the requirement that the open reading frames (ORFs) that form a QuintOP mutually pick up each other in all five genomes as top-scoring BLAST hits. The reason that some members of the chlorophyll biosynthetic pathways are not assembled into QuintOPs is that there are multiple paralogous genes present in some of those genomes (especially in the Chlorobium and Chloroflexus genomes), and these prevent proper QuintOPs from being formed. We manually compiled the extended datasets for bchH/chlH, bchI/chlI, bchD/chlD, bchN/chlN genes and calculated the bootstrap support values for bipartitions A, E and G with different phylogenetic methods (Figure 5). In all cases the members of the photosynthetic pathway do not support the plurality bipartition, but significantly support the bipartitions reported by Xiong et al. 14. This suggests that the genes from the chlorophyll biosynthetic pathway have a phylogenetic history different from the apparent plurality consensus.

Genes in eukaryotes are proposed to represent different contributions from different organisms (Figure 6). If appropriate representatives of the bacterial and archaeal domains are chosen, the genes that were acquired from different putative contributors to the eukaryotic lineage can be differentiated through different tree topologies. Here we attempt to partition a eukaryotic genome with respect to the different contributions. We selected the genome quintet containing one well-annotated eukaryote (Saccharomyces cerevisiae), two archaea representing two archaeal kingdoms (the euryarchaeote Archaeoglobus fulgidus and the crenarchaeote Sulfolobus solfataricus), and two bacteria (the alpha-proteobacterium Rhodobacter capsulatus and the Gram-positive bacterium Bacillus subtilis).

For the interdomain genome quintet (Figures 7, 8) most support-value vectors map close to four vertices: topology 11 (corresponding to the traditional ribosomal RNA tree as described by 15), topology 12 (supporting the eocyte hypothesis, 16), topology 9 (predicted for the genes of mitochondrial origin) and topology 4 (eukaryotic homolog with other bacteria). Notably, there are some datasets that support other topologies (see Table 1): the large subunit of carbamoyl-phosphate synthase supports topology 2, which groups a euryarchaeote within the Bacteria, and ribosomal protein S3 homologs support topology 15, which groups yeast with Archaeoglobus. The large subunit of carbamoyl-phosphate synthase contains an internal duplication (171819, and A. Lazcano, personal communication) and its phylogeny was described as being consistent with an interdomain horizontal gene transfer from the bacteria to the ancestor of the euryarchaeota 202122. Topologies 4 and 12 might represent different prokaryotic contributions to the yeast genome, transfers between the two prokaryotic domains, or a single bacterial contribution to the eukaryotic cell 2324. In all those datasets that group the eukaryotic homolog with bacterial sequences we were not able to detect any consistent phylogenetic signature. This finding is in agreement with the 'you are what you eat' hypothesis 25, but it also could be due to limited phylogenetic information surviving in the individual datasets.

The dekapentagonal maps depicted in Figures 7 and 8 emphasize the mosaicism of the eukaryotic genome of yeast, and delineate different contributions to the yeast genome that have occurred over the course of evolution. The map reveals that individual datasets support different, in some instances conflicting, hypotheses proposed to explain the origin of eukaryotes. While the resulting maps illustrate the mosaic nature of the eukaryotic genome, their discriminatory power regarding different proposed contributions is limited. For example, the datasets that support the traditional topology (number 11) are equally compatible with genes that were contributed to the eukaryotic cell via the chronocyte 26. Because our approach only considers unrooted trees, the two scenarios result in identical topologies, with only the branch lengths differing under the two scenarios, that is, the genes contributed by the chronocyte are expected to have the eukaryotic genes on very long branches 27. Another shortcoming is that the map includes only two bacterial taxa. Without inspecting the phylogenies inferred from the extended datasets (see above) it is impossible to decide if many genes were contributed from a single bacterium, as assumed in hypotheses proposed in 232428, or were acquired through many independent transfers 25.

The first genome quintet consists of five photosynthetic bacteria from five bacterial phyla: Rhodobacter capsulatus, Chlorobium tepidum, Chloroflexus aurantiacus, Heliobacillus mobilis and Synechocystis sp. PCC 6803.

The second genome quintet consists of genomes representing all three domains of life: the yeast genome of Saccharomyces cerevisiae, the alpha-proteobacterium Rhodobacter capsulatus, the Gram-positive bacterium Bacillus subtilis, the euryarchaeote Archaeoglobus fulgidus and the crenarchaeote Sulfolobus solfataricus.

The Rhodobacter capsulatus and Heliobacillus mobilis genome data were obtained from Integrated Genomics 30. Genome sequence for Chlorobium tepidum was downloaded from The Institute for Genomic Research (TIGR) 31. The Rhodopseudomonas palustris genome was downloaded from the DOE Joint Genome Institute 32. Other genomes for the genome quintets were downloaded from the National Center for Biotechnology Information (NCBI) 33.

Detection of QuintOPs was analogous to detection of quartets of orthologous proteins 2. In brief, for each genome in a genome quintet, BLAST 34 searches of every ORF in one genome against the other three genomes were performed using the blastp program. The E-value cutoff for the BLAST searches was set to 10^-4. We defined QuintOPs as those sets of genes that mutually pick each other as the top-scoring hit in all pairwise genome BLAST comparisons. The amino-acid sequences for each QuintOP were retrieved and the datasets were aligned with ClustalW 35. Maximum likelihoods for 15 tree topologies for each QuintOP were calculated using TREE-PUZZLE version 5.1 36 under the auto-detected substitution model. Posterior probability vectors were calculated from ML values.

For each sequence in a QuintOP we detect the top-scoring BLAST 34 hit with an E-value above 10^-8 in each of 60 completely sequenced archaeal and bacterial reference genomes (Aeropyrum pernix, Archaeoglobus fulgidus, Anabaena sp., Aquifex aeolicus, Agrobacterium tumefaciens, Borrelia burgdorferi, Bradyrhizobium japonicum, Bifidobacterium longum, Bacillus subtilis, Brucella suis, Buchnera sp., Clostridium acetobutylicum, Caulobacter crescentus, Corynebacterium glutamicum, Campylobacter jejuni, Clamydophila pneumoniae, Deinococcus radiodurans, Escherichia coli K12, Fusobacterium nucleatum, Halobacterium sp., Haemophilus influenzae, Helicobacter pylori, Leptospira interrogans, Lactococcus lactis, Listeria monocytogenes, Lactobacillus plantarum, Mycoplasma genitalium, Methanococcus jannaschii, Methanopyrus kandleri, Mezorhizobium loti, Methanosarcina mazei, Methanobacterium thermoautotrophicum, Mycobacterium tuberculosis, Neisseria meningitides, Oceanobacillus iheyensis, Pseudomonas aeruginosa, Pyrobaculum aerophilum, Pyrococcus horikoshii, Pasteurella multocida, Rickettsia conorii, Ralstonia solanacearum, Staphylococcus aureus, Streptomyces coelicolor, Sinorhizobium meliloti, Shewanella oneidensis, Sulfolobus solfataricus, Salmonella typhi, Synechocystis sp., Thermoplasma acidophilum, Thermosynechococcus elongates, Thermotoga maritime, Treponema pallidum, Thermoanaerobacter tengcongensis, Tropheryma whipplei, Ureaplasma urealyticum, Vibrio cholerae, Wigglesworthia brevipalpis, Xanthomonas campestris, Xylella fastidiosa, Yersinia pestis). These genomes were downloaded from the NCBI 33. The resulting sequences were added to the QuintOP dataset and duplicated sequences were eliminated. The datasets were aligned with ClustalW 35, and 100 bootstrap samples were generated using the SEQBOOT program from the PHYLIP package version 3.6a2.1 37. The distances were generated using TREE-PUZZLE version 5.1 36 under the auto-detected substitution model. Neighbor-joining trees were calculated from these distances using NEIGHBOR from the PHYLIP package version 3.6a2.1 37. The resulting trees were parsed with respect to which of the 15 five-taxon subtrees they contain.

The dekapentagon was placed into the Cartesian coordinate system with its center coinciding with the origin of the coordinate system. Then the coordinates (x_i, y_i) of a vertex i are x_i = R*cos(i*360/15), y_i = R*sin(i*360/15), where R is the distance from origin to the vertex (equal for all the vertices due to the location of the origin of the coordinate system), and 1 ≤ i ≤ 15. For each pair of vertices i and j the coordinates of the center of gravity M_ij (x_M, y_M) are calculated according to the law of the lever: x_M = x_i + (x_j - x_i)*p_j/(p_i + p_j), y_M = y_i + (y_j - y_i)*p_j/(p_i + p_j), where p_i and p_j are the posterior probabilities of vertices i and j. The process is repeated for all pairs of vertices, and then iteratively for all 'intermediate' centers of gravities until only one pair of coordinates remains, which gives the center of gravity of the dekapentagon that is equivalent to the location of probability vector. The resulting coordinates of the dekapentagon's center of gravity do not depend on the order in which the masses are combined.

There are (15 - 1)!/2 = 14!/2 ≈ 4*10¹⁰ possible arrangements of topologies on dekapentagon's vertices (only free circular permutations 38 are counted, and the arrangements that become equivalent by rotation of dekapentagon or flipping the dekapentagon over are considered as the same arrangements). The arrangement was considered optimal when the topologies arranged at the polygon vertices in such way that maximizes the sum of all distances of the barycentric points from the center of the polygon. There are too many arrangements of topologies around the dekapentagon to search for the optimal arrangement exhaustively. Therefore, we used a heuristic search for optimal solutions based on a hybrid genetic algorithm 39. Each tree topology was assigned a numerical identifier (1 through 15), and the arrangements of topologies around the dekapentagon's vertices were encoded as arrays of the tree topology identifiers where each position in the array represents a position on the polygon circumference. The genetic algorithm applies mutation and cross-over operations to each successive generation of arrangements until the optimal solution is obtained 40. Each generation consisted of a population of 300 individuals. In order to preserve diversity among the individuals as much as possible and prevent premature convergence of the algorithm the population was divided into 10 demes (subpopulations) each with 30 individuals and with controlled migration between demes.

We hybridized the genetic algorithm by equipping the algorithm with a local search heuristic in addition to the global search strategy based on the genetic operators to explore better the space of possible arrangements. A manuscript reporting details on the algorithm for finding the optimal arrangements is in preparation (L.H., O.Z. and J.P.G., unpublished work). The program calculating the optimal arrangement of topologies is available on request.

To test the reproducibility, the search for the optimal arrangement was repeated independently 50 times with different starting seeds.

The resulting posterior probability and bootstrap support vectors were plotted into dekapentagonal maps using GNUPLOT version 3.7 41.

Sequences from the genome quintet were supplemented with homologous sequences from other photosynthetic bacteria to improve taxon sampling, aligned with ClustalW 35, and phylogenetic trees were reconstructed. For distance and parsimony analyses, 100 bootstrap samples were generated with SEQBOOT 37. Distances were calculated in TREE-PUZZLE v. 5.1 36 with among-site rate variation taken into account. Neighbor-joining trees were calculated with NEIGHBOR 37, Fitch-Margoliash trees with FITCH 37, protein parsimony trees with PROTPARS 37. MrBayes version 3.0B4 42 analyses were run three times independently for 500,000 generations per run (100,000 of which were burned in), under the JTT substitution model 43, and with an exponential prior set for branch length.

Scripts for data manipulation were written in Perl and used many of the SEALS package subroutines 44. Tree-parsing programs were written in Java utilizing PAL library classes 45. The genetic algorithm was written in C++ and is based on the genetic algorithm library GALIB version 2.4.5 46.