Supervised harvesting of expression trees

Background

We propose a new method for supervised learning from gene expression data. We call it 'tree harvesting'. This technique starts with a hierarchical clustering of genes, then models the outcome variable as a sum of the average expression profiles of chosen clusters and their products. It can be applied to many different kinds of outcome measures such as censored survival times, or a response falling in two or more classes (for example, cancer classes). The method can discover genes that have strong effects on their own, and genes that interact with other genes.

Results

We illustrate the method on data from a lymphoma study, and on a dataset containing samples from eight different cancers. It identified some potentially interesting gene clusters. In simulation studies we found that the procedure may require a large number of experimental samples to successfully discover interactions.

Conclusions

Tree harvesting is a potentially useful tool for exploration of gene expression data and identification of interesting clusters of genes worthy of further investigation.     

Detection of evolutionarily stable fragments of cellular pathways by hierarchical clustering of phyletic patterns

Background

Phyletic patterns denote the presence and absence of orthologous genes in completely sequenced genomes and are used to infer functional links between genes, on the assumption that genes involved in the same pathway or functional system are co-inherited by the same set of genomes. However, this basic premise has not been quantitatively tested, and the limits of applicability of the phyletic-pattern method remain unknown.

Results

We characterized a hierarchy of 3,688 phyletic patterns encompassing more than 5,000 known protein-coding genes from 66 complete microbial genomes, using different distances, clustering algorithms, and measures of cluster quality. The most sensitive set of parameters recovered 223 clusters, each consisting of genes that belong to the same metabolic pathway or functional system. Fifty-six clusters included unexpected genes with plausible functional links to the rest of the cluster. Only a small percentage of known pathways and multiprotein complexes are co-inherited as one cluster; most are split into many clusters, indicating that gene loss and displacement has occurred in the evolution of most pathways.

Conclusions

Phyletic patterns of functionally linked genes are perturbed by differential gains, losses and displacements of orthologous genes in different species, reflecting the high plasticity of microbial genomes. Groups of genes that are co-inherited can, however, be recovered by hierarchical clustering, and may represent elementary functional modules of cellular metabolism. The phyletic patterns approach alone can confidently predict the functional linkages for about 24% of the entire data set.     

Influence of microarrays experiments missing values on the stability of gene groups by hierarchical clustering

Background

Microarray technologies produced large amount of data. The hierarchical clustering is commonly used to identify clusters of co-expressed genes. However, microarray datasets often contain missing values (MVs) representing a major drawback for the use of the clustering methods. Usually the MVs are not treated, or replaced by zero or estimated by the k-Nearest Neighbor (kNN) approach. The topic of the paper is to study the stability of gene clusters, defined by various hierarchical clustering algorithms, of microarrays experiments including or not MVs.

Results

In this study, we show that the MVs have important effects on the stability of the gene clusters. Moreover, the magnitude of the gene misallocations is depending on the aggregation algorithm. The most appropriate aggregation methods (e.g. complete-linkage and Ward) are highly sensitive to MVs, and surprisingly, for a very tiny proportion of MVs (e.g. 1%). In most of the case, the MVs must be replaced by expected values. The MVs replacement by the kNN approach clearly improves the identification of co-expressed gene clusters. Nevertheless, we observe that kNN approach is less suitable for the extreme values of gene expression.

Conclusion

The presence of MVs (even at a low rate) is a major factor of gene cluster instability. In addition, the impact depends on the hierarchical clustering algorithm used. Some methods should be used carefully. Nevertheless, the kNN approach constitutes one efficient method for restoring the missing expression gene values, with a low error level. Our study highlights the need of statistical treatments in microarray data to avoid misinterpretation.

     

Model-based cluster analysis of microarray gene-expression data

Background

Microarray technologies are emerging as a promising tool for genomic studies. The challenge now is how to analyze the resulting large amounts of data. Clustering techniques have been widely applied in analyzing microarray gene-expression data. However, normal mixture model-based cluster analysis has not been widely used for such data, although it has a solid probabilistic foundation. Here, we introduce and illustrate its use in detecting differentially expressed genes. In particular, we do not cluster gene-expression patterns but a summary statistic, the t-statistic.

Results

The method is applied to a data set containing expression levels of 1,176 genes of rats with and without pneumococcal middle-ear infection. Three clusters were found, two of which contain more than 95% genes with almost no altered gene-expression levels, whereas the third one has 30 genes with more or less differential gene-expression levels.

Conclusions

Our results indicate that model-based clustering of t-statistics (and possibly other summary statistics) can be a useful statistical tool to exploit differential gene expression for microarray data.     

AGGRESCAN: a server for the prediction and evaluation of "hot spots" of aggregation in polypeptides

Background

A tremendous amount of efforts have been devoted to identifying genes for diagnosis and prognosis of diseases using microarray gene expression data. It has been demonstrated that gene expression data have cluster structure, where the clusters consist of co-regulated genes which tend to have coordinated functions. However, most available statistical methods for gene selection do not take into consideration the cluster structure.

Results

We propose a supervised group Lasso approach that takes into account the cluster structure in gene expression data for gene selection and predictive model building. For gene expression data without biological cluster information, we first divide genes into clusters using the K-means approach and determine the optimal number of clusters using the Gap method. The supervised group Lasso consists of two steps. In the first step, we identify important genes within each cluster using the Lasso method. In the second step, we select important clusters using the group Lasso. Tuning parameters are determined using V-fold cross validation at both steps to allow for further flexibility. Prediction performance is evaluated using leave-one-out cross validation. We apply the proposed method to disease classification and survival analysis with microarray data.

Conclusion

We analyze four microarray data sets using the proposed approach: two cancer data sets with binary cancer occurrence as outcomes and two lymphoma data sets with survival outcomes. The results show that the proposed approach is capable of identifying a small number of influential gene clusters and important genes within those clusters, and has better prediction performance than existing methods.     

OSIRISv1.2: A named entity recognition system for sequence variants of genes in biomedical literature

Background

The hierarchical clustering tree (HCT) with a dendrogram [1] and the singular value decomposition (SVD) with a dimension-reduced representative map [2] are popular methods for two-way sorting the gene-by-array matrix map employed in gene expression profiling. While HCT dendrograms tend to optimize local coherent clustering patterns, SVD leading eigenvectors usually identify better global grouping and transitional structures.

Results

This study proposes a flipping mechanism for a conventional agglomerative HCT using a rank-two ellipse (R2E, an improved SVD algorithm for sorting purpose) seriation by Chen [3] as an external reference. While HCTs always produce permutations with good local behaviour, the rank-two ellipse seriation gives the best global grouping patterns and smooth transitional trends. The resulting algorithm automatically integrates the desirable properties of each method so that users have access to a clustering and visualization environment for gene expression profiles that preserves coherent local clusters and identifies global grouping trends.

Conclusion

We demonstrate, through four examples, that the proposed method not only possesses better numerical and statistical properties, it also provides more meaningful biomedical insights than other sorting algorithms. We suggest that sorted proximity matrices for genes and arrays, in addition to the gene-by-array expression matrix, can greatly aid in the search for comprehensive understanding of gene expression structures. Software for the proposed methods can be obtained at http://gap.stat.sinica.edu.tw/Software/GAP.     

A robust approach based on Weibull distribution for clustering gene expression data

Background

Clustering is a widely used technique for analysis of gene expression data. Most clustering methods group genes based on the distances, while few methods group genes according to the similarities of the distributions of the gene expression levels. Furthermore, as the biological annotation resources accumulated, an increasing number of genes have been annotated into functional categories. As a result, evaluating the performance of clustering methods in terms of the functional consistency of the resulting clusters is of great interest.

Results

In this paper, we proposed the WDCM (Weibull Distribution-based Clustering Method), a robust approach for clustering gene expression data, in which the gene expressions of individual genes are considered as the random variables following unique Weibull distributions. Our WDCM is based on the concept that the genes with similar expression profiles have similar distribution parameters, and thus the genes are clustered via the Weibull distribution parameters. We used the WDCM to cluster three cancer gene expression data sets from the lung cancer, B-cell follicular lymphoma and bladder carcinoma and obtained well-clustered results. We compared the performance of WDCM with k-means and Self Organizing Map (SOM) using functional annotation information given by the Gene Ontology (GO). The results showed that the functional annotation ratios of WDCM are higher than those of the other methods. We also utilized the external measure Adjusted Rand Index to validate the performance of the WDCM. The comparative results demonstrate that the WDCM provides the better clustering performance compared to k-means and SOM algorithms. The merit of the proposed WDCM is that it can be applied to cluster incomplete gene expression data without imputing the missing values. Moreover, the robustness of WDCM is also evaluated on the incomplete data sets.

Conclusions

The results demonstrate that our WDCM produces clusters with more consistent functional annotations than the other methods. The WDCM is also verified to be robust and is capable of clustering gene expression data containing a small quantity of missing values.     

TILLING in the two-rowed barley cultivar 'Barke' reveals preferred sites of functional diversity in the gene HvHox1

Background

Many clustering procedures only allow the user to input a pairwise dissimilarity or distance measure between objects. We propose a clustering method that can input a multi-point dissimilarity measure d(i1, i2, ..., iP) where the number of points P can be larger than 2. The work is motivated by gene network analysis where clusters correspond to modules of highly interconnected nodes. Here, we define modules as clusters of network nodes with high multi-node topological overlap. The topological overlap measure is a robust measure of interconnectedness which is based on shared network neighbors. In previous work, we have shown that the multi-node topological overlap measure yields biologically meaningful results when used as input of network neighborhood analysis.

Findings

We adapt network neighborhood analysis for the use of module detection. We propose the Module Affinity Search Technique (MAST), which is a generalized version of the Cluster Affinity Search Technique (CAST). MAST can accommodate a multi-node dissimilarity measure. Clusters grow around user-defined or automatically chosen seeds (e.g. hub nodes). We propose both local and global cluster growth stopping rules. We use several simulations and a gene co-expression network application to argue that the MAST approach leads to biologically meaningful results. We compare MAST with hierarchical clustering and partitioning around medoid clustering.

Conclusion

Our flexible module detection method is implemented in the MTOM software which can be downloaded from the following webpage: http://www.genetics.ucla.edu/labs/horvath/MTOM/     

Transient process of cortical activity during Necker cube perception: from local clusters to global synchrony

Background

It has been discussed that neural phase-synchrony across distant cortical areas (or global phase-synchrony) was correlated with various aspects of consciousness. The generating process of the synchrony, however, remains largely unknown. As a first step, we investigate transient process of global phase-synchrony, focusing on phase-synchronized clusters. We hypothesize that the phase-synchronized clusters are dynamically organized before global synchrony and clustering patterns depend on perceptual conditions.

Methods

In an EEG study, Kitajo reported that phase-synchrony across distant cortical areas was selectively enhanced by top-down attention around 4 Hz in Necker cube perception. Here, we further analyzed the phase-synchronized clusters using hierarchical clustering which sequentially binds up the nearest electrodes based on similarity of phase locking between the cortical signals. First, we classified dominant components of the phase-synchronized clusters over time. We then investigated how the phase-synchronized clusters change with time, focusing on their size and spatial structure.

Results

Phase-locked clusters organized a stable spatial pattern common to the perceptual conditions. In addition, the phase-locked clusters were modulated transiently depending on the perceptual conditions and the time from the perceptual switch. When top-down attention succeeded in switching perception as subjects intended, independent clusters at frontal and occipital areas grew to connect with each other around the time of the perceptual switch. However, the clusters in the occipital and left parietal areas remained divided when top-down attention failed in switching perception. When no primary biases exist, the cluster in the occipital area grew to its maximum at the time of the perceptual switch within the occipital area.

Conclusions

Our study confirmed the existence of stable phase-synchronized clusters. Furthermore, these clusters were transiently connected with each other. The connecting pattern depended on subjects’ internal states. These results suggest that subjects’ attentional states are associated with distinct spatio-temporal patterns of the phase-locked clusters.

     

Structural interpretation of protein-protein interaction network

Background

Currently a huge amount of protein-protein interaction data is available from high throughput experimental methods. In a large network of protein-protein interactions, groups of proteins can be identified as functional clusters having related functions where a single protein can occur in multiple clusters. However experimental methods are error-prone and thus the interactions in a functional cluster may include false positives or there may be unreported interactions. Therefore correctly identifying a functional cluster of proteins requires the knowledge of whether any two proteins in a cluster interact, whether an interaction can exclude other interactions, or how strong the affinity between two interacting proteins is.

Methods

In the present work the yeast protein-protein interaction network is clustered using a spectral clustering method proposed by us in 2006 and the individual clusters are investigated for functional relationships among the member proteins. 3D structural models of the proteins in one cluster have been built – the protein structures are retrieved from the Protein Data Bank or predicted using a comparative modeling approach. A rigid body protein docking method (Cluspro) is used to predict the protein-protein interaction complexes. Binding sites of the docked complexes are characterized by their buried surface areas in the docked complexes, as a measure of the strength of an interaction.

Results

The clustering method yields functionally coherent clusters. Some of the interactions in a cluster exclude other interactions because of shared binding sites. New interactions among the interacting proteins are uncovered, and thus higher order protein complexes in the cluster are proposed. Also the relative stability of each of the protein complexes in the cluster is reported.

Conclusions

Although the methods used are computationally expensive and require human intervention and judgment, they can identify the interactions that could occur together or ones that are mutually exclusive. In addition indirect interactions through another intermediate protein can be identified. These theoretical predictions might be useful for crystallographers to select targets for the X-ray crystallographic determination of protein complexes.

     

Spatial analysis of BSE cases in the Netherlands

Background

In many of the European countries affected by Bovine Spongiform Encephalopathy (BSE), case clustering patterns have been observed. Most of these patterns have been interpreted in terms of heterogeneities in exposure of cattle to the BSE agent. Here we investigate whether spatial clustering is present in the Dutch BSE case data.

Results

We have found three spatial case clusters in the Dutch BSE epidemic. The clusters are geographically distinct and each cluster appears in a different birth cohort. When testing all birth cohorts together, only one significant cluster was detected. The fact that we found stronger spatial clustering when using a cohort-based analysis, is consistent with the evidence that most BSE infections occur in animals less than 12 or 18 months old.

Conclusion

Significant spatial case clustering is present in the Dutch BSE epidemic. The spatial clusters of BSE cases are most likely due to time-dependent heterogeneities in exposure related to feed production.

     

Reordering hierarchical tree based on bilateral symmetric distance

Background

In microarray data analysis, hierarchical clustering (HC) is often used to group samples or genes according to their gene expression profiles to study their associations. In a typical HC, nested clustering structures can be quickly identified in a tree. The relationship between objects is lost, however, because clusters rather than individual objects are compared. This results in a tree that is hard to interpret.

Methodology/Principal Findings

This study proposes an ordering method, HC-SYM, which minimizes bilateral symmetric distance of two adjacent clusters in a tree so that similar objects in the clusters are located in the cluster boundaries. The performance of HC-SYM was evaluated by both supervised and unsupervised approaches and compared favourably with other ordering methods.

Conclusions/Significance

The intuitive relationship between objects and flexibility of the HC-SYM method can be very helpful in the exploratory analysis of not only microarray data but also similar high-dimensional data.     

A multiple kernel density clustering algorithm for incomplete datasets in bioinformatics

Background

While there are a large number of bioinformatics datasets for clustering, many of them are incomplete, i.e., missing attribute values in some data samples needed by clustering algorithms. A variety of clustering algorithms have been proposed in the past years, but they usually are limited to cluster on the complete dataset. Besides, conventional clustering algorithms cannot obtain a trade-off between accuracy and efficiency of the clustering process since many essential parameters are determined by the human user’s experience.

Results

The paper proposes a Multiple Kernel Density Clustering algorithm for Incomplete datasets called MKDCI. The MKDCI algorithm consists of recovering missing attribute values of input data samples, learning an optimally combined kernel for clustering the input dataset, reducing dimensionality with the optimal kernel based on multiple basis kernels, detecting cluster centroids with the Isolation Forests method, assigning clusters with arbitrary shape and visualizing the results.

Conclusions

Extensive experiments on several well-known clustering datasets in bioinformatics field demonstrate the effectiveness of the proposed MKDCI algorithm. Compared with existing density clustering algorithms and parameter-free clustering algorithms, the proposed MKDCI algorithm tends to automatically produce clusters of better quality on the incomplete dataset in bioinformatics.

     

Model-based analysis of oligonucleotide arrays: model validation, design issues and standard error application

Background

A model-based analysis of oligonucleotide expression arrays we developed previously uses a probe-sensitivity index to capture the response characteristic of a specific probe pair and calculates model-based expression indexes (MBEI). MBEI has standard error attached to it as a measure of accuracy. Here we investigate the stability of the probe-sensitivity index across different tissue types, the reproducibility of results in replicate experiments, and the use of MBEI in perfect match (PM)-only arrays.

Results

Probe-sensitivity indexes are stable across tissue types. The target gene's presence in many arrays of an array set allows the probe-sensitivity index to be estimated accurately. We extended the model to obtain expression values for PM-only arrays, and found that the 20-probe PM-only model is comparable to the 10-probe PM/MM difference model, in terms of the expression correlations with the original 20-probe PM/MM difference model. MBEI method is able to extend the reliable detection limit of expression to a lower mRNA concentration. The standard errors of MBEI can be used to construct confidence intervals of fold changes, and the lower confidence bound of fold change is a better ranking statistic for filtering genes. We can assign reliability indexes for genes in a specific cluster of interest in hierarchical clustering by resampling clustering trees. A software dChip implementing many of these analysis methods is made available.

Conclusions

The model-based approach reduces the variability of low expression estimates, and provides a natural method of calculating expression values for PM-only arrays. The standard errors attached to expression values can be used to assess the reliability of downstream analysis.