Analysis of variance components in gene expression data

MOTIVATION: A microarray experiment is a multi-step process, and each step is a potential source of variation. There are two major sources of variation: biological variation and technical variation. This study presents a variance-components approach to investigating animal-to-animal, between-array, within-array and day-to-day variations for two data sets. The first data set involved estimation of technical variances for pooled control and pooled treated RNA samples. The variance components included between-array, and two nested within-array variances: between-section (the upper- and lower-sections of the array are replicates) and within-section (two adjacent spots of the same gene are printed within each section). The second experiment was conducted on four different weeks. Each week there were reference and test samples with a dye-flip replicate in two hybridization days. The variance components included week-to-week, animal-to-animal and between-array and within-array variances. RESULTS: We applied the linear mixed-effects model to quantify different sources of variation. In the first data set, we found that the between-array variance is greater than the between-section variance, which, in turn, is greater than the within-section variance. In the second data set, for the reference samples, the week-to-week variance is larger than the between-array variance, which, in turn, is slightly larger than the within-array variance. For the test samples, the week-to-week variance has the largest variation. The animal-to-animal variance is slightly larger than the between-array and within-array variances. However, in a gene-by-gene analysis, the animal-to-animal variance is smaller than the between-array variance in four out of five housekeeping genes. In summary, the largest variation observed is the week-to-week effect. Another important source of variability is the animal-to-animal variation. Finally, we describe the use of variance-component estimates to determine optimal numbers of animals, arrays per animal and sections per array in planning microarray experiments.     

Analysis of qPCR data by converting exponentially related Ct values into linearly related X0 values

A common method for calculating results from qPCR experiments is the comparative Ct method, also called the 2(-ΔΔCt) method. However, several assumptions are included in the 2(-ΔΔCt) method and standard statistical analyses are not directly applicable. Here, we describe a different method, the X(0) method, for result calculations and statistical analysis from qPCR experiments. The X(0) method differs from the 2(-ΔΔCt) method by introducing a conversion of the exponentially related Ct values into linearly related X(0) values, which represent the amount of starting material in a qPCR experiment. Results calculated by the X(0) method are illustrated for qPCR experiments with technical and biological replicates, including procedures to calculate standard deviations. Incorporation of primer efficiencies in calculations by the X(0) method is also described. Altogether, the X(0) method constitutes a very simple and accurate alternative to the 2(-ΔΔCt) method for result calculations from qPCR data.     

Comparison of software tools to improve the detection of carcinogen induced changes in the rat liver proteome by analyzing SELDI-TOF-MS spectra

A common animal model of chemical hepatocarcinogenesis was used to demonstrate the potential identification of carcinogenicity related protein signatures/biomarkers. Therefore, an animal study in which rats were treated with the known liver carcinogen N-nitrosomorpholine (NNM) or the corresponding vehicle was evaluated. Histopathological investigation as well as SELDI-TOF-MS analysis was performed. SELDI-TOF-MS is an affinity-based mass spectrometry method in which subsets of proteins from biological samples are selectively adsorbed to a chemically modified surface. The proteins are subsequently analyzed with respect to their mass-charge ratios (m/z) by a time of flight (TOF) mass spectrometry (MS) approach. As data preprocessing of SELDI-TOF-MS spectra is essential, baseline correction, normalization, peak detection, and alignment of raw spectra were performed using either the Ciphergen ProteinChip Software 3.1 or functions implemented in the library PROcess of the BioConductor Project. Baseline correction and normalization algorithms of both tools lead to comparable results, whereas results after peak detection and alignment steps differed. Variability between technical and biological replicates was investigated. A linear mixed model with factors experimental group and time point was applied for each protein peak, taking into account the different correlation structure of technical and biological replicates. Alternatively, only median intensity values of technical replicates were used. Results of both models were similar and correlated well with those of the histopathological evaluation of the study. In conclusion, statistical analyses lead to comparable results, whereas parameter settings for preprocessing proved to be crucial.     

A probabilistic treatment of the missing spot problem in 2D gel electrophoresis experiments

Two-dimensional SDS-PAGE gel electrophoresis using post-run staining is widely used to measure the abundances of thousands of protein spots simultaneously. Usually, the protein abundances of two or more biological groups are compared using biological and technical replicates. After gel separation and staining, the spots are detected, spot volumes are quantified, and spots are matched across gels. There are almost always many missing values in the resulting data set. The missing values arise either because the corresponding proteins have very low abundances (or are absent) or because of experimental errors such as incomplete/over focusing in the first dimension or varying run times in the second dimension as well as faulty spot detection and matching. In this study, we show that the probability for a spot to be missing can be modeled by a logistic regression function of the logarithm of the volume. Furthermore, we present an algorithm that takes a set of gels with technical and biological replicates as input and estimates the average protein abundances in the biological groups from the number of missing spots and measured volumes of the present spots using a maximum likelihood approach. Confidence intervals for abundances and p-values for differential expression between two groups are calculated using bootstrap sampling. The algorithm is compared to two standard approaches, one that discards missing values and one that sets all missing values to zero. We have evaluated this approach in two different gel data sets of different biological origin. An R-program, implementing the algorithm, is freely available at http://bioinfo.thep .lu.se/MissingValues2Dgels.html.     

Improved statistical tests for differential gene expression by shrinking variance components estimates

Combining information across genes in the statistical analysis of microarray data is desirable because of the relatively small number of data points obtained for each individual gene. Here we develop an estimator of the error variance that can borrow information across genes using the James-Stein shrinkage concept. A new test statistic (FS) is constructed using this estimator. The new statistic is compared with other statistics used to test for differential expression: the gene-specific F test (F1), the pooled-variance F statistic (F3), a hybrid statistic (F2) that uses the average of the individual and pooled variances, the regularized t-statistic, the posterior odds statistic B, and the SAM t-test. The FS-test shows best or nearly best power for detecting differentially expressed genes over a wide range of simulated data in which the variance components associated with individual genes are either homogeneous or heterogeneous. Thus FS provides a powerful and robust approach to test differential expression of genes that utilizes information not available in individual gene testing approaches and does not suffer from biases of the pooled variance approach.     

Identification of suitable reference genes for expression studies in pomegranate under different biotic and abiotic stress conditions

Pomegranate (Punica granatum L.) is an important economic fruit crop, facing many biotic and abiotic challenges during cultivation. Several research programs are in progress to understand both biotic and abiotic stress factors and mitigate these challenges using gene expression studies based on the qPCR approach. However, research publications are not available yet to select the standard reference gene for normalizing target gene expression values in pomegranate. The most suitable candidate reference gene is required to ensure precise and reliable results for qPCR analysis. Eight candidate reference genes' stability was evaluated under different stress conditions using different algorithms such as ?Ct, geNorm, BestKeeper, NormFinder, and RefFinder. The various algorithms revealed that EFA1 and 18S rRNA were common and most stable reference genes (RGs) under abiotic and wilt stress. Whereas comprehensive ranking by RefFinder showed GAPDH and CYPF were the most stable RGs under combined biotic (pooled samples of all biotic stress) and bacterial blight samples. For normalizing target gene expression under wilt, nematode, bacterial blight, and abiotic stress conditions both GAPDH and CYPFreference genes are adequate for qPCR. The above data provide comprehensive details for the selection of a candidate reference gene in various stresses in pomegranate

     

Preprocessing of gene expression data by optimally robust estimators

Background  

The preprocessing of gene expression data obtained from several platforms routinely includes the aggregation of multiple raw signal intensities to one expression value. Examples are the computation of a single expression measure based on the perfect match (PM) and mismatch (MM) probes for the Affymetrix technology, the summarization of bead level values to bead summary values for the Illumina technology or the aggregation of replicated measurements in the case of other technologies including real-time quantitative polymerase chain reaction (RT-qPCR) platforms. The summarization of technical replicates is also performed in other "-omics" disciplines like proteomics or metabolomics.     

Microarray Data Analysis

The analysis of differential gene expression in microarray experiments requires the development of adequate statistical tools. This article describes a simple statistical method for detecting differential expression between two conditions with a low number of replicates. When comparing two group means using a traditional t-test, gene-specific variance estimates are unstable and can lead to wrong conclusions. We construct a likelihood ratio test while modelling these variances hierarchically across all genes, and express it as a t-test statistic. By borrowing information across genes we can take advantage of their large numbers, and still yield a gene-specific test statistic. We show that this hierarchical t-test is more powerful than its traditional version and generates less false positives in a simulation study, especially with small sample sizes. This approach can be extended to cases where there are more than two groups.