Network constrained clustering for gene microarray data

Many bioinformatics problems can be tackled from a fresh angle offered by the network perspective. Directly inspired by metabolic network structural studies, we propose an improved gene clustering approach for inferring gene signaling pathways from gene microarray data. Based on the construction of co-expression networks that consists of both significantly linear and non-linear gene associations together with controlled biological and statistical significance, our approach tends to group functionally related genes into tight clusters despite their expression dissimilarities. We illustrate our approach and compare it to the traditional clustering approaches on a yeast galactose metabolism dataset and a retinal gene expression dataset. Our approach greatly outperforms the traditional approach in rediscovering the relatively well known galactose metabolism pathway in yeast and in clustering genes of the photoreceptor differentiation pathway. AVAILABILITY: The clustering method has been implemented in an R package "GeneNT" that is freely available from: http://www.cran.org.     

From hormones to secondary metabolism: the emergence of metabolic gene clusters in plants

Gene clusters for the synthesis of secondary metabolites are a common feature of microbial genomes. Well-known examples include clusters for the synthesis of antibiotics in actinomycetes, and also for the synthesis of antibiotics and toxins in filamentous fungi. Until recently it was thought that genes for plant metabolic pathways were not clustered, and this is certainly true in many cases; however, five plant secondary metabolic gene clusters have now been discovered, all of them implicated in synthesis of defence compounds. An obvious assumption might be that these eukaryotic gene clusters have arisen by horizontal gene transfer from microbes, but there is compelling evidence to indicate that this is not the case. This raises intriguing questions about how widespread such clusters are, what the significance of clustering is, why genes for some metabolic pathways are clustered and those for others are not, and how these clusters form. In answering these questions we may hope to learn more about mechanisms of genome plasticity and adaptive evolution in plants. It is noteworthy that for the five plant secondary metabolic gene clusters reported so far, the enzymes for the first committed steps all appear to have been recruited directly or indirectly from primary metabolic pathways involved in hormone synthesis. This may or may not turn out to be a common feature of plant secondary metabolic gene clusters as new clusters emerge.     

Weighted rank aggregation of cluster validation measures: a Monte Carlo cross-entropy approach

MOTIVATION: Biologists often employ clustering techniques in the explorative phase of microarray data analysis to discover relevant biological groupings. Given the availability of numerous clustering algorithms in the machine-learning literature, an user might want to select one that performs the best for his/her data set or application. While various validation measures have been proposed over the years to judge the quality of clusters produced by a given clustering algorithm including their biological relevance, unfortunately, a given clustering algorithm can perform poorly under one validation measure while outperforming many other algorithms under another validation measure. A manual synthesis of results from multiple validation measures is nearly impossible in practice, especially, when a large number of clustering algorithms are to be compared using several measures. An automated and objective way of reconciling the rankings is needed. RESULTS: Using a Monte Carlo cross-entropy algorithm, we successfully combine the ranks of a set of clustering algorithms under consideration via a weighted aggregation that optimizes a distance criterion. The proposed weighted rank aggregation allows for a far more objective and automated assessment of clustering results than a simple visual inspection. We illustrate our procedure using one simulated as well as three real gene expression data sets from various platforms where we rank a total of eleven clustering algorithms using a combined examination of 10 different validation measures. The aggregate rankings were found for a given number of clusters k and also for an entire range of k. AVAILABILITY: R code for all validation measures and rank aggregation is available from the authors upon request. SUPPLEMENTARY INFORMATION: Supplementary information are available at http://www.somnathdatta.org/Supp/RankCluster/supp.htm.     

Entropy-based cluster validation and estimation of the number of clusters in gene expression data

Many external and internal validity measures have been proposed in order to estimate the number of clusters in gene expression data but as a rule they do not consider the analysis of the stability of the groupings produced by a clustering algorithm. Based on the approach assessing the predictive power or stability of a partitioning, we propose the new measure of cluster validation and the selection procedure to determine the suitable number of clusters. The validity measure is based on the estimation of the "clearness" of the consensus matrix, which is the result of a resampling clustering scheme or consensus clustering. According to the proposed selection procedure the stable clustering result is determined with the reference to the validity measure for the null hypothesis encoding for the absence of clusters. The final number of clusters is selected by analyzing the distance between the validity plots for initial and permutated data sets. We applied the selection procedure to estimate the clustering results on several datasets. As a result the proposed procedure produced an accurate and robust estimate of the number of clusters, which are in agreement with the biological knowledge and gold standards of cluster quality.     

Co-clustering of biological networks and gene expression data

MOTIVATION: Large scale gene expression data are often analysed by clustering genes based on gene expression data alone, though a priori knowledge in the form of biological networks is available. The use of this additional information promises to improve exploratory analysis considerably. RESULTS: We propose constructing a distance function which combines information from expression data and biological networks. Based on this function, we compute a joint clustering of genes and vertices of the network. This general approach is elaborated for metabolic networks. We define a graph distance function on such networks and combine it with a correlation-based distance function for gene expression measurements. A hierarchical clustering and an associated statistical measure is computed to arrive at a reasonable number of clusters. Our method is validated using expression data of the yeast diauxic shift. The resulting clusters are easily interpretable in terms of the biochemical network and the gene expression data and suggest that our method is able to automatically identify processes that are relevant under the measured conditions.     

特征代谢通路上的基因表达相关性及共调控表达模式

利用随机森林-通路分析法,通过袋外样本OOB的分类错误率筛选特征代谢通路,在特征通路上作基因表达相关性研究并对通路上的基因采用MAP(Mining attribute profile)算法挖掘不同实验条件下基因的共调控表达模式,对共调控表达模式进行聚类.分析结果显示同一特征代谢通路上的基因表达倾向相似,有2条特征代谢通路存在共表达模式.其中一条通路含108个表达模式,对这些模式进行聚类,其最低聚类的相似系数仍高达0.623.说明同一特征代谢通路上的基因共表达模式在不同实验条件下仍具有高度的相似性.对以通路作为基因模块进行复杂疾病的研究具有借鉴意义.     

Robust cluster analysis of microarray gene expression data with the number of clusters determined biologically

MOTIVATION: The success of each method of cluster analysis depends on how well its underlying model describes the patterns of expression. Outlier-resistant and distribution-insensitive clustering of genes are robust against violations of model assumptions. RESULTS: A measure of dissimilarity that combines advantages of the Euclidean distance and the correlation coefficient is introduced. The measure can be made robust using a rank order correlation coefficient. A robust graphical method of summarizing the results of cluster analysis and a biological method of determining the number of clusters are also presented. These methods are applied to a public data set, showing that rank-based methods perform better than log-based methods. AVAILABILITY: Software is available from http://www.davidbickel.com.     

The correlation of gene expression and co-regulated gene patterns in characteristic KEGG pathways

There is great interest in chromosome- and pathway-based techniques for genomics data analysis in the current work in order to understand the mechanism of disease. However, there are few studies addressing the abilities of machine learning methods in incorporating pathway information for analyzing microarray data. In this paper, we identified the characteristic pathways by combining the classification error rates of out-of-bag (OOB) in random forests with pathways information. At each characteristic pathway, the correlation of gene expression was studied and the co-regulated gene patterns in different biological conditions were mined by Mining Attribute Profile (MAP) algorithm. The discovered co-regulated gene patterns were clustered by the average-linkage hierarchical clustering technique. The results showed that the expression of genes at the same characteristic pathway were approximate. Furthermore, two characteristic pathways were discovered to present co-regulated gene patterns in which one contained 108 patterns and the other contained one pattern. The results of cluster analysis showed that the smallest similarity coefficient of clusters was more than 0.623, which indicated that the co-regulated patterns in different biological conditions were more approximate at the same characteristic pathway. The methods discussed in this paper can provide additional insight into the study of microarray data.     

Data-Fusion in Clustering Microarray Data: Balancing Discovery and Interpretability

While clustering genes remains one of the most popular exploratory tools for expression data, it often results in a highly variable and biologically uninformative clusters. This paper explores a data fusion approach to clustering microarray data. Our method, which combined expression data and Gene Ontology (GO)-derived information, is applied on a real data set to perform genome-wide clustering. A set of novel tools is proposed to validate the clustering results and pick a fair value of infusion coefficient. These tools measure stability, biological relevance, and distance from the expression-only clustering solution. Our results indicate that a data-fusion clustering leads to more stable, biologically relevant clusters that are still representative of the experimental data.     

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.     

Genomic profiling of cortical neurons following exposure to beta-amyloid

In vitro and in vivo studies have shown that beta-amyloid peptide induces neuronal cell death. To explore the molecular basis underlying beta-amyloid-induced toxicity, we analyzed gene expression profiles of cultured rat cortical neurons treated for 24 and 48 h with synthetic beta-amyloid peptide. From the 8740 genes interrogated by oligonucleotide microarray analysis, 241 genes were found to be differentially expressed and segregated into distinct clusters. Functional clustering based on gene ontologies showed coordinated expression of genes with common biological functions and metabolic pathways. The comparison with genes differentially expressed in cerebellar granule neurons following serum and potassium deprivation indicates the existence of common regulatory mechanisms underlying neuronal cell death. Our results offer a genomic view of the changes that accompany beta-amyloid-induced neurodegeneration.     

Wrangling Phosphoproteomic Data to Elucidate Cancer Signaling Pathways

The interpretation of biological data sets is essential for generating hypotheses that guide research, yet modern methods of global analysis challenge our ability to discern meaningful patterns and then convey results in a way that can be easily appreciated. Proteomic data is especially challenging because mass spectrometry detectors often miss peptides in complex samples, resulting in sparsely populated data sets. Using the R programming language and techniques from the field of pattern recognition, we have devised methods to resolve and evaluate clusters of proteins related by their pattern of expression in different samples in proteomic data sets. We examined tyrosine phosphoproteomic data from lung cancer samples. We calculated dissimilarities between the proteins based on Pearson or Spearman correlations and on Euclidean distances, whilst dealing with large amounts of missing data. The dissimilarities were then used as feature vectors in clustering and visualization algorithms. The quality of the clusterings and visualizations were evaluated internally based on the primary data and externally based on gene ontology and protein interaction networks. The results show that t-distributed stochastic neighbor embedding (t-SNE) followed by minimum spanning tree methods groups sparse proteomic data into meaningful clusters more effectively than other methods such as k-means and classical multidimensional scaling. Furthermore, our results show that using a combination of Spearman correlation and Euclidean distance as a dissimilarity representation increases the resolution of clusters. Our analyses show that many clusters contain one or more tyrosine kinases and include known effectors as well as proteins with no known interactions. Visualizing these clusters as networks elucidated previously unknown tyrosine kinase signal transduction pathways that drive cancer. Our approach can be applied to other data types, and can be easily adopted because open source software packages are employed.     

Using Hierarchical Clustering and Dendrograms to Quantify the Clustering of Membrane Proteins

Cell biologists have developed methods to label membrane proteins with gold nanoparticles and then extract spatial point patterns of the gold particles from transmission electron microscopy images using image processing software. Previously, the resulting patterns were analyzed using the Hopkins statistic, which distinguishes nonclustered from modestly and highly clustered distributions, but is not designed to quantify the number or sizes of the clusters. Clusters were defined by the partitional clustering approach which required the choice of a distance. Two points from a pattern were put in the same cluster if they were closer than this distance. In this study, we present a new methodology based on hierarchical clustering to quantify clustering. An intrinsic distance is computed, which is the distance that produces the maximum number of clusters in the biological data, eliminating the need to choose a distance. To quantify the extent of clustering, we compare the clustering distance between the experimental data being analyzed with that from simulated random data. Results are then expressed as a dimensionless number, the clustering ratio that facilitates the comparison of clustering between experiments. Replacing the chosen cluster distance by the intrinsic clustering distance emphasizes densely packed clusters that are likely more important to downstream signaling events.     

Distinct Protein Classes in Human Red Cell Proteome Revealed by Similarity of Phylogenetic Profiles

The minimal set of proteins necessary to maintain a vertebrate cell forms an interesting core of cellular machinery. The known proteome of human red blood cell consists of about 1400 proteins. We treated this protein complement of one of the simplest human cells as a model and asked the questions on its function and origins. The proteome was mapped onto phylogenetic profiles, i.e. vectors of species possessing homologues of human proteins. A novel clustering approach was devised, utilising similarity in the phylogenetic spread of homologues as distance measure. The clustering based on phylogenetic profiles yielded several distinct protein classes differing in phylogenetic taxonomic spread, presumed evolutionary history and functional properties. Notably, small clusters of proteins common to vertebrates or Metazoa and other multicellular eukaryotes involve biological functions specific to multicellular organisms, such as apoptosis or cell-cell signaling, respectively. Also, a eukaryote-specific cluster is identified, featuring GTP-ase signalling and ubiquitination. Another cluster, made up of proteins found in most organisms, including bacteria and archaea, involves basic molecular functions such as oxidation-reduction and glycolysis. Approximately one third of erythrocyte proteins do not fall in any of the clusters, reflecting the complexity of protein evolution in comparison to our simple model. Basically, the clustering obtained divides the proteome into old and new parts, the former originating from bacterial ancestors, the latter from inventions within multicellular eukaryotes. Thus, the model human cell proteome appears to be made up of protein sets distinct in their history and biological roles. The current work shows that phylogenetic profiles concept allows protein clustering in a way relevant both to biological function and evolutionary history.