Analysis of temporal gene expression profiles: clustering by simulated annealing and determining the optimal number of clusters

MOTIVATION: Cluster analysis of genome-wide expression data from DNA microarray hybridization studies has proved to be a useful tool for identifying biologically relevant groupings of genes and samples. In the present paper, we focus on several important issues related to clustering algorithms that have not yet been fully studied. RESULTS: We describe a simple and robust algorithm for the clustering of temporal gene expression profiles that is based on the simulated annealing procedure. In general, this algorithm guarantees to eventually find the globally optimal distribution of genes over clusters. We introduce an iterative scheme that serves to evaluate quantitatively the optimal number of clusters for each specific data set. The scheme is based on standard approaches used in regular statistical tests. The basic idea is to organize the search of the optimal number of clusters simultaneously with the optimization of the distribution of genes over clusters. The efficiency of the proposed algorithm has been evaluated by means of a reverse engineering experiment, that is, a situation in which the correct distribution of genes over clusters is known a priori. The employment of this statistically rigorous test has shown that our algorithm places greater than 90% genes into correct clusters. Finally, the algorithm has been tested on real gene expression data (expression changes during yeast cell cycle) for which the fundamental patterns of gene expression and the assignment of genes to clusters are well understood from numerous previous studies.     

More taxa or more characters revisited: combining data from nuclear protein-encoding genes for phylogenetic analyses of Noctuoidea (Insecta: Lepidoptera)

A central question concerning data collection strategy for molecular phylogenies has been, is it better to increase the number of characters or the number of taxa sampled to improve the robustness of a phylogeny estimate? A recent simulation study concluded that increasing the number of taxa sampled is preferable to increasing the number of nucleotide characters, if taxa are chosen specifically to break up long branches. We explore this hypothesis by using empirical data from noctuoid moths, one of the largest superfamilies of insects. Separate studies of two nuclear genes, elongation factor-1 alpha (EF-1 alpha) and dopa decarboxylase (DDC), have yielded similar gene trees and high concordance with morphological groupings for 49 exemplar species. However, support levels were quite low for nodes deeper than the subfamily level. We tested the effects on phylogenetic signal of (1) increasing the taxon sampling by nearly 60%, to 77 species, and (2) combining data from the two genes in a single analysis. Surprisingly, the increased taxon sampling, although designed to break up long branches, generated greater disagreement between the two gene data sets and decreased support levels for deeper nodes. We appear to have inadvertently introduced new long branches, and breaking these up may require a yet larger taxon sample. Sampling additional characters (combining data) greatly increased the phylogenetic signal. To contrast the potential effect of combining data from independent genes with collection of the same total number of characters from a single gene, we simulated the latter by bootstrap augmentation of the single-gene data sets. Support levels for combined data were at least as high as those for the bootstrap-augmented data set for DDC and were much higher than those for the augmented EF-1 alpha data set. This supports the view that in obtaining additional sequence data to solve a refractory systematic problem, it is prudent to take them from an independent gene.     

Feature Selection for high Dimensional DNA Microarray data using hybrid approaches

Feature selection from DNA microarray data is a major challenge due to high dimensionality in expression data. The number of samples in the microarray data set is much smaller compared to the number of genes. Hence the data is improper to be used as the training set of a classifier. Therefore it is important to select features prior to training the classifier. It should be noted that only a small subset of genes from the data set exhibits a strong correlation with the class. This is because finding the relevant genes from the data set is often non-trivial. Thus there is a need to develop robust yet reliable methods for gene finding in expression data. We describe the use of several hybrid feature selection approaches for gene finding in expression data. These approaches include filtering (filter out the best genes from the data set) and wrapper (best subset of genes from the data set) phases. The methods use information gain (IG) and Pearson Product Moment Correlation (PPMC) as the filtering parameters and biogeography based optimization (BBO) as the wrapper approach. K nearest neighbour algorithm (KNN) and back propagation neural network are used for evaluating the fitness of gene subsets during feature selection. Our analysis shows that an impressive performance is provided by the IG-BBO-KNN combination in different data sets with high accuracy (>90%) and low error rate.     

Can deliberately incomplete gene sample augmentation improve a phylogeny estimate for the advanced moths and butterflies (Hexapoda: Lepidoptera)?

This paper addresses the question of whether one can economically improve the robustness of a molecular phylogeny estimate by increasing gene sampling in only a subset of taxa, without having the analysis invalidated by artifacts arising from large blocks of missing data. Our case study stems from an ongoing effort to resolve poorly understood deeper relationships in the large clade Ditrysia ( > 150,000 species) of the insect order Lepidoptera (butterflies and moths). Seeking to remedy the overall weak support for deeper divergences in an initial study based on five nuclear genes (6.6 kb) in 123 exemplars, we nearly tripled the total gene sample (to 26 genes, 18.4 kb) but only in a third (41) of the taxa. The resulting partially augmented data matrix (45% intentionally missing data) consistently increased bootstrap support for groupings previously identified in the five-gene (nearly) complete matrix, while introducing no contradictory groupings of the kind that missing data have been predicted to produce. Our results add to growing evidence that data sets differing substantially in gene and taxon sampling can often be safely and profitably combined. The strongest overall support for nodes above the family level came from including all nucleotide changes, while partitioning sites into sets undergoing mostly nonsynonymous versus mostly synonymous change. In contrast, support for the deepest node for which any persuasive molecular evidence has yet emerged (78-85% bootstrap) was weak or nonexistent unless synonymous change was entirely excluded, a result plausibly attributed to compositional heterogeneity. This node (Gelechioidea + Apoditrysia), tentatively proposed by previous authors on the basis of four morphological synapomorphies, is the first major subset of ditrysian superfamilies to receive strong statistical support in any phylogenetic study. A "more-genes-only" data set (41 taxa×26 genes) also gave strong signal for a second deep grouping (Macrolepidoptera) that was obscured, but not strongly contradicted, in more taxon-rich analyses.     

Tests for gene clustering.

Comparing chromosomal gene order in two or more related species is an important approach to studying the forces that guide genome organization and evolution. Linked clusters of similar genes found in related genomes are often used to support arguments of evolutionary relatedness or functional selection. However, as the gene order and the gene complement of sister genomes diverge progressively due to large scale rearrangements, horizontal gene transfer, gene duplication and gene loss, it becomes increasingly difficult to determine whether observed similarities in local genomic structure are indeed remnants of common ancestral gene order, or are merely coincidences. A rigorous comparative genomics requires principled methods for distinguishing chance commonalities, within or between genomes, from genuine historical or functional relationships. In this paper, we construct tests for significant groupings against null hypotheses of random gene order, taking incomplete clusters, multiple genomes, and gene families into account. We consider both the significance of individual clusters of prespecified genes and the overall degree of clustering in whole genomes.     

Identification of novel stem cell markers using gap analysis of gene expression data

We describe a method for detecting marker genes in large heterogeneous collections of gene expression data. Markers are identified and characterized by the existence of demarcations in their expression values across the whole dataset, which suggest the presence of groupings of samples. We apply this method to DNA microarray data generated from 83 mouse stem cell related samples and describe 426 selected markers associated with differentiation to establish principles of stem cell evolution.     

An ensemble method for gene discovery based on DNA microarray data

DNA microarrays are now able to measure the expressions of thousands of genes simultaneously. These measurements or gene profiling provides a snapshot?of life that maps to a cross section of ge-netic activities in a four-dimension space of time and the biological entity. Although recent microarray ex-periments[1, 2] hold the promise of the innovative tech-nology to cast new insights onto discovery of secrets of life, development of powerful and efficient analysis strategies for microarray dat…     

An ensemble method for gene discovery based on DNA microarray data

The advent of DNA microarray technology has offered the promise of casting new insights onto deciphering secrets of life by monitoring activities of thousands of genes simultaneously. Current analyses of microarray data focus on precise classification of biological types, for example, tumor versus normal tissues. A further scientific challenging task is to extract disease-relevant genes from the bewildering amounts of raw data, which is one of the most critical themes in the post-genomic era, but it is generally ignored due to lack of an efficient approach. In this paper, we present a novel ensemble method for gene extraction that can be tailored to fulfill multiple biological tasks including (i) precise classification of biological types; (ii) disease gene mining; and (iii) target-driven gene networking. We also give a numerical application for(i) and (ii) using a public microarrary data set and set aside a separate paper to address (iii).     

Shaking the Diptera tree of life: performance analysis of nuclear and mitochondrial sequence data partitions

The value of mitochondrial versus nuclear gene sequence data in phylogenetic analysis has received much attention without yielding definitive conclusions. Theoretical arguments and empirical data suggest a lower phylogenetic utility than equivalent nuclear gene sequences, but there are many examples of important progress made using mitochondrial sequences. We undertook a systematic performance analysis of mitochondrial and nuclear sequence partitions taken from a representative sample of dipteran species. When analysed alone, mitochondrial genes generally performed less well than nuclear genes; however, these genes resolved some branches for which nuclear genes failed. Moreover, the combined use of mitochondrial and nuclear sequences produced superior results without artifacts for nodes where mitochondrial and nuclear gene data generated conflicting topologies. These findings strongly advocate the inclusion of mitochondrial sequences, even in deep phylogeny reconstruction. Comparison of tree support between our and previous analyses identified robustly supported high‐confidence clades in the Diptera, but also revealed problematic groupings in need of further analysis.     

Evidence for diversity in transcriptional profiles of single hematopoietic stem cells

Hematopoietic stem cells replenish all the cells of the blood throughout the lifetime of an animal. Although thousands of stem cells reside in the bone marrow, only a few contribute to blood production at any given time. Nothing is known about the differences between individual stem cells that dictate their particular state of activation readiness. To examine such differences between individual stem cells, we determined the global gene expression profile of 12 single stem cells using microarrays. We showed that at least half of the genetic expression variability between 12 single cells profiled was due to biological variation in 44% of the genes analyzed. We also identified specific genes with high biological variance that are candidates for influencing the state of readiness of individual hematopoietic stem cells, and confirmed the variability of a subset of these genes using single-cell real-time PCR. Because apparent variation of some genes is likely due to technical factors, we estimated the degree of biological versus technical variation for each gene using identical RNA samples containing an RNA amount equivalent to that of single cells. This enabled us to identify a large cohort of genes with low technical variability whose expression can be reliably measured on the arrays at the single-cell level. These data have established that gene expression of individual stem cells varies widely, despite extremely high phenotypic homogeneity. Some of this variation is in key regulators of stem cell activity, which could account for the differential responses of particular stem cells to exogenous stimuli. The capacity to accurately interrogate individual cells for global gene expression will facilitate a systems approach to biological processes at a single-cell level.     

Algorithm to find gene expression profiles of deregulation and identify families of disease-altered genes

MOTIVATION: Alteration of gene expression often results in up- or down-regulated genes and the most common analysis strategies look for such differentially expressed genes. However, molecular disease mechanisms typically constitute abnormalities in the regulation of genes producing strong alterations in the expression levels. The search for such deregulation states in the genomic expression profiles will help to identify disease-altered genes better. RESULTS: We have developed an algorithm that searches for the genes which present a significant alteration in the variability of their expression profiles, by comparing an altered state with a control state. The algorithm provides groups of genes and assigns a statistical measure of significance to each group of genes selected. The method also includes a prefilter tool to select genes with a threshold of differential expression that can be set by the user ad casum. The method is evaluated using an experimental set of microarrays of human control and cancer samples from patients with acute promyelocytic leukemia.     

Uniform approximation is more appropriate for Wilcoxon Rank-Sum Test in gene set analysis

Gene set analysis is widely used to facilitate biological interpretations in the analyses of differential expression from high throughput profiling data. Wilcoxon Rank-Sum (WRS) test is one of the commonly used methods in gene set enrichment analysis. It compares the ranks of genes in a gene set against those of genes outside the gene set. This method is easy to implement and it eliminates the dichotomization of genes into significant and non-significant in a competitive hypothesis testing. Due to the large number of genes being examined, it is impractical to calculate the exact null distribution for the WRS test. Therefore, the normal distribution is commonly used as an approximation. However, as we demonstrate in this paper, the normal approximation is problematic when a gene set with relative small number of genes is tested against the large number of genes in the complementary set. In this situation, a uniform approximation is substantially more powerful, more accurate, and less intensive in computation. We demonstrate the advantage of the uniform approximations in Gene Ontology (GO) term analysis using simulations and real data sets.     

Integrating functional knowledge during sample clustering for microarray data using unsupervised decision trees

Clustering of microarray gene expression data is performed routinely, for genes as well as for samples. Clustering of genes can exhibit functional relationships between genes; clustering of samples on the other hand is important for finding e.g. disease subtypes, relevant patient groups for stratification or related treatments. Usually this is done by first filtering the genes for high-variance under the assumption that they carry most of the information needed for separating different sample groups. If this assumption is violated, important groupings in the data might be lost. Furthermore, classical clustering methods do not facilitate the biological interpretation of the results. Therefore, we propose to methodologically integrate the clustering algorithm with prior biological information. This is different from other approaches as knowledge about classes of genes can be directly used to ease the interpretation of the results and possibly boost clustering performance. Our approach computes dendrograms that resemble decision trees with gene classes used to split the data at each node which can help to find biologically meaningful differences between the sample groups. We have tested the proposed method both on simulated and real data and conclude its usefulness as a complementary method, especially when assumptions of few differentially expressed genes along with an informative mapping of genes to different classes are met.     

CGI: a new approach for prioritizing genes by combining gene expression and protein-protein interaction data

MOTIVATION: Identifying candidate genes associated with a given phenotype or trait is an important problem in biological and biomedical studies. Prioritizing genes based on the accumulated information from several data sources is of fundamental importance. Several integrative methods have been developed when a set of candidate genes for the phenotype is available. However, how to prioritize genes for phenotypes when no candidates are available is still a challenging problem. RESULTS: We develop a new method for prioritizing genes associated with a phenotype by Combining Gene expression and protein Interaction data (CGI). The method is applied to yeast gene expression data sets in combination with protein interaction data sets of varying reliability. We found that our method outperforms the intuitive prioritizing method of using either gene expression data or protein interaction data only and a recent gene ranking algorithm GeneRank. We then apply our method to prioritize genes for Alzheimer's disease. AVAILABILITY: The code in this paper is available upon request.     

'Gene shaving' as a method for identifying distinct sets of genes with similar expression patterns

Background  

Large gene expression studies, such as those conducted using DNA arrays, often provide millions of different pieces of data. To address the problem of analyzing such data, we describe a statistical method, which we have called 'gene shaving'. The method identifies subsets of genes with coherent expression patterns and large variation across conditions. Gene shaving differs from hierarchical clustering and other widely used methods for analyzing gene expression studies in that genes may belong to more than one cluster, and the clustering may be supervised by an outcome measure. The technique can be 'unsupervised', that is, the genes and samples are treated as unlabeled, or partially or fully supervised by using known properties of the genes or samples to assist in finding meaningful groupings.     

Directed indices for exploring gene expression data

MOTIVATION: Large expression studies with clinical outcome data are becoming available for analysis. An important goal is to identify genes or clusters of genes where expression is related to patient outcome. While clustering methods are useful data exploration tools, they do not directly allow one to relate the expression data to clinical outcome. Alternatively, methods which rank genes based on their univariate significance do not incorporate gene function or relationships to genes that have been previously identified. In addition, after sifting through potentially thousands of genes, summary estimates (e.g. regression coefficients or error rates) algorithms should address the potentially large bias introduced by gene selection. RESULTS: We developed a gene index technique that generalizes methods that rank genes by their univariate associations to patient outcome. Genes are ordered based on simultaneously linking their expression both to patient outcome and to a specific gene of interest. The technique can also be used to suggest profiles of gene expression related to patient outcome. A cross-validation method is shown to be important for reducing bias due to adaptive gene selection. The methods are illustrated on a recently collected gene expression data set based on 160 patients with diffuse large cell lymphoma (DLCL).