Replicated Microarray Experiments Research Articles

The exact probability distribution of the rank product statistics for replicated experiments

The rank product method is a widely accepted technique for detecting differentially regulated genes in replicated microarray experiments. To approximate the sampling distribution of the rank product statistic, the original publication proposed a permutation approach, whereas recently an alternative approximation based on the continuous gamma distribution was suggested. However, both approximations are imperfect for estimating small tail probabilities. In this paper we relate the rank product statistic to number theory and provide a derivation of its exact probability distribution and the true tail probabilities.

Changes in matrix protein gene expression associated with mineralization in the differentiating chick limb-bud micromass culture system

Chick limb-bud mesenchymal stem cells plated in high density culture in the presence of 4 mM inorganic phosphate and vitamin C differentiate and form a mineralizable matrix, resembling that of the chick growth plate. To further elucidate the mechanism that allows these cultures to form physiologic hydroxyapatite deposits, and how the process can be manipulated to gain insight into mineralization mechanisms, we compared gene expression in mineralizing (with 4 mM inorganic phosphate) and non-mineralizing cultures (containing only 1 mM inorganic phosphate) at the start of mineralization (day 11) and after mineralization reached a plateau (day 17) using a chick specific microarray. Based on replicate microarray experiments and K-cluster analysis, several genes associated with the mineralization process were identified, and their expression patterns confirmed throughout the culture period by quantitative RT-PCR. The functions of bone morphogenetic protein 1, BMP1, dentin matrix protein 1, DMP1, the sodium phosphate co-transporter, NaPi IIb, matrix metalloprotease 13. MMP-13, and alkaline phosphatase, along with matrix protein genes (type X collagen, bone sialoprotein, and osteopontin) usually associated with initiation of mineralization are discussed.

Variation of gene expression in Bacillus subtilis samples of fermentation replicates

The application of comprehensive gene expression profiling technologies to compare wild and mutated microorganism samples or to assess molecular differences between various treatments has been widely used. However, little is known about the normal variation of gene expression in microorganisms. In this study, an Agilent customized microarray representing 4,106 genes was used to quantify transcript levels of five-repeated flasks to assess normal variation in Bacillus subtilis gene expression. CV analysis and analysis of variance were employed to investigate the normal variance of genes and the components of variance, respectively. The results showed that above 80% of the total variation was caused by biological variance. For the 12 replicates, 451 of 4,106 genes exhibited variance with CV values over 10%. The functional category enrichment analysis demonstrated that these variable genes were mainly involved in cell type differentiation, cell type localization, cell cycle and DNA processing, and spore or cyst coat. Using power analysis, the minimal biological replicate number for a B. subtilis microarray experiment was determined to be six. The results contribute to the definition of the baseline level of variability in B. subtilis gene expression and emphasize the importance of replicate microarray experiments.

The rank product method with two samples

Breitling et al. (2004) [1] introduced a statistical technique, the rank product method, for detecting differentially regulated genes in replicated microarray experiments. The technique has achieved widespread acceptance and is now used more broadly, in such diverse fields as RNAi analysis, proteomics, and machine learning. In this note, we extend the rank product method to the two sample setting, provide distribution theory attending the rank product method in this setting, and give numerical details for implementing the method.

A New Symbolic Representation for the Identification of Informative Genes in Replicated Microarray Experiments

Microarray experiments generate massive amounts of data, necessitating innovative algorithms to distinguish biologically relevant information from noise. Because the variability of gene expression data is an important factor in determining which genes are differentially expressed, analysis techniques that take into account repeated measurements are critically important. Additionally, the selection of informative genes is typically done by searching for the individual genes that vary the most across conditions. Yet because genes tend to act in groups rather than individually, it may be possible to glean more information from the data by searching specifically for concerted behavior in a set of genes. Applying a symbolic transformation to the gene expression data allows the detection overrepresented patterns in the data, in contrast to looking only for genes that exhibit maximal differential expression. These challenges are approached by introducing an algorithm based on a new symbolic representation that searches for concerted gene expression patterns; furthermore, the symbolic representation takes into account the variance in multiple replicates and can be applied to long time series data. The proposed algorithm's ability to discover biologically relevant signals in gene expression data is exhibited by applying it to three datasets that measure gene expression in the rat liver.

Comments on the rank product method for analyzing replicated experiments

Breitling et al. [1] introduced a statistical technique, the rank product method, for detecting differentially regulated genes in replicated microarray experiments. The technique has achieved widespread acceptance and is now used more broadly, in such diverse fields as RNAi analysis, proteomics, and machine learning. In this note, we relate the rank product method to linear rank statistics and provide an alternative derivation of distribution theory attending the rank product method.

A heavy-tailed empirical Bayes method for replicated microarray data

DNA microarray has been recognized as being an important tool for studying the expression of thousands of genes simultaneously. These experiments allow us to compare two different samples of cDNA obtained under different conditions. A novel method for the analysis of replicated microarray experiments based upon the modelling of gene expression distribution as a mixture of α -stable distributions is presented. Some features of the distribution of gene expression, such as Pareto tails and the fact that the variance of any given array increases concomitantly with an increase in the number of genes studied, suggest the possibility of modelling gene expression distribution on the basis of α -stable density. The proposed methodology uses very well known properties of α -stable distribution, such as the scale mixture of normals. A Bayesian log-posterior odds is calculated, which allows us to decide whether a gene is expressed differentially or not. The proposed methodology is illustrated using simulated and experimental data and the results are compared with other existing statistical approaches. The proposed heavy-tail model improves the performance of other distributions and is easily applicable to microarray gene data, specially if the dataset contains outliers or presents high variance between replicates.

Multivariate hierarchical Bayesian model for differential gene expression analysis in microarray experiments

BackgroundIdentification of differentially expressed genes is a typical objective when analyzing gene expression data. Recently, Bayesian hierarchical models have become increasingly popular to solve this type of problems. These models show good performance in accommodating noise, variability and low replication of microarray data. However, the correlation between different fluorescent signals measured from a gene spot is ignored, which can diversely affect the data analysis step. In fact, the intensities of the two signals are significantly correlated across samples. The larger the log-transformed intensities are, the smaller the correlation is.ResultsMotivated by the complicated error relations in microarray data, we propose a multivariate hierarchical Bayesian framework for data analysis in the replicated microarray experiments. Gene expression data are modelled by a multivariate normal distribution, parameterized by the corresponding mean vectors and covariance matrixes with a conjugate prior distribution. Within the Bayesian framework, a generalized likelihood ratio test (GLRT) is also developed to infer the gene expression patterns. Simulation studies show that the proposed approach presents better operating characteristics and lower false discovery rate (FDR) than existing methods, especially when the correlation coefficient is large. The approach is illustrated with two examples of microarray analysis. The proposed method successfully detects significant genes closely related to the experimental states, which are verified by the biological information.ConclusionsThe multivariate Bayesian model, compatible with the dependence between mean and variance in the univariate Bayesian model, relaxes the constant coefficient of variation assumption between measurements by adding a covariance structure. This model improves the identification of differentially expressed genes significantly since the Bayesian model fit well with the microarray data.

In vivo endothelial gene regulation in diabetes

BackgroundAn authentic survey of the transcript-level response of the diabetic endothelium in vivo is key to understanding diabetic cardiovascular complications such as accelerated atherosclerosis and endothelial dysfunction.MethodsWe used streptozotocin to induce a model of type I diabetes in transgenic mice that express green fluorescent protein under the control of an endothelial-specific promoter (Tie2-GFP) allowing rapid isolation of aortic endothelium. Three weeks after treatment, endothelial cells were isolated from animals with blood glucose > 350 mg/dl. Aortae from the root to the renal bifurcation were rapidly processed by mincing and proteolytic digestion followed by fluorescent activated cell sorting to yield endothelial cell populations of >95% purity. RNA was isolated from >50,000 endothelial cells and subjected to oligo dT amplification prior to transcriptional analysis on microarrays displaying long oligonucleotides representing 32,000 murine transcripts. Five regulated transcripts were selected for analysis by real-time PCR.ResultsWithin replicate microarray experiments, 19 transcripts were apparently dysregulated by at least 70% within diabetic mice. Up-regulation of glycam1, slc36a2, ces3, adipsin and adiponectin was confirmed by real-time PCR.ConclusionBy comprehensively examining cellular gene responses in vivo in a whole animal model of type I diabetes, we have identified novel regulation of key endothelial transcripts that likely contribute to the metabolic and pro-inflammatory responses that accompany diabetes.

Gene expression profiling by massively parallel sequencing

Massively parallel sequencing holds great promise for expression profiling, as it combines the high throughput of SAGE with the accuracy of EST sequencing. Nevertheless, until now only very limited information had been available on the suitability of the current technology to meet the requirements. Here, we evaluate the potential of 454 sequencing technology for expression profiling using Drosophila melanogaster. We show that short (< approximately 80 bp) and long (> approximately 300-400 bp) cDNA fragments are under-represented in 454 sequence reads. Nevertheless, sequencing of 3' cDNA fragments generated by nebulization could be used to overcome the length bias of the 454 sequencing technology. Gene expression measurements generated by restriction analysis and nebulization for fragments within the 80- to 300-bp range showed correlations similar to those reported for replicated microarray experiments (0.83-0.91); 97% of the cDNA fragments could be unambiguously mapped to the genomic DNA, demonstrating the advantage of longer sequence reads. Our analyses suggest that the 454 technology has a large potential for expression profiling, and the high mapping accuracy indicates that it should be possible to compare expression profiles across species.

TECHNICAL ADVANCE: EVE (external variance estimation) increases statistical power for detecting differentially expressed genes

Accurately identifying differentially expressed genes from microarray data is not a trivial task, partly because of poor variance estimates of gene expression signals. Here, after analyzing 380 replicated microarray experiments, we found that probesets have typical, distinct variances that can be estimated based on a large number of microarray experiments. These probeset-specific variances depend at least in part on the function of the probed gene: genes for ribosomal or structural proteins often have a small variance, while genes implicated in stress responses often have large variances. We used these variance estimates to develop a statistical test for differentially expressed genes called EVE (external variance estimation). The EVE algorithm performs better than the t-test and LIMMA on some real-world data, where external information from appropriate databases is available. Thus, EVE helps to maximize the information gained from a typical microarray experiment. Nonetheless, only a large number of replicates will guarantee to identify nearly all truly differentially expressed genes. However, our simulation studies suggest that even limited numbers of replicates will usually result in good coverage of strongly differentially expressed genes.

Utilization of Lymphoblastoid Cell Lines as a System for the Molecular Modeling of Autism

In order to provide an alternative approach for understanding the biology and genetics of autism, we performed statistical analysis of gene expression profiles of lymphoblastoid cell lines derived from children with autism and their families. The goal was to assess the feasibility of using this model in identifying autism-associated genes. Replicate microarray experiments demonstrated that expression data from the cell lines were consistent and highly reproducible. Further analyses identified differentially expressed genes between cell lines derived from children with autism and those derived from their normally developing siblings. These genes were then used to identify biochemical pathways potentially involved in autism. This study suggests that lymphoblastoid cell lines may be a viable tool for identifying genes associated with autism.

A Powerful Approach for Effective Finding of Significantly Differentially Expressed Genes

The problem of identifying significantly differentially expressed genes for replicated microarray experiments is accepted as significant and has been tackled by several researchers. Patterns from Gene Expression (PaGE) and q-values are two of the well-known approaches developed to handle this problem. This paper proposes a powerful approach to handle this problem. We first propose a method for estimating the prior probabilities used in the first version of the PaGE algorithm. This way, the problem definition of PaGE stays intact and we just estimate the needed prior probabilities. Our estimation method is similar to Storey's estimator without being its direct extension. Then, we modify the problem formulation to find significantly differentially expressed genes and present an efficient method for finding them. This formulation increases the power by directly incorporating Storey's estimator. We report the preliminary results on the BRCA data set to demonstrate the applicability and effectiveness of our approach.

A Renewed Approach to the Nonparametric Analysis of Replicated Microarray Experiments

DNA-microarrays find broad employment in biochemical research. This technology allows the monitoring of the expression levels of thousands of genes at the same time. Often, the goal of a microarray study is to find differentially expressed genes in two different types of tissue, for example normal and cancerous. Multiple hypothesis testing is a useful statistical tool for such studies. One approach using multiple hypothesis testing is nonparametric analysis for replicated microarray experiments. In this paper we present an improved version of this method. We also show how p-values are calculated for all significant genes detected with this testing procedure. All algorithms were implemented in an R-package, and instructions on it's use are included. The package can be downloaded at http://www.statistik.unidortmund.de/de/content/einrichtungen/lehrstuehle/personen/jung.html

USING WEIGHTED PERMUTATION SCORES TO DETECT DIFFERENTIAL GENE EXPRESSION WITH MICROARRAY DATA

A class of nonparametric statistical methods, including a nonparametric empirical Bayes (EB) method, the Significance Analysis of Microarrays (SAM) and the mixture model method (MMM) have been proposed to detect differential gene expression for replicated microarray experiments. They all depend on constructing a test statistic, for example, a t-statistic, and then using permutation to draw inferences. However, due to special features of microarray data, using standard permutation scores may not estimate the null distribution of the test statistic well, leading to possibly too conservative inferences. We propose a new method of constructing weighted permutation scores to overcome the problem: posterior probabilities of having no differential expression from the EB method are used as weights for genes to better estimate the null distribution of the test statistic. We also propose a weighted method to estimate the false discovery rate (FDR) using the posterior probabilities. Using simulated data and real data for time-course microarray experiments, we show the improved performance of the proposed methods when implemented in MMM, EB and SAM.

High Reproducibility using Sodium Hydroxide-Stripped Long Oligonucleotide DNA Microarrays

Recently, long oligonucleotide (60- to 70-mer) microarrays for two-color experiments have been developed and are gaining widespread use. In addition, when there is limited availability of mRNA from tissue sources, RNA amplification can and is being used to produce sufficient quantities of cRNA for microarray hybridization. Taking advantage of the selective degradation of RNA under alkaline conditions, we have developed a method to "strip" glass-based oligonucleotide microarrays that use fluorescent RNA in the hybridization, while leaving the DNA oligonucleotide probes intact and usable for a second experiment. Replicate microarray experiments conducted using stripped arrays showed high reproducibility, however, we found that arrays could only be stripped and reused once without compromising data quality. The intraclass correlation (ICC) between a virgin array and a stripped array hybridized with the same sample showed a range of 0.90-0.98, which is comparable to the ICC of two virgin arrays hybridized with the same sample. Using this method, once-stripped oligonucleotide microarrays are usable, reliable, and help to reduce costs.

A Robust Statistical Method for Detecting Differentially Expressed Genes

DNA microarray technology allows researchers to monitor the expressions of thousands of genes under different conditions, and to measure the levels of thousands of different DNA molecules at a given point in the life of an organism, tissue or cell. A wide variety of different diseases that are characterised by unregulated gene expression, DNA replication, cell division and cell death, can be detected early using microarrays. One of the major objectives of microarray experiments is to identify differentially expressed genes under various conditions. The detection of differential gene expression under two different conditions is very important in biological studies, and allows us to identify experimental variables that affect different biological processes. Most of the tests available in the literature are based on the assumption of normal distribution. However, the assumption of normality may not be true in real-life data, particularly with respect to microarray data.A test is proposed for the identification of differentially expressed genes in replicated microarray experiments conducted under two different conditions. The proposed test does not assume the distribution of the parent population; thus, the proposed test is strictly nonparametric in nature. We calculate the p-value and the asymptotic power function of the proposed test statistic. The proposed test statistic is compared with some of its competitors under normal, gamma and exponential population setup using the Monte Carlo simulation technique. The application of the proposed test statistic is presented using microarray data. The proposed test is robust and highly efficient when populations are non-normal.

Simulated Annealing of Microarray Data Reduces Noise and Enables Cross-Experimental Comparisons

Microarrays are a powerful tool for assessing the genome-wide induction of a transcriptional response to internal or external stimuli, but are not considered quantitatively rigorous (i.e., the signal intensity of hybridized probe is normally used to quantify relative transcript abundance). Thus, it is difficult, if not impossible, to accurately compare separate microarray experiments without a reference standard. However, even among replicated microarray experiments, each gene varies significantly in the amount of signal detected, suggesting no single gene would be appropriate as a standard. We propose and test a method to "align" experimental transcription profiles to a set of reference experiments using simulated annealing (SA), essentially using the relative positions of all genes as a reference standard. SA attempts to find a globally optimal adjustment factor for the relative expression level of each experimental gene expression signal, given a previously observed range of gene expression measurements. By defining a relative dynamic range of gene expression under control conditions for all genes, we can more accurately compare transcription profiles between separate experiments and, potentially, between species--enabling comparative transcriptomics. Testing SA on a published dataset, we find that it significantly reduces interexperimental variation, suggesting it holds promise to accomplish this goal.

Simulated Annealing of Microarray Data Reduces Noise and Enables Cross-Experimental Comparisons

Microarrays are a powerful tool for assessing the genome-wide induction of a transcriptional response to internal or external stimuli, but are not considered quantitatively rigorous (i.e., the signal intensity of hybridized probe is normally used to quantify relative transcript abundance). Thus, it is difficult, if not impossible, to accurately compare separate microarray experiments without a reference standard. However, even among replicated microarray experiments, each gene varies significantly in the amount of signal detected, suggesting no single gene would be appropriate as a standard. We propose and test a method to "align" experimental transcription profiles to a set of reference experiments using simulated annealing (SA), essentially using the relative positions of all genes as a reference standard. SA attempts to find a globally optimal adjustment factor for the relative expression level of each experimental gene expression signal, given a previously observed range of gene expression measurements. By defining a relative dynamic range of gene expression under control conditions for all genes, we can more accurately compare transcription profiles between separate experiments and, potentially, between species—enabling comparative transcriptomics. Testing SA on a published dataset, we find that it significantly reduces interexperimental variation, suggesting it holds promise to accomplish this goal.

Nonparametric analysis of replicated microarray experiments

Microarrays are part of a new class of biotechnologies, which allow the monitoring of expression levels of thousands of genes simultaneously. In microarray data analysis, the comparison of gene expression profiles with respect to different conditions and the selection of biologically interesting genes are crucial tasks. Multivariate statistical methods have been applied to analyze these large data sets. To identify genes with altered expression under two experimental conditions, we propose a nonparametric statistical approach. Specifically, we propose estimating the distributions of a t-type statistic and its null statistic, using kernel methods. A comparison of these two distributions by means of a likelihood ratio test can identify genes with significantly changed expressions. A new method to provide more stable estimates of tail probabilities is proposed, as well as a method for the calculation of the cut-off point and the acceptance region. The methodology is applied to a leukaemia data set containing expression levels of 7129 genes, and is compared with normal mixture model and the traditional t-test.