Ortholog clustering on a multipartite graph

We present a method for automatically extracting groups of orthologous genes from a large set of genomes by a new clustering algorithm on a weighted multipartite graph. The method assigns a score to an arbitrary subset of genes from multiple genomes to assess the orthologous relationships between genes in the subset. This score is computed using sequence similarities between the member genes and the phylogenetic relationship between the corresponding genomes. An ortholog cluster is found as the subset with the highest score, so ortholog clustering is formulated as a combinatorial optimization problem. The algorithm for finding an ortholog cluster runs in time O(|E| + |V| log |V|), where V and E are the sets of vertices and edges, respectively, in the graph. However, if we discretize the similarity scores into a constant number of bins, the runtime improves to O(|E| + |V|). The proposed method was applied to seven complete eukaryote genomes on which the manually curated database of eukaryotic ortholog clusters, KOG, is constructed. A comparison of our results with the manually curated ortholog clusters shows that our clusters are well correlated with the existing clusters     

Automatic clustering of orthologs and inparalogs shared by multiple proteomes

MOTIVATION: The complete sequencing of many genomes has made it possible to identify orthologous genes descending from a common ancestor. However, reconstruction of evolutionary history over long time periods faces many challenges due to gene duplications and losses. Identification of orthologous groups shared by multiple proteomes therefore becomes a clustering problem in which an optimal compromise between conflicting evidences needs to be found. RESULTS: Here we present a new proteome-scale analysis program called MultiParanoid that can automatically find orthology relationships between proteins in multiple proteomes. The software is an extension of the InParanoid program that identifies orthologs and inparalogs in pairwise proteome comparisons. MultiParanoid applies a clustering algorithm to merge multiple pairwise ortholog groups from InParanoid into multi-species ortholog groups. To avoid outparalogs in the same cluster, MultiParanoid only combines species that share the same last ancestor. To validate the clustering technique, we compared the results to a reference set obtained by manual phylogenetic analysis. We further compared the results to ortholog groups in KOGs and OrthoMCL, which revealed that MultiParanoid produces substantially fewer outparalogs than these resources. AVAILABILITY: MultiParanoid is a freely available standalone program that enables efficient orthology analysis much needed in the post-genomic era. A web-based service providing access to the original datasets, the resulting groups of orthologs, and the source code of the program can be found at http://multiparanoid.cgb.ki.se.     

Automatic detection of conserved gene clusters in multiple genomes by graph comparison and P-quasi grouping

We previously reported two graph algorithms for analysis of genomic information: a graph comparison algorithm to detect locally similar regions called correlated clusters and an algorithm to find a graph feature called P-quasi complete linkage. Based on these algorithms we have developed an automatic procedure to detect conserved gene clusters and align orthologous gene orders in multiple genomes. In the first step, the graph comparison is applied to pairwise genome comparisons, where the genome is considered as a one-dimensionally connected graph with genes as its nodes, and correlated clusters of genes that share sequence similarities are identified. In the next step, the P-quasi complete linkage analysis is applied to grouping of related clusters and conserved gene clusters in multiple genomes are identified. In the last step, orthologous relations of genes are established among each conserved cluster. We analyzed 17 completely sequenced microbial genomes and obtained 2313 clusters when the completeness parameter P was 40%. About one quarter contained at least two genes that appeared in the metabolic and regulatory pathways in the KEGG database. This collection of conserved gene clusters is used to refine and augment ortholog group tables in KEGG and also to define ortholog identifiers as an extension of EC numbers.     

Attribute clustering for grouping, selection, and classification of gene expression data

This paper presents an attribute clustering method which is able to group genes based on their interdependence so as to mine meaningful patterns from the gene expression data. It can be used for gene grouping, selection, and classification. The partitioning of a relational table into attribute subgroups allows a small number of attributes within or across the groups to be selected for analysis. By clustering attributes, the search dimension of a data mining algorithm is reduced. The reduction of search dimension is especially important to data mining in gene expression data because such data typically consist of a huge number of genes (attributes) and a small number of gene expression profiles (tuples). Most data mining algorithms are typically developed and optimized to scale to the number of tuples instead of the number of attributes. The situation becomes even worse when the number of attributes overwhelms the number of tuples, in which case, the likelihood of reporting patterns that are actually irrelevant due to chances becomes rather high. It is for the aforementioned reasons that gene grouping and selection are important preprocessing steps for many data mining algorithms to be effective when applied to gene expression data. This paper defines the problem of attribute clustering and introduces a methodology to solving it. Our proposed method groups interdependent attributes into clusters by optimizing a criterion function derived from an information measure that reflects the interdependence between attributes. By applying our algorithm to gene expression data, meaningful clusters of genes are discovered. The grouping of genes based on attribute interdependence within group helps to capture different aspects of gene association patterns in each group. Significant genes selected from each group then contain useful information for gene expression classification and identification. To evaluate the performance of the proposed approach, we applied it to two well-known gene expression data sets and compared our results with those obtained by other methods. Our experiments show that the proposed method is able to find the meaningful clusters of genes. By selecting a subset of genes which have high multiple-interdependence with others within clusters, significant classification information can be obtained. Thus, a small pool of selected genes can be used to build classifiers with very high classification rate. From the pool, gene expressions of different categories can be identified.     

Appearance of new tetraspanin genes during vertebrate evolution

A detailed phylogenetic analysis of tetraspanins from 10 fully sequenced metazoan genomes and several fungal and protist genomes gives insight into their evolutionary origins and organization. Our analysis suggests that the superfamily can be divided into four large families. These four families-the CD family, CD63 family, uroplakin family, and RDS family-are further classified as consisting of several ortholog groups. The clustering of several ortholog groups together, such as the CD9/Tsp2/CD81 cluster, suggests functional relatedness of those ortholog groups. The fact that our studies are based on whole genome analysis enabled us to estimate not only the phylogenetic relationships among the tetraspanins, but also the first appearance in the tree of life of certain tetraspanin ortholog groups. Taken together, our data suggest that the tetraspanins are derived from a single (or a few) ancestral gene(s) through sequence divergence, rather than convergence, and that the majority of tetraspanins found in the human genome are vertebrate (21 instances), tetrapod (4 instances), or mammalian (6 instances) inventions.     

Complementary hierarchical clustering

When applying hierarchical clustering algorithms to cluster patient samples from microarray data, the clustering patterns generated by most algorithms tend to be dominated by groups of highly differentially expressed genes that have closely related expression patterns. Sometimes, these genes may not be relevant to the biological process under study or their functions may already be known. The problem is that these genes can potentially drown out the effects of other genes that are relevant or have novel functions. We propose a procedure called complementary hierarchical clustering that is designed to uncover the structures arising from these novel genes that are not as highly expressed. Simulation studies show that the procedure is effective when applied to a variety of examples. We also define a concept called relative gene importance that can be used to identify the influential genes in a given clustering. Finally, we analyze a microarray data set from 295 breast cancer patients, using clustering with the correlation-based distance measure. The complementary clustering reveals a grouping of the patients which is uncorrelated with a number of known prognostic signatures and significantly differing distant metastasis-free probabilities.     

Comparative genomic analysis by microbial COGs self-attraction rate

Whole genome analysis provides new perspectives to determine phylogenetic relationships among microorganisms. The availability of whole nucleotide sequences allows different levels of comparison among genomes by several approaches. In this work, self-attraction rates were considered for each cluster of orthologous groups of proteins (COGs) class in order to analyse gene aggregation levels in physical maps. Phylogenetic relationships among microorganisms were obtained by comparing self-attraction coefficients. Eighteen-dimensional vectors were computed for a set of 168 completely sequenced microbial genomes (19 archea, 149 bacteria). The components of the vector represent the aggregation rate of the genes belonging to each of 18 COGs classes. Genes involved in nonessential functions or related to environmental conditions showed the highest aggregation rates. On the contrary genes involved in basic cellular tasks showed a more uniform distribution along the genome, except for translation genes. Self-attraction clustering approach allowed classification of Proteobacteria, Bacilli and other species belonging to Firmicutes. Rearrangement and Lateral Gene Transfer events may influence divergences from classical taxonomy. Each set of COG classes’ aggregation values represents an intrinsic property of the microbial genome. This novel approach provides a new point of view for whole genome analysis and bacterial characterization.     

A systematic comparison and evaluation of biclustering methods for gene expression data

MOTIVATION: In recent years, there have been various efforts to overcome the limitations of standard clustering approaches for the analysis of gene expression data by grouping genes and samples simultaneously. The underlying concept, which is often referred to as biclustering, allows to identify sets of genes sharing compatible expression patterns across subsets of samples, and its usefulness has been demonstrated for different organisms and datasets. Several biclustering methods have been proposed in the literature; however, it is not clear how the different techniques compare with each other with respect to the biological relevance of the clusters as well as with other characteristics such as robustness and sensitivity to noise. Accordingly, no guidelines concerning the choice of the biclustering method are currently available. RESULTS: First, this paper provides a methodology for comparing and validating biclustering methods that includes a simple binary reference model. Although this model captures the essential features of most biclustering approaches, it is still simple enough to exactly determine all optimal groupings; to this end, we propose a fast divide-and-conquer algorithm (Bimax). Second, we evaluate the performance of five salient biclustering algorithms together with the reference model and a hierarchical clustering method on various synthetic and real datasets for Saccharomyces cerevisiae and Arabidopsis thaliana. The comparison reveals that (1) biclustering in general has advantages over a conventional hierarchical clustering approach, (2) there are considerable performance differences between the tested methods and (3) already the simple reference model delivers relevant patterns within all considered settings.     

Clustering of main orthologs for multiple genomes

The identification of orthologous genes shared by multiple genomes is critical for both functional and evolutionary studies in comparative genomics. While it is usually done by sequence similarity search and reconciled tree construction in practice, recently a new combinatorial approach and high-throughput system MSOAR for ortholog identification between closely related genomes based on genome rearrangement and gene duplication has been proposed in Fu et al. MSOAR assumes that orthologous genes correspond to each other in the most parsimonious evolutionary scenario, minimizing the number of genome rearrangement and (postspeciation) gene duplication events. However, the parsimony approach used by MSOAR limits it to pairwise genome comparisons. In this paper, we extend MSOAR to multiple (closely related) genomes and propose an ortholog clustering method, called MultiMSOAR, to infer main orthologs in multiple genomes. As a preliminary experiment, we apply MultiMSOAR to rat, mouse, and human genomes, and validate our results using gene annotations and gene function classifications in the public databases. We further compare our results to the ortholog clusters predicted by MultiParanoid, which is an extension of the well-known program InParanoid for pairwise genome comparisons. The comparison reveals that MultiMSOAR gives more detailed and accurate orthology information, since it can effectively distinguish main orthologs from inparalogs.     

Gene ordering in partitive clustering using microarray expressions

A central step in the analysis of gene expression data is the identification of groups of genes that exhibit similar expression patterns. Clustering and ordering the genes using gene expression data into homogeneous groups was shown to be useful in functional annotation, tissue classification, regulatory motif identification, and other applications. Although there is a rich literature on gene ordering in hierarchical clustering framework for gene expression analysis, there is no work addressing and evaluating the importance of gene ordering in partitive clustering framework, to the best knowledge of the authors. Outside the framework of hierarchical clustering, different gene ordering algorithms are applied on the whole data set, and the domain of partitive clustering is still unexplored with gene ordering approaches. A new hybrid method is proposed for ordering genes in each of the clusters obtained from partitive clustering solution, using microarray gene expressions.Two existing algorithms for optimally ordering cities in travelling salesman problem (TSP), namely, FRAG_GALK and Concorde, are hybridized individually with self organizing MAP to show the importance of gene ordering in partitive clustering framework. We validated our hybrid approach using yeast and fibroblast data and showed that our approach improves the result quality of partitive clustering solution, by identifying subclusters within big clusters, grouping functionally correlated genes within clusters, minimization of summation of gene expression distances, and the maximization of biological gene ordering using MIPS categorization. Moreover, the new hybrid approach, finds comparable or sometimes superior biological gene order in less computation time than those obtained by optimal leaf ordering in hierarchical clustering solution.     

Spectral Preprocessing for Clustering Time-Series Gene Expressions

Based on gene expression profiles, genes can be partitioned into clusters, which might be associated with biological processes or functions, for example, cell cycle, circadian rhythm, and so forth. This paper proposes a novel clustering preprocessing strategy which combines clustering with spectral estimation techniques so that the time information present in time series gene expressions is fully exploited. By comparing the clustering results with a set of biologically annotated yeast cell-cycle genes, the proposed clustering strategy is corroborated to yield significantly different clusters from those created by the traditional expression-based schemes. The proposed technique is especially helpful in grouping genes participating in time-regulated processes.     

Annotation-free delineation of prokaryotic homology groups

Phylogenomic studies of prokaryotic taxa often assume conserved marker genes are homologous across their length. However, processes such as horizontal gene transfer or gene duplication and loss may disrupt this homology by recombining only parts of genes, causing gene fission or fusion. We show using simulation that it is necessary to delineate homology groups in a set of bacterial genomes without relying on gene annotations to define the boundaries of homologous regions. To solve this problem, we have developed a graph-based algorithm to partition a set of bacterial genomes into Maximal Homologous Groups of sequences (MHGs) where each MHG is a maximal set of maximum-length sequences which are homologous across the entire sequence alignment. We applied our algorithm to a dataset of 19 Enterobacteriaceae species and found that MHGs cover much greater proportions of genomes than markers and, relatedly, are less biased in terms of the functions of the genes they cover. We zoomed in on the correlation between each individual marker and their overlapping MHGs, and show that few phylogenetic splits supported by the markers are supported by the MHGs while many marker-supported splits are contradicted by the MHGs. A comparison of the species tree inferred from marker genes with the species tree inferred from MHGs suggests that the increased bias and lack of genome coverage by markers causes incorrect inferences as to the overall relationship between bacterial taxa.     

Genomic distribution and characterization of EST-derived resistance gene analogs (RGAs) in sugarcane

A large sugarcane EST (expressed sequence tag) project recently gave us access to 261,609 EST sequences from sugarcane, assembled into 81,223 clusters. Among these, we identified 88 resistance gene analogs (RGAs) based on their homology to typical pathogen resistance genes, using a stringent BLAST search with a threshold e-value of e(-50). They included representatives of the three major groups of resistance genes with NBS/LRR, LRR or S/T KINASE domains. Fifty RGAs showed a total of 148 single-dose polymorphic RFLP markers, which could be located on the sugarcane reference genetic map (constructed in cultivar R570, 2n=approximately 115). Fifty-five SSR loci corresponding to 134 markers in R570 were also mapped to enable the classification of the various haplotypes into homology groups. Several RGA clusters were found. One cluster of two LRR-like loci mapped close to the only disease resistance gene known so far in sugarcane, which confers resistance to common rust. Detailed sequence comparison between two NBS/LRR RGA clusters in relation to their orthologs in rice and maize suggests their polyphyletic origins, and indicates that the degree of divergence between paralogous RGAs in sugarcane can be larger than that from an ortholog in a distant species.     

Clustering of multiple specific genes and gene-rich R-bands around SC-35 domains: evidence for local euchromatic neighborhoods

Typically, eukaryotic nuclei contain 10-30 prominent domains (referred to here as SC-35 domains) that are concentrated in mRNA metabolic factors. Here, we show that multiple specific genes cluster around a common SC-35 domain, which contains multiple mRNAs. Nonsyntenic genes are capable of associating with a common domain, but domain "choice" appears random, even for two coordinately expressed genes. Active genes widely separated on different chromosome arms associate with the same domain frequently, assorting randomly into the 3-4 subregions of the chromosome periphery that contact a domain. Most importantly, visualization of six individual chromosome bands showed that large genomic segments ( approximately 5 Mb) have striking differences in organization relative to domains. Certain bands showed extensive contact, often aligning with or encircling an SC-35 domain, whereas others did not. All three gene-rich reverse bands showed this more than the gene-poor Giemsa dark bands, and morphometric analyses demonstrated statistically significant differences. Similarly, late-replicating DNA generally avoids SC-35 domains. These findings suggest a functional rationale for gene clustering in chromosomal bands, which relates to nuclear clustering of genes with SC-35 domains. Rather than random reservoirs of splicing factors, or factors accumulated on an individual highly active gene, we propose a model of SC-35 domains as functional centers for a multitude of clustered genes, forming local euchromatic "neighborhoods."     

Scoring clustering solutions by their biological relevance

MOTIVATION: A central step in the analysis of gene expression data is the identification of groups of genes that exhibit similar expression patterns. Clustering gene expression data into homogeneous groups was shown to be instrumental in functional annotation, tissue classification, regulatory motif identification, and other applications. Although there is a rich literature on clustering algorithms for gene expression analysis, very few works addressed the systematic comparison and evaluation of clustering results. Typically, different clustering algorithms yield different clustering solutions on the same data, and there is no agreed upon guideline for choosing among them. RESULTS: We developed a novel statistically based method for assessing a clustering solution according to prior biological knowledge. Our method can be used to compare different clustering solutions or to optimize the parameters of a clustering algorithm. The method is based on projecting vectors of biological attributes of the clustered elements onto the real line, such that the ratio of between-groups and within-group variance estimators is maximized. The projected data are then scored using a non-parametric analysis of variance test, and the score's confidence is evaluated. We validate our approach using simulated data and show that our scoring method outperforms several extant methods, including the separation to homogeneity ratio and the silhouette measure. We apply our method to evaluate results of several clustering methods on yeast cell-cycle gene expression data. AVAILABILITY: The software is available from the authors upon request.     

Detecting clusters of different geometrical shapes in microarray gene expression data

MOTIVATION: Clustering has been used as a popular technique for finding groups of genes that show similar expression patterns under multiple experimental conditions. Many clustering methods have been proposed for clustering gene-expression data, including the hierarchical clustering, k-means clustering and self-organizing map (SOM). However, the conventional methods are limited to identify different shapes of clusters because they use a fixed distance norm when calculating the distance between genes. The fixed distance norm imposes a fixed geometrical shape on the clusters regardless of the actual data distribution. Thus, different distance norms are required for handling the different shapes of clusters. RESULTS: We present the Gustafson-Kessel (GK) clustering method for microarray gene-expression data. To detect clusters of different shapes in a dataset, we use an adaptive distance norm that is calculated by a fuzzy covariance matrix (F) of each cluster in which the eigenstructure of F is used as an indicator of the shape of the cluster. Moreover, the GK method is less prone to falling into local minima than the k-means and SOM because it makes decisions through the use of membership degrees of a gene to clusters. The algorithmic procedure is accomplished by the alternating optimization technique, which iteratively improves a sequence of sets of clusters until no further improvement is possible. To test the performance of the GK method, we applied the GK method and well-known conventional methods to three recently published yeast datasets, and compared the performance of each method using the Saccharomyces Genome Database annotations. The clustering results of the GK method are more significantly relevant to the biological annotations than those of the other methods, demonstrating its effectiveness and potential for clustering gene-expression data. AVAILABILITY: The software was developed using Java language, and can be executed on the platforms that JVM (Java Virtual Machine) is running. It is available from the authors upon request. SUPPLEMENTARY INFORMATION: Supplementary data are available at http://dragon.kaist.ac.kr/gk.     

Mixture models with multiple levels, with application to the analysis of multifactor gene expression data

Model-based clustering is a popular tool for summarizing high-dimensional data. With the number of high-throughput large-scale gene expression studies still on the rise, the need for effective data- summarizing tools has never been greater. By grouping genes according to a common experimental expression profile, we may gain new insight into the biological pathways that steer biological processes of interest. Clustering of gene profiles can also assist in assigning functions to genes that have not yet been functionally annotated. In this paper, we propose 2 model selection procedures for model-based clustering. Model selection in model-based clustering has to date focused on the identification of data dimensions that are relevant for clustering. However, in more complex data structures, with multiple experimental factors, such an approach does not provide easily interpreted clustering outcomes. We propose a mixture model with multiple levels, , that provides sparse representations both "within" and "between" cluster profiles. We explore various flexible "within-cluster" parameterizations and discuss how efficient parameterizations can greatly enhance the objective interpretability of the generated clusters. Moreover, we allow for a sparse "between-cluster" representation with a different number of clusters at different levels of an experimental factor of interest. This enhances interpretability of clusters generated in multiple-factor contexts. Interpretable cluster profiles can assist in detecting biologically relevant groups of genes that may be missed with less efficient parameterizations. We use our multilevel mixture model to mine a proliferating cell line expression data set for annotational context and regulatory motifs. We also investigate the performance of the multilevel clustering approach on several simulated data sets.