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.     

Combining gene expression and molecular marker information for mapping complex trait genes: a simulation study

A method for mapping complex trait genes using cDNA microarray and molecular marker data jointly is presented and illustrated via simulation. We introduce a novel approach for simulating phenotypes and genotypes conditionally on real, publicly available, microarray data. The model assumes an underlying continuous latent variable (liability) related to some measured cDNA expression levels. Partial least-squares logistic regression is used to estimate the liability under several scenarios where the level of gene interaction, the gene effect, and the number of cDNA levels affecting liability are varied. The results suggest that: (1) the usefulness of microarray data for gene mapping increases when both the number of cDNA levels in the underlying liability and the QTL effect decrease and when genes are coexpressed; (2) the correlation between estimated and true liability is large, at least under our simulation settings; (3) it is unlikely that cDNA clones identified as significant with partial least squares (or with some other technique) are the true responsible cDNAs, especially as the number of clones in the liability increases; (4) the number of putatively significant cDNA levels increases critically if cDNAs are coexpressed in a cluster (however, the proportion of true causal cDNAs within the significant ones is similar to that in a no-coexpression scenario); and (5) data reduction is needed to smooth out the variability encountered in expression levels when these are analyzed individually.     

Annotating gene function by combining expression data with a modular gene network

MOTIVATION: A promising and reliable approach to annotate gene function is clustering genes not only by using gene expression data but also literature information, especially gene networks. RESULTS: We present a systematic method for gene clustering by combining these totally different two types of data, particularly focusing on network modularity, a global feature of gene networks. Our method is based on learning a probabilistic model, which we call a hidden modular random field in which the relation between hidden variables directly represents a given gene network. Our learning algorithm which minimizes an energy function considering the network modularity is practically time-efficient, regardless of using the global network property. We evaluated our method by using a metabolic network and microarray expression data, changing with microarray datasets, parameters of our model and gold standard clusters. Experimental results showed that our method outperformed other four competing methods, including k-means and existing graph partitioning methods, being statistically significant in all cases. Further detailed analysis showed that our method could group a set of genes into a cluster which corresponds to the folate metabolic pathway while other methods could not. From these results, we can say that our method is highly effective for gene clustering and annotating gene function.     

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.     

Evaluation of experimental designs for two-color cDNA microarrays.

The major goal of two-color cDNA microarray experiments is to measure the relative gene expression level (i.e., relative amount of mRNA) of each gene between samples in studies of gene expression. More specifically, given an N-sample experiment, we need all N(N - 1)/2 relative expression levels of all sample pairs of each gene for identification of the differentially expressed genes and for clustering of gene expression patterns. However, the intensities observed from two-color cDNA microarray experiments do not simply represent the relative gene expression level. They are composed of signal (gene expression level), noise, and other factors. In discussions on the experimental design of two-color cDNA microarray experiments, little attention has been given to the fact that different combinations of test and control samples will produce microarray intensities data with varying intrinsic composition of factors. As a consequence, not all experimental designs for two-color cDNA microarray experiments are able to provide all possible relative gene expression levels. This phenomenon has never been addressed. To obtain all possible relative gene expression levels, a novel method for two-color cDNA microarray experimental design evaluation is necessary that will allow the making of an accurate choice. In this study, we propose a model-based approach to illustrate how the factor composition of microarray intensities changed with different experimental designs in two-color cDNA microarray experiments. By analyzing 12 experimental designs (including 5 general forms), we demonstrate that not all experimental designs are able to provide all possible relative gene expression levels due to the differences in factor composition. Our results indicate that whether an experimental design can provide all possible relative expression levels of all sample pairs for each gene should be the first criterion to be considered in an evaluation of experimental designs for two-color cDNA microarray experiments.     

Dynamic modeling of gene expression in prokaryotes: application to glucose-lactose diauxie in Escherichia coli

Coexpression of genes or, more generally, similarity in the expression profiles poses an unsurmountable obstacle to inferring the gene regulatory network (GRN) based solely on data from DNA microarray time series. Clustering of genes with similar expression profiles allows for a course-grained view of the GRN and a probabilistic determination of the connectivity among the clusters. We present a model for the temporal evolution of a gene cluster network which takes into account interactions of gene products with genes and, through a non-constant degradation rate, with other gene products. The number of model parameters is reduced by using polynomial functions to interpolate temporal data points. In this manner, the task of parameter estimation is reduced to a system of linear algebraic equations, thus making the computation time shorter by orders of magnitude. To eliminate irrelevant networks, we test each GRN for stability with respect to parameter variations, and impose restrictions on its behavior near the steady state. We apply our model and methods to DNA microarray time series' data collected on Escherichia coli during glucose-lactose diauxie and infer the most probable cluster network for different phases of the experiment. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1007/s11693-011-9079-2) contains supplementary material, which is available to authorized users.     

Accounting for probe-level noise in principal component analysis of microarray data

MOTIVATION: Principal Component Analysis (PCA) is one of the most popular dimensionality reduction techniques for the analysis of high-dimensional datasets. However, in its standard form, it does not take into account any error measures associated with the data points beyond a standard spherical noise. This indiscriminate nature provides one of its main weaknesses when applied to biological data with inherently large variability, such as expression levels measured with microarrays. Methods now exist for extracting credibility intervals from the probe-level analysis of cDNA and oligonucleotide microarray experiments. These credibility intervals are gene and experiment specific, and can be propagated through an appropriate probabilistic downstream analysis. RESULTS: We propose a new model-based approach to PCA that takes into account the variances associated with each gene in each experiment. We develop an efficient EM-algorithm to estimate the parameters of our new model. The model provides significantly better results than standard PCA, while remaining computationally reasonable. We show how the model can be used to 'denoise' a microarray dataset leading to improved expression profiles and tighter clustering across profiles. The probabilistic nature of the model means that the correct number of principal components is automatically obtained.     

A probabilistic framework for microarray data analysis: Fundamental probability models and statistical inference

Gene expression studies generate large quantities of data with the defining characteristic that the number of genes (whose expression profiles are to be determined) exceed the number of available replicates by several orders of magnitude. Standard spot-by-spot analysis still seeks to extract useful information for each gene on the basis of the number of available replicates, and thus plays to the weakness of microarrays. On the other hand, because of the data volume, treating the entire data set as an ensemble, and developing theoretical distributions for these ensembles provides a framework that plays instead to the strength of microarrays. We present theoretical results that under reasonable assumptions, the distribution of microarray intensities follows the Gamma model, with the biological interpretations of the model parameters emerging naturally. We subsequently establish that for each microarray data set, the fractional intensities can be represented as a mixture of Beta densities, and develop a procedure for using these results to draw statistical inference regarding differential gene expression. We illustrate the results with experimental data from gene expression studies on Deinococcus radiodurans following DNA damage using cDNA microarrays.     

Asymptotic Conditional Singular Value Decomposition for High‐Dimensional Genomic Data

Summary High‐dimensional data, such as those obtained from a gene expression microarray or second generation sequencing experiment, consist of a large number of dependent features measured on a small number of samples. One of the key problems in genomics is the identification and estimation of factors that associate with many features simultaneously. Identifying the number of factors is also important for unsupervised statistical analyses such as hierarchical clustering. A conditional factor model is the most common model for many types of genomic data, ranging from gene expression, to single nucleotide polymorphisms, to methylation. Here we show that under a conditional factor model for genomic data with a fixed sample size, the right singular vectors are asymptotically consistent for the unobserved latent factors as the number of features diverges. We also propose a consistent estimator of the dimension of the underlying conditional factor model for a finite fixed sample size and an infinite number of features based on a scaled eigen‐decomposition. We propose a practical approach for selection of the number of factors in real data sets, and we illustrate the utility of these results for capturing batch and other unmodeled effects in a microarray experiment using the dependence kernel approach of Leek and Storey (2008, Proceedings of the National Academy of Sciences of the United States of America 105 , 18718–18723) .     

Gene profile of replicative senescence is different from progeria or elderly donor

In vitro cellular senescence of human diploid fibroblast has been a good model for aging research, which shows similar phenotypes to in vivo aging. Gene expression profiling would provide an insight to understand the mechanism of senescence. Using cDNA microarray containing 384 known genes, we compared the expression profiles of three different types of aging models: replicative senescence, fibroblasts from progeria or from elderly donor. Although all of them showed senescence phenotypes, distinct sets of genes were altered in each group. Pairwise plots or cluster analysis of activation fold of gene expression revealed closer relationships between fibroblasts from progeria or from old individual, but not between replicative senescence fibroblasts and either models. Differential expression pattern of several genes were confirmed by RT-PCR. We suggest that the replicative senescence model might behave differently to other types of aging models due to the distinct gene expression.     

Spearman Correlation Identifies Statistically Significant Gene Expression Clusters in Spinal Cord Development and Injury

An important problem in the analysis of large-scale gene expression data is the validation of gene expression clusters. By examining the temporal expression patterns of 74 genes expressed in rat spinal cord under three different experimental conditions, we have found evidence that some genes cluster together under multiple conditions. Using RT-PCR data from spinal cord development and two sets of microarray data from spinal injury, we applied Spearman correlation to identify clusters and to assign P values to pairs of genes with highly similar temporal expression patterns. We found that 15% of genes occurred in statistically significant pairs in all three experimental conditions, providing both statistical and experimental support for the idea that genes that cluster together are co-regulated. In addition, we demonstrated that DNA microarray and RT-PCR data are comparable, and can be combined to confirm gene expression relationships.     

ADGO: analysis of differentially expressed gene sets using composite GO annotation

MOTIVATION: Genes are typically expressed in modular manners in biological processes. Recent studies reflect such features in analyzing gene expression patterns by directly scoring gene sets. Gene annotations have been used to define the gene sets, which have served to reveal specific biological themes from expression data. However, current annotations have limited analytical power, because they are classified by single categories providing only unary information for the gene sets. RESULTS: Here we propose a method for discovering composite biological themes from expression data. We intersected two annotated gene sets from different categories of Gene Ontology (GO). We then scored the expression changes of all the single and intersected sets. In this way, we were able to uncover, for example, a gene set with the molecular function F and the cellular component C that showed significant expression change, while the changes in individual gene sets were not significant. We provided an exemplary analysis for HIV-1 immune response. In addition, we tested the method on 20 public datasets where we found many 'filtered' composite terms the number of which reached approximately 34% (a strong criterion, 5% significance) of the number of significant unary terms on average. By using composite annotation, we can derive new and improved information about disease and biological processes from expression data. AVAILABILITY: We provide a web application (ADGO: http://array.kobic.re.kr/ADGO) for the analysis of differentially expressed gene sets with composite GO annotations. The user can analyze Affymetrix and dual channel array (spotted cDNA and spotted oligo microarray) data for four species: human, mouse, rat and yeast. CONTACT: chu@kribb.re.kr SUPPLEMENTARY INFORMATION: http://array.kobic.re.kr/ADGO.     

A simple method to improve probe set estimates from oligonucleotide arrays

A popular commercially available oligonucleotide microarray technology employs sets of 25 base pair oligonucleotide probes for measurement of gene expression levels. A mathematical algorithm is required to compute an estimate of gene expression from the multiple probes. Previously proposed methods for summarizing gene expression data have either been substantially ad hoc or have relied on model assumptions that may be easily violated. Here we present a new algorithm for calculating gene expression from probe sets. Our approach is functionally related to leave-one-out cross-validation, a non-parametric statistical technique that is often applied in limited data situations. We illustrate this approach using data from our study seeking a molecular fingerprint of STAT3 regulated genes for early detection of human cancer.     

Microarray reality checks in the context of a complex disease

A problem in analyzing microarray-based gene expression data is the separation of genes causally involved in a disease from innocent bystander genes, whose expression levels have been secondarily altered by primary changes elsewhere. To investigate this issue systematically in the context of a class of complex human diseases, we have compared microarray-based gene expression data with non-microarray-based clinical and biological data about the schizophrenias to ask whether these two approaches prioritize the same genes. We find that genes whose expression changes are deemed to be of importance from microarrays are rarely those classified as of importance from clinical, in situ, molecular, single-nucleotide polymorphism (SNP) association, knockout and drug perturbation data. This disparity is not limited to the schizophrenias but characterizes other human disease data sets. It also extends to biological validation of microarray data in model organisms, in which genome-wide phenotypic data have been systematically compared with microarray data. In addition, different bioinformatic protocols applied to the same microarray data yield quite different gene sets and thus make clinical decisions less straightforward. We discuss how progress may be improved in the clinical area by the assignment of high-quality phenotypic values to each member of a microarray-assigned gene set.     

Biclustering models for structured microarray data

Microarrays have become a standard tool for investigating gene function and more complex microarray experiments are increasingly being conducted. For example, an experiment may involve samples from several groups or may investigate changes in gene expression over time for several subjects, leading to large three-way data sets. In response to this increase in data complexity, we propose some extensions to the plaid model, a biclustering method developed for the analysis of gene expression data. This model-based method lends itself to the incorporation of any additional structure such as external grouping or repeated measures. We describe how the extended models may be fitted and illustrate their use on real data.     

Use of gene networks for identifying and validating drug targets

We propose a new method for identifying and validating drug targets by using gene networks, which are estimated from cDNA microarray gene expression profile data. We created novel gene disruption and drug response microarray gene expression profile data libraries for the purpose of drug target elucidation. We use two types of microarray gene expression profile data for estimating gene networks and then identifying drug targets. The estimated gene networks play an essential role in understanding drug response data and this information is unattainable from clustering methods, which are the standard for gene expression analysis. In the construction of gene networks, we use the Bayesian network model. We use an actual example from analysis of the Saccharomyces cerevisiae gene expression profile data to express a concrete strategy for the application of gene network information to drug discovery.