- Methodology article
- Open Access
Clustering evolving proteins into homologous families
© Chan et al.; licensee BioMed Central Ltd. 2013
Received: 17 August 2012
Accepted: 27 March 2013
Published: 8 April 2013
Clustering sequences into groups of putative homologs (families) is a critical first step in many areas of comparative biology and bioinformatics. The performance of clustering approaches in delineating biologically meaningful families depends strongly on characteristics of the data, including content bias and degree of divergence. New, highly scalable methods have recently been introduced to cluster the very large datasets being generated by next-generation sequencing technologies. However, there has been little systematic investigation of how characteristics of the data impact the performance of these approaches.
Using clusters from a manually curated dataset as reference, we examined the performance of a widely used graph-based Markov clustering algorithm (MCL) and a greedy heuristic approach (UCLUST) in delineating protein families coded by three sets of bacterial genomes of different G+C content. Both MCL and UCLUST generated clusters that are comparable to the reference sets at specific parameter settings, although UCLUST tends to under-cluster compositionally biased sequences (G+C content 33% and 66%). Using simulated data, we sought to assess the individual effects of sequence divergence, rate heterogeneity, and underlying G+C content. Performance decreased with increasing sequence divergence, decreasing among-site rate variation, and increasing G+C bias. Two MCL-based methods recovered the simulated families more accurately than did UCLUST. MCL using local alignment distances is more robust across the investigated range of sequence features than are greedy heuristics using distances based on global alignment.
Our results demonstrate that sequence divergence, rate heterogeneity and content bias can individually and in combination affect the accuracy with which MCL and UCLUST can recover homologous protein families. For application to data that are more divergent, and exhibit higher among-site rate variation and/or content bias, MCL may often be the better choice, especially if computational resources are not limiting.
Homology is the basis of comparative biology , and recognising sets of homologous genes or proteins underlies much of modern bioscience including genome annotation, phylogenetic inference and studies of protein structure. Particularly in high-throughput applications, these molecules are usually arranged into putatively homologous sets based on sequence similarity. A greater degree of shared similarity (smaller distance) observed among a set of sequences relative to the others in the dataset indicates a likely homologous history.
In recent studies [2, 3], clustering approaches have been loosely grouped into three classes based on their algorithmic design: hierarchical, greedy heuristic, and Bayesian. Hierarchical clustering approaches, e.g. ESPRIT-Tree , operate on pairwise distances (an estimate of pairwise relatedness) that are commonly generated by local alignment (e.g. using BLAST) and group sequences at a defined threshold of similarity. While computationally demanding of space and memory, greedy heuristic approaches such as CD-HIT  and UCLUST  are more scalable, in substantial part because they simultaneously compute pairwise similarity and group the sequences using a greedy global-alignment algorithm. CD-HIT has been adopted in major databases [7, 8] to delineate protein families and reduce data redundancy, while UCLUST, which uses a fast global-alignment algorithm (UBLAST) that takes only best hits into consideration, can accurately delineate highly conserved protein sets . In addition to these three categories, MCL , adopting probability and graph flow theory within a Markov matrix framework, has been widely adopted for delineating families in phylogenetic studies [10-14]. The performance of these approaches necessarily varies depending on features of the data, including content bias (i.e. G+C bias in genes, or the consequent bias in the proteins these genes encode), and the degree to which the sequences have diverged in the course of evolution. A recent benchmarking analysis  using both empirical and simulated data suggests that hierarchical approaches are more accurate in recovering sequence clusters than are greedy heuristics. Nevertheless the contribution of these features individually on the performance of clustering approaches remains unclear.
Here we assess the clustering performance of MCL in comparison to the fast, greedy heuristic clustering method, UCLUST. We approach this issue in two ways. First, we examine the performance of these two approaches in clustering empirical protein datasets from three sets of bacterial genomes at varied levels of G+C content: Staphylococcus at ∼ 33% G+C , Mycobacterium at ∼ 66% G+C (http://www.tbdb.org/) and Escherichia coli/Shigella with ∼ 50% G+C . Different clustering performance across these three datasets would therefore indicate, at least partially, the sensitivity of these approaches to G+C content of the genomes. Second, we generated sets of sequences by simulation on a tree, in order to assess individually the impact on clustering performance of sequence divergence, rate heterogeneity, and bias in G+C content.
Results and discussion
We examined, respectively for MCL and UCLUST, the similarity between two sets of clusters (i.e. similarity of clustering assignments between two sets), as estimated by comparing all possible paired member assignments using the Adjusted Rand Index (ARI ), which ranges between −1 and 1. This measure, based on the agreement of cluster memberships between two sets of data, has been widely adopted to measure clustering accuracy, e.g. [18, 19]. ARI > 0 indicates that the two sets share a number of identical clusters (ARI = 1 indicates identical clustering assignments between the two sets), ARI = 0 indicates the two sets do not agree exactly on any cluster memberships, and ARI < 0 indicates the deviation between the two sets is greater than expected by chance.
Analysis of empirical data
Sets of protein sequences encoded by genomes of three bacterial genera were obtained from previously published work, or from public databases: 34066 proteins from 13 Staphylococcus genomes , 86393 proteins from 19 Mycobacterium genomes http://www.tbdb.org/ as of 5 December 2011, and 123136 proteins from 27 Escherichia coli and Shigella genomes . As our reference cluster dataset we extracted all relevant clusters (i.e. clusters containing proteins from the genomes used in this study) from the manually curated protein cluster database FigFam , as available from the Pathosystems Resource Integration Center (PATRIC) website , http://www.patricbrc.org/. For MCL, we used both BLASTP and UBLAST to generate the distance matrices (see Methods for detail). The MCL results based on BLAST+ and UBLAST searches are designated BLAST+MCL and UBLAST+MCL respectively.
The number of clusters increases drastically with increasing ID in UCLUST (particularly of clusters of size N < 4), in comparison to MCL (both BLAST+ and UBLAST+MCL), in which the number of clusters remains similar across I (Additional file 1: Figure S1). When comparing cluster sizes, we focus on those of size N ≥ 4 as these clusters are phylogenetically meaningful. For Staphylococcus, Escherichia coli/Shigella and Mycobacterium, the reference numbers of clusters (N ≥ 4) are 2602, 5974 and 5429 respectively. The results closest to these, although not necessarily the most accurate (i.e. not the highest ARI), are those generated using BLAST+MCL with 2611 (I = 6.0, ARI = 0.67), 5302 (I = 10.0, ARI = 0.73), and 5433 (I = 8.0, ARI = 0.80), in comparison to 2663 (ID = 0.50, ARI = 0.88), 5797 (ID = 0.90, ARI = 0.89) and 5353 (ID = 0.80, ARI = 0.45) using UCLUST (Additional file 1: Figure S1).
We observed an increase in ARI as I increases in MCL across all data. A similar trend is observed in UCLUST for the Escherichia coli/Shigella data, in which ARI increases proportionately with ID, with the maximum achieved at ID 0.90. However, for Mycobacterium and Staphylococcus (data with G+C bias), a reverse trend is observed in UCLUST. In these instances, ARI decreases when higher ID threshold was applied. This trend can partly be explained by the lower within-cluster sequence similarity observed for the Mycobacterium and Staphylococcus dataset than for Escherichia coli/Shigella (Additional file 1: Figure S2). FigFam protein families of Mycobacterium (mean identity 51.3%, median 83.2%) and of Staphylococcus (mean identity 55.8%, median 77.5%) are more divergent (less similar) than those of Escherichia coli/Shigella (mean identity 63.9%, median 98.2%). Although such low within-cluster similarity (peaks in region of < 20% identity in Additional file 1: Figure S2) could be explained by single-member clusters (within-cluster identity 0%), such divergence could partly be explained by compositional biases in these genomes. Therefore a lower ID threshold in UCLUST appears to perform better in these cases. We expect clustering performance to increase as annotation of these proteins improves as more genome data become available.
These results, if general, indicate that the greedy heuristics approach tends to under-cluster compositionally biased sequences. This is not due to the UBLAST algorithm implemented in UCLUST, as MCL generates about the same numbers of clusters when we take bit scores from UBLAST (compare BLAST+MCL versus UBLAST+MCL). In addition to G+C bias, other evolutionary parameters e.g. among-site variation of substitution rates and/or convergence could also have contributed to our result. Highly similar sequences play to the strength of global alignment (as implemented in UCLUST) more than to local alignment (BLAST), as shown by the high ARI values in Figure 1. Our MCL clustering results shown in Figure 1 are based on the BLAST e-value cut-off at 10−3. As we applied more-stringent thresholds at 10−10 and 10−25, we observe higher clustering accuracy in MCL (Additional file 1: Figure S3). For instance, in the case of Staphylococcus, MCL clustering at I = 10.0 yielded ARI 0.88 (the highest ARI for UCLUST is 0.89 at ID = 0.50) based on BLAST e ≤ 10−25, in comparison to 0.79 and 0.77 (I = 10.0) at e ≤ 10−10 and 10−3, respectively. Our results support the notion that selecting an appropriate threshold of similarity measures is key in optimising clustering performance . Because with empirical data it is difficult to isolate or distinguish individual causative factors, we next simulated the evolution of families of homologous proteins under controlled settings of branch length (sequence divergence), rate heterogeneity and compositional bias.
Analysis of simulated data
The ARI described above measures clustering accuracy in these methods, but does not provide any insights into cluster numbers and sizes, which could be useful in understanding the exact nature of mis-clustering. As we know the exact cluster size and numbers in our simulated data, here we adopted an additional, independent measure for performance accuracy based on cluster sizes. Given N C = mean N among the resulting clusters, and N R = mean N observed in the reference set, we denote δ as a measure of fold difference of the average cluster size against the reference: δ = N C /N R . Here we follow Clark et al.  in defining the instances of over-clustering and under-clustering. Over-clustering is observed when δ > 1 (i.e., the average cluster size is larger than in the reference), and under-clustering when δ < 1 (i.e., the average cluster size is smaller than in the reference). We apply δ to all clusters, i.e. δ is simply the overall average cluster size divided by the known size N = 4. If our clustering methods perform perfectly, we expect to recover 2500 protein sets each of size N = 4 (δ = 1 and ARI = 1). We might also anticipate that as sequences grow more divergent, patchy or biased, clustering methods may become less efficient in grouping them correctly within families, and/or in distinguishing these families from each other. The results we present here are averages across five replicates. Given that the minimum cluster size is 1, the minimum δ across these instances is 1/4 = 0.25. For all the results described below, all instances where δ = 1 yielded sets that are identical to the reference (ARI = 1).
To assess the effect of sequence divergence, we simulated the sequence data on an unrooted tree (Figure 2), progressively set the internal branch length x = 0.10, 0.25, 0.50, 0.75 and 1.00 substitutions per site, and used a discrete approximation of the gamma distribution (shape parameter α = 1.0, 8 categories).
These results suggest that local alignment-based approaches using MCL are more effective in recovering homologous protein families than the global alignment-based method, when sequences are (or appear to be) more evolutionarily distant from each other. Some proteins, although sharing little sequence similarity, are known to be structural homologs, i.e. sharing high similarity in folding structure due to a common ancestral origin [25, 26]. In these instances, clustering of these highly divergent sequences (but with conserved structural features) into a single homologous family would be desirable. When the level of sequence divergence is the only determining factor for the protein clusters, MCL with I ≤ 2 appears to be a better option than UCLUST.
Among-site rate heterogeneity
We modelled rate heterogeneity (distribution of among-site rate variation) across-sequence under the discrete approximation of the (continuous) gamma distribution, with the shape of the distribution determined by the α parameter. A small value (α ≤ 1) implies that substitution differs greatly across sites, e.g. a few sites have diversified quickly while the others little or not at all. This condition is analogous to having multiple conserved domains within a protein sequence. A large value (α > 1), on the other hand, indicates that most sites have diversified at about the same rate. To assess the effect of rate heterogeneity we fixed x = 0.10 and progressively set α = 0.5, 1.0 and 2.0 under the same 8-category discrete gamma distribution.
By itself, increased across-sites rate heterogeneity does not affect clustering accuracy as much as does greater sequence divergence. All three clustering approaches recovered the correct number of families more efficiently when rate heterogeneity was high (α ≤ 1) than when it was low (α > 1). The local alignment-based approach using MCL is more robust than the greedy heuristic of UCLUST to heterogeneity of rate across sites. We examined the data across other α values and found negligible difference, i.e. cases of α = 5 and 10 are similar to the case of α = 2, while the case of α = 0.1 is similar to the case of α = 0.5.
Compositional bias of coding sequences
For UCLUST, sequence identity settings ID > 0.50 appear to be too stringent, as few sets of N = 4 were recovered (e.g. at ID = 0.60, where both ARI and δ approximate 0.50 at 80% and 90% G+C). Interestingly, at the most-extreme G+C content considered here (90%), BLAST+MCL at I = 1.1 recognised 2503 clusters (ARI = 0.92, δ = 0.99), of which 2498 have N = 4; in comparison, UCLUST at ID = 0.50 found 2784 clusters (ARI = 0.93, δ = 0.90), of which 2216 are of N = 4. The variation of G+C proportion across these simulated DNA sequences does not cause significant changes in pairwise sequence similarity within protein clusters (ranging between 58.6 and 64.6% with broader distribution at 90% G+C; see Additional file 1: Figure S5c), explaining why our results did not drastically change, particularly in UCLUST (Figure 5 and Additional file 1: Figure S7). In order to assess whether our simulated conditions in this experiment are intrinsically unfavourable to UCLUST in general (where no invariant sites were simulated), we examined the performance of UCLUST across instances of 50% G+C with an increasing proportion of invariant sites (inv) in the sequences, from 0.1 to 0.9, as shown in panels (a) to (i) in Additional file 1: Figure S8. Panel (j) in the same figure shows the average within-cluster pairwise sequence similarity of each of these cases. Evidently, as the proportion of invariant sites across the sequences increases, the efficiency of UCLUST in correctly identifying the four-member clusters increases. For instance, at ID = 0.7, UCLUST recovered almost 2500 clusters of N = 4 when inv > 0.7 (average within-cluster sequence similarity > 70% in Additional file 1: Figure S8j. Therefore, proportion of invariant sites (and thus sequence similarity) remains a key factor influencing the performance of UCLUST. Such conserved regions and invariant sites across sequences are expected in empirical data.
G+C bias inevitably influences codon usage in protein translation [27, 28]. Given that changes at the third codon position (compared to those at first or second position) are more likely to be cryptic, the usage of codons ending in G or C is expected to increase with G+C bias. This was indeed observed in a recent study of various prokaryote and eukaryote genomes , except for two codons. The same study demonstrates that usage of some codons is non-linear to G+C bias. Whereas the different levels of G+C content causes little difference in the accuracies of the two approaches in clustering the resulting protein sequences, MCL is more robust to such fluctuation than UCLUST, as observed by number of protein sets of N < 4 (gray bars across the panels in column ii; Additional file 1: Figure S7). To analyse the effect of G+C bias, we allowed our simulated DNAs only a low degree of divergence (x = 0.1 in Figure 2). At the most-extreme G+C content we examined (90%) there is much-reduced scope for sequences (both DNA and the encoding proteins) to be recognisably different from each other, whether viewed locally or globally. As such, our observation that both MCL and UCLUST failed to recover the known number of families across most parameter-value settings is not surprising. Fortunately, few empirical data are biased to this degree.
The MCL-based methods are computationally more expensive than UCLUST. The most time-consuming step is the generation of the matrix of sequence relatedness using all-versus-all BLAST. For this study, all computation was done using a 640-node Linux high-performance computer cluster (each node consisting of 8 cores with 8GB memory, i.e. 2 × Quad-core AMD Opteron 2356 2.3 GHz). For a set of 10000 protein sequences, the BLAST analysis on a single CPU required 250-300 MB of memory and took ca 1 to 12 hours depending on sequence variation within the set, with analysis of protein sequences generated at 90% G+C bias requiring the most time and memory.
We assessed the performance accuracy of two clustering approaches designed for different purposes. UCLUST was designed for de novo clustering of large datasets (e.g. sequence reads) to reduce data redundancy and size, while MCL is commonly used to delineate homologous sequence sets. The former is usually done at higher level of sequence similarities than the latter. Our study demonstrates that evolutionary aspects other than sequence divergence, e.g. among-site rate heterogeneity and G+C content bias, affect the clustering performance of these two approaches. We have demonstrated that sequence divergence, rate heterogeneity and content bias can individually and in combination affect the accuracy with which MCL and greedy heuristic algorithms can recover homologous protein families. We found the impact to be broader and more severe on the heuristics-based UCLUST than on two variants of MCL implementations. The simple global percent identity among sequences adopted in the former may be advantageous when sets of proteins or ribosomal RNAs  are highly similar or contain overlapping or redundant regions (e.g. sequencing reads), or when extreme scalability is required, as the clustering of these sequences is computationally more tractable than MCL. For application to data that are more divergent, and exhibit higher among-site rate variation and/or content bias, MCL may often be the better choice, especially if computational resources are not limiting.
Simulation of protein families
All simulated datasets were generated using evolver as implemented in PAML 4.5 . For each designated parameter setting, we generated 2500 protein families each of size N = 4 (sequences A-D) and of length 800 amino acids, by simulation on an unrooted symmetrical tree (Figure 2) on which all internal branches (x) are of the same length. To assess the effect of sequence divergence, we progressively set x = 0.10, 0.25, 0.50, 0.75 and 1.00 substitutions per site, and used a discrete approximation of the gamma distribution (shape parameter α = 1.0, 8 categories). To assess the effect of rate heterogeneity we fixed x = 0.10 and progressively set α = 0.5, 1.0 and 2.0 under the same 8-category discrete gamma distribution. For protein-sequence simulations we used the WAG substitution model .
To assess the effect of G+C content on clustering performance, simulation was similarly carried out at the nucleotide level for 2500 families, each of N = 4 and length = 2400 bases, with G+C proportion progressively at 0.5, 0.6, 0.7, 0.8 and 0.9, under the REV substitution model and a discrete gamma distribution (α = 1.0, 8 categories) but with x fixed at 0.1. We consider only cases of G+C proportion > 0.5 because sequences with G+C proportion > 0.5 are equivalent to sequences with A+T proportion < 0.5; these two instances (e.g. G+C 0.8 versus A+T 0.2, and the reverse situation of G+C 0.2) would have similar, if not identical, effects on our analysis. The nucleotide sequences were translated into protein sequences in frame +1. For stop codons (TAG, TAA and TGA), if present in a protein-coding region, the thymine residue was arbitrarily replaced with adenine to avoid interruption in protein translation (each protein consists of 800 amino acid residues). These stop codons were randomly distributed across all sequences and columns, therefore do not contribute to any clustering biases. To assess the impact of invariant site proportions on the performance of UCLUST, datasets with each specific proportion of invariant sites were simulated using INDELible , a more-flexible successor to PAML’s evolver. Across all simulated data, five replicates were generated for each parameter setting.
Clustering using MCL
For each dataset, a distance matrix was first generated using an all-versus-all BLAST approach as described by Harlow et al. . For this purpose we used BLASTP as implemented in NCBI BLAST+ version 2.2.25, and kept all matches with e ≤10−3. In parallel we also used UBLAST as implemented in USEARCH version 5.1.221  as an alternative local alignment method to generate the distance matrix, using the option −−nousort (all hits, not only the top hit, were kept). Relatedness between sequences a and b (R ab ) is based on their shared similarity, as observed in alignment bit scores: a normalised bit score (B) was first determined for each of a and b, in which B a = score of a hitting b over the score of a hitting itself (S ab /S aa ), and B b = score of b hitting a, divided by the score of b hitting itself (S ba /S bb ). R ab is then defined as max(B a , B b ). This definition of sequence relatedness has been described in a number of empirical studies [11, 32-34], in which greater R ab represents greater shared similarity (i.e. shorter distance) between the sequences. This matrix was used as input to MCL, with the inflation parameter I set at 1.1, 2.0, 4.0, 6.0, 8.0 or 10.0. The MCL results based on BLAST+ and UBLAST searches are designated BLAST+MCL and UBLAST+MCL respectively.
Greedy heuristic clustering using UCLUST
We carried out UCLUST  using USEARCH version 5.1.221 (http://www.drive5.com/usearch/) with minimum proportion of identity of matches (−id) set at 0.5, 0.6, 0.7, 0.8, 0.9 or 0.97 (default). For datasets that consist of sequences of varied lengths, sequences were sorted by length in descending order (−sort option in USEARCH) prior to clustering, as required in the implementation of the program.
Assessment of clustering performance
The ARI values  are calculated using the pdfCluster package  in R. For the analysis of simulated data, the δ values are derived from mean N among the resulting clusters (N C ) divided by mean N observed in the reference set (N R ) in each comparison. Within-cluster similarity is determined based on average pairwise similarity between each sequence in a cluster to the centroid sequence (i.e. the most-representative sequence) of the same cluster; pairwise identity is derived from BLAST (e ≤ 10−3). The centroid sequence of a cluster is identified based on the sequence that yielded the single highest bit score across all pairwise comparisons within the cluster. Between-cluster similarity is calculated based on percent identity observed for all possible pairwise comparisons of these centroid sequences.
We thank Australian Research Council (grant CE0348221) and the University of Queensland for funding.
- Homology. The Hierarchical Basis of Comparative Biology. Edited by: Hall BK. 1994, San Diego: Academic PressGoogle Scholar
- Cheng L, Walker AW, Corander J: Bayesian estimation of bacterial community composition from 454 sequencing data. Nucleic Acids Res. 2012, 40: 5240-5249. 10.1093/nar/gks227.PubMed CentralView ArticlePubMedGoogle Scholar
- Sun Y, Cai Y, Huse SM, Knight R, Farmerie WG, Wang X, Mai V: A large-scale benchmark study of existing algorithms for taxonomy-independent microbial community analysis. Brief Bioinform. 2012, 13: 107-121. 10.1093/bib/bbr009.PubMed CentralView ArticlePubMedGoogle Scholar
- Cai Y, Sun Y: ESPRIT-Tree: hierarchical clustering analysis of millions of 16S rRNA pyrosequences in quasilinear computational time. Nucleic Acids Res. 2011, 39: e95-10.1093/nar/gkr349.PubMed CentralView ArticlePubMedGoogle Scholar
- Li W, Godzik A: CD-HIT: a fast program for clustering and comparing large sets of protein or nucleotide sequences. Bioinformatics. 2006, 22: 1658-1659. 10.1093/bioinformatics/btl158.View ArticlePubMedGoogle Scholar
- Edgar RC: Search and clustering orders of magnitude faster than BLAST. Bioinformatics. 2010, 26: 2460-2461. 10.1093/bioinformatics/btq461.View ArticlePubMedGoogle Scholar
- Berman HM, Westbrook J, Feng Z, Gilliland G, Bhat TN, Weissig H, Shindyalov IN, Bourne PE: The protein data bank. Nucleic Acids Res. 2000, 28: 235-242. 10.1093/nar/28.1.235.PubMed CentralView ArticlePubMedGoogle Scholar
- Suzek BE, Huang H, McGarvey P, Mazumder R, Wu CH: UniRef: comprehensive and non-redundant UniProt reference clusters. Bioinformatics. 2007, 23: 1282-1288. 10.1093/bioinformatics/btm098.View ArticlePubMedGoogle Scholar
- Enright AJ, Van Dongen S, Ouzounis CA: An efficient algorithm for large-scale detection of protein families. Nucleic Acids Res. 2002, 30: 1575-1584. 10.1093/nar/30.7.1575.PubMed CentralView ArticlePubMedGoogle Scholar
- Harlow TJ, Gogarten JP, Ragan MA: A hybrid clustering approach to recognition of protein families in 114 microbial genomes. BMC Bioinformatics. 2004, 5: 45-10.1186/1471-2105-5-45.PubMed CentralView ArticlePubMedGoogle Scholar
- Beiko RG, Harlow TJ, Ragan MA: Highways of gene sharing in prokaryotes. Proc Natl Acad Sci U S A. 2005, 102: 14332-14337. 10.1073/pnas.0504068102.PubMed CentralView ArticlePubMedGoogle Scholar
- Treangen TJ, Rocha EP: Horizontal transfer, not duplication, drives the expansion of protein families in prokaryotes. PLoS Genet. 2011, 7: e1001284-10.1371/journal.pgen.1001284.PubMed CentralView ArticlePubMedGoogle Scholar
- Wong S, Ragan MA: MACHOS: markov clusters of homologous subsequences. Bioinformatics. 2008, 24: i77-i85. 10.1093/bioinformatics/btn144.PubMed CentralView ArticlePubMedGoogle Scholar
- Wu D, Hugenholtz P, Mavromatis K, Pukall R, Dalin E, Ivanova NN, Kunin V, Goodwin L, Wu M, Tindall BJ, Hooper SD, Pati A, Lykidis A, Spring S, Anderson IJ, D’haeseleer P, Zemla A, Singer M, Lapidus A, Nolan M, Copeland A, Han C, Chen F, Cheng JF, Lucas S, Kerfeld C, Lang E, Gronow S, Chain P, Bruce D, Rubin EM, Kyrpides NC, Klenk HP, Eisen JA: A phylogeny-driven genomic encyclopaedia of bacteria and archaea. Nature. 2009, 462: 1056-1060. 10.1038/nature08656.PubMed CentralView ArticlePubMedGoogle Scholar
- Chan CX, Beiko RG, Ragan MA: Lateral transfer of genes and gene fragments in Staphylococcus extends beyond mobile elements. J Bacteriol. 2011, 193: 3964-3977. 10.1128/JB.01524-10.PubMed CentralView ArticlePubMedGoogle Scholar
- Skippington E, Ragan MA: Within-species lateral genetic transfer and the evolution of transcriptional regulation in Escherichia coli and Shigella. BMC Genomics. 2011, 12: 532-10.1186/1471-2164-12-532.PubMed CentralView ArticlePubMedGoogle Scholar
- Hubert L, Arabie P: Comparing partitions. J Classif. 1985, 2: 193-218. 10.1007/BF01908075.View ArticleGoogle Scholar
- Wang C, Taciroglu A, Maetschke SR, Nelson CC, Ragan MA, Davis MJ: mCOPA: analysis of heterogeneous features in cancer expression data. J Clin Bioinform. 2012, 2: 222-Google Scholar
- Handl J, Knowles J, Kell DB: Computational cluster validation in post-genomic data analysis. Bioinformatics. 2005, 21: 3201-3212. 10.1093/bioinformatics/bti517.View ArticlePubMedGoogle Scholar
- Meyer F, Overbeek R, Rodriguez A: FIGfams: yet another set of protein families. Nucleic Acids Res. 2009, 37: 6643-6654. 10.1093/nar/gkp698.PubMed CentralView ArticlePubMedGoogle Scholar
- Gillespie JJ, Wattam AR, Cammer SA, Gabbard JL, Shukla MP, Dalay O, Driscoll T, Hix D, Mane SP, Mao C, Nordberg EK, Scott M, Schulman JR, Snyder EE, Sullivan DE, Wang C, Warren A, Williams KP, Xue T, Yoo HS, Zhang C, Zhang Y, Will R, Kenyon RW, Sobral BW: PATRIC: the comprehensive bacterial bioinformatics resource with a focus on human pathogenic species. Infect Immun. 2011, 79: 4286-4298. 10.1128/IAI.00207-11.PubMed CentralView ArticlePubMedGoogle Scholar
- Apeltsin L, Morris JH, Babbitt PC, Ferrin TE: Improving the quality of protein similarity network clustering algorithms using the network edge weight distribution. Bioinformatics. 2011, 27: 326-333. 10.1093/bioinformatics/btq655.PubMed CentralView ArticlePubMedGoogle Scholar
- Yang Z: PAML 4: phylogenetic analysis by maximum likelihood. Mol Biol Evol. 2007, 24: 1586-1591. 10.1093/molbev/msm088.View ArticlePubMedGoogle Scholar
- Clark MD, Hennig S, Herwig R, Clifton SW, Marra MA, Lehrach H, Johnson SL, WU-GSC EST Group: An oligonucleotide fingerprint normalized and expressed sequence tag characterized zebrafish cDNA library. Genome Res. 2001, 11: 1594-1602. 10.1101/gr.186901.PubMed CentralView ArticlePubMedGoogle Scholar
- Fribourg S, Conti E: Structural similarity in the absence of sequence homology of the messenger RNA export factors Mtr2 and p15. EMBO Rep. 2003, 4: 699-703. 10.1038/sj.embor.embor883.PubMed CentralView ArticlePubMedGoogle Scholar
- Sadowski MI, Jones DT: The sequence-structure relationship and protein function prediction. Curr Opin Struct Biol. 2009, 19: 357-362. 10.1016/j.sbi.2009.03.008.View ArticlePubMedGoogle Scholar
- Bernardi G: Isochores and the evolutionary genomics of vertebrates. Gene. 2000, 241: 3-17. 10.1016/S0378-1119(99)00485-0.View ArticlePubMedGoogle Scholar
- Muto A, Osawa S: The guanine and cytosine content of genomic DNA and bacterial evolution. Proc Natl Acad Sci U S A. 1987, 84: 166-169. 10.1073/pnas.84.1.166.PubMed CentralView ArticlePubMedGoogle Scholar
- Palidwor GA, Perkins TJ, Xia XH: A general model of codon bias due to GC mutational bias. PLoS One. 2010, 5: e13431-10.1371/journal.pone.0013431.PubMed CentralView ArticlePubMedGoogle Scholar
- Whelan S, Goldman N: A general empirical model of protein evolution derived from multiple protein families using a maximum-likelihood approach. Mol Biol Evol. 2001, 18: 691-699. 10.1093/oxfordjournals.molbev.a003851.View ArticlePubMedGoogle Scholar
- Fletcher W, Yang Z: INDELible: a flexible simulator of biological sequence evolution. Mol Biol Evol. 2009, 26: 1879-1888. 10.1093/molbev/msp098.PubMed CentralView ArticlePubMedGoogle Scholar
- Bansal AK: An automated comparative analysis of 17 complete microbial genomes. Bioinformatics. 1999, 15: 900-908. 10.1093/bioinformatics/15.11.900.View ArticlePubMedGoogle Scholar
- Bansal AK, Bork P, Stuckey PJ: Automated pair-wise comparisons of microbial genomes. Math Modelling Sci Comput. 1998, 9: 1-23. 10.1007/BF02404081.View ArticleGoogle Scholar
- Chan CX, Beiko RG, Darling AE, Ragan MA: Lateral transfer of genes and gene fragments in prokaryotes. Genome Biol Evol. 2009, 1: 429-438.PubMed CentralView ArticlePubMedGoogle Scholar
- Azzalini A, Menardi G, Rosolin T: pdfCluster: Cluster analysis via nonparametric density estimation (version 1.0-0). [http://cran.r-project.org/web/packages/pdfCluster/index.html]
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