Tumorigenesis is characterised by changes in transcriptional control. Extensive transcript expression data have been acquired over the last decade and used to classify prostate cancers. Prostate cancer is, however, a heterogeneous multifocal cancer and this poses challenges in identifying robust transcript biomarkers.In this study, we have undertaken a meta-analysis of publicly available transcriptomic data spanning datasets and technologies from the last decade and encompassing laser capture microdissected and macrodissected sample sets.We identified a 33 gene signature that can discriminate between benign tissue controls and localised prostate cancers irrespective of detection platform or dissection status. These genes were significantly overexpressed in localised prostate cancer versus benign tissue in at least three datasets within the Oncomine Compendium of Expression Array Data. In addition, they were also overexpressed in a recent exon-array dataset as well a prostate cancer RNA-seq dataset generated as part of the The Cancer Genomics Atlas (TCGA) initiative. Biologically, glycosylation was the single enriched process associated with this 33 gene signature, encompassing four glycosylating enzymes. We went on to evaluate the performance of this signature against three individual markers of prostate cancer, v-ets avian erythroblastosis virus E26 oncogene homolog (ERG) expression, prostate specific antigen (PSA) expression and androgen receptor (AR) expression in an additional independent dataset. Our signature had greater discriminatory power than these markers both for localised cancer and metastatic disease relative to benign tissue, or in the case of metastasis, also localised prostate cancer.In conclusion, robust transcript biomarkers are present within datasets assembled over many years and cohorts and our study provides both examples and a strategy for refining and comparing datasets to obtain additional markers as more data are generated.The online version of this article (doi:10.1186/s12920-014-0074-9) contains supplementary material, which is available to authorized users. Gene Expression Microarray Analysis and more recently high-throughput RNA sequencing (RNA-seq) are commonly used techniques when trying to acquire an unbiased view of the expression levels of large numbers of genes. In order to define more compact and manageable expression modules that might predict risk or prognosis, various approaches have been used across several studies. These include the identification of consensus profiles across multiple datasets  and iden samples , and lasfication . The lasgnatures . It is, In this study, we have therefore set out with a number of goals. First and foremost amongst these was to determine whether we could identify gene signatures that were statistically significant in datasets generated from both whole tissue sections and laser capture microdissected material. If so, this might indicate that with the right filtering approach, sample heterogeneity might not be a completely confounding challenge to transcriptomic analysis. Secondly, if we were able to identify such signatures, we then wanted to be able to refine them to a point that the signature and any pathway or process enriched within it could be easily validated by other experimental and clinical research groups. Here, we report a concise 33-gene signature with biological enrichment for glycosylation, which discriminates between benign tissue and prostate cancer (PCa) across multiple transcript detection platforms and sample types.et al., using the Affymetrix Human Genome U133 Plus 2.0 Array platform. The dataset consisted of 13 macrodissected individual benign prostate, primary and metastatic PCa samples and 6 pooled samples from benign, primary or metastatic PCa tissues. The expression array data were downloaded from GEO under accession number GSE3325 (http://www.ncbi.nlm.nih.gov/geo/query/acc.cgi?acc=GSE3325).A 19-sample dataset generated by Varambally et al., using an in-house cDNA microarray platform (Chinnaiyan Human 20K Hs6). Laser capture microdissection was used to isolate 101 specific cell populations from 44 individuals representing PCa progression in a range of sample categories encompassing 12 stromal and 89 epithelial cell populations. These were subcategorised as EPI_BPH (benign prostatic hyperplasia epithelium), EPI_ADJ_PCA , EPI_ATR (atrophic epithelium – simple atrophy), EPI_ATR_PIA (atrophic epithelium), PIN , PCA (prostate carcinoma), MET_HN (Metastatic Prostate Carcinoma - Hormone Naïve), MET_HR (Metastatic Prostate Carcinoma - Hormone Refractory), STROMA_EPIBPH , STROMA_NOR , STROMA_ADJ_PCA . In addition three samples were EPI_NOR . In our study we maintain this nomenclature in describing the dataset. The expression array data were downloaded from GEO under accession number GSE6099 (http://www.ncbi.nlm.nih.gov/geo/query/acc.cgi?acc=GSE6099).A 104-sample dataset generated by Tomlins et al., and consisting of 218 tumour samples, spanning 14 common tumour types, and 90 normal tissue samples and profiled on Affymetrix oligonucleotide microarrays (Hu6800 and Hu35KsubA GeneChips). The 14 tumour types incorporated into this study were breast adenocarcinoma, prostate adenocarcinoma, lung adenocarcinoma, colorectal adenocarcinoma, lymphoma, bladder transitional cell carcinoma, melanoma, uterine adenocarcinoma, leukemia, renal cell carcinoma, pancreatic adenocarcinoma, ovarian adenocarcinoma, pleural mesothelioma and cancers of the central nervous system. The dataset was downloaded from the Broad Institute website (http://www.broadinstitute.org/cgi-bin/cancer/publications/pub_paper.cgi?mode=view&paper_id=61).A multi-cancer microarray dataset generated by Ramaswamy et al., for 150 tumours, 29 matched normal samples, and 6 cell lines using the Affymetrix Human Exon 1.0 ST array platform. There were 27 metastatic samples amongst the 150 tumours and 35 cases of biochemical relapse . The expression array data were downloaded from GEO under accession number GSE21034 (http://www.ncbi.nlm.nih.gov/geo/query/acc.cgi?acc=GSE21034).A PCa dataset generated by Taylor https://genome-cancer.ucsc.edu/) - TCGA_PRAD_exp_HiSeqV2-2014-05-02.tgz. Associated clinical data were downloaded from the TCGA Data Portal (https://tcga-data.nci.nih.gov/tcga/).High throughput RNA sequencing data were generated by the The Cancer Genomics Atlas (TCGA) consortium for 383 samples, 50 benign samples and 333 primary tumours. 48 of these samples represented advanced disease with Gleason grade ≥8 and 13 cases had undergone progression as characterised by post-operative biochemical recurrence. Data were downloaded from the UCSC Cancer Genome Browser  and whole human genome oligo microarray (G4112A ). The expression array data were downloaded from GEO under accession number GSE35988 (http://www.ncbi.nlm.nih.gov/geo/query/acc.cgi?acc=GSE35988).A PCa dataset generated by Grasso www.oncomine.org).Additional datasets were interrogated for the expression of individual genes within signatures through the Oncomine Compendium of Expression Array data (Five datasets were downloaded and used in this study.th quantile (3.91) in more than 75% of the samples were also removed. We identified progression associated expression changes by linear model. Primary tumour versus benign and metastatic versus primary contrasts were run and differential reporters identified using a 0.01 FDR threshold. Reporters were further filtered selecting those with a differential effect size of greater than or equal to 2-fold. This resulted in a progression signature set of 4662 reporters, 3021 genes . Signatures derived from this primary dataset were subsequently applied to two additional datasets, one prostate dataset generated by Tomlins et al. [et al. [http://www.broadinstitute.org/cgi-bin/cancer/datasets.cgi).To generate an initial broad progression dependent gene set, we used the prostate progression expression dataset GSE3325 (NCBI GEO database). We quantile normalised probe level intensity values and generated probe set signal estimates using RMA . We first characterised reporters with a coefficient of variance of less than or equal to 0.05 as uninformative and removed them from further analysis. Reporters having intensities below the 10We clustered our progression gene set using hierarchical clustering with a Ward agglomerative method designed to minimize intra-cluster variance  and a 1 - Pearson correlation coefficient dissimilarity measure. We found this method produced a more highly correlated clustering structure when compared to other methods leading to more compact sub-clusters . We then scaled PIN samples to EPI_ADJ_PCA control samples, PCA samples to PIN, MET_HNF to PCA and MET_HR to PCA. To identify hormone refractory dependent expression changes MET_HR samples were scaled to the median across the non-refractory samples MET_HN. To determine module induction or repression within the scaled samples we tested for enrichment of module genes within the sample associated expression changes using a hypergeometric distribution, <= 0.05 fdr. Mapping was achieved across array platforms using NCBI Entrez gene ids. Modules with an intersection of less than 3 were discarded from the analysis.To determine if any of the enriched modules were capable of segregating samples on phenotype we built contingency tables across clinical conditions from each of the data sets  to log10(3000) in increments of log10(3000/0.05)/39. Branch length threshold intervals were chosen to produce a broad range of cluster numbers.To determine the best clustering method and branch length thresholds to apply to our analysis we clustered our 4662 reporter prostate tumour progression signature  dissimilarity values across the array of branch length thresholds can be seen plotted against cluster number in Additional file where To quantify the information content of our clusters from a biological perceptive we assigned GO terms to cluster members. This was achieved by mapping GO terms via reporter entrez gene id assignments using the GO.db annotation package from Bioconductor. To quantify the GO information content of a cluster we calculated Shannon Entropy bit values given by:xi is a cluster associated GO term, p(xi) is the probability of choosing xi from all cluster GO terms , i = 1,2,…N where N is the total number of unique cluster GO terms, k = 1,2,…K where K is the total number of clusters and b = 2. H(X) bit values for different branch length thresholds can be seen plotted against cluster number for the different clustering techniques in Additional file where http://jexpress.bioinfo.no/site/). Subsequently, both sample groups and genes were hierarchically clustered using complete linkage and Euclidian distance using the freely available software Cluster 3.0 (http://bonsai.hgc.jp/~mdehoon/software/cluster/software.htm). Heatmaps were produced using Java Tree View (http://jtreeview.sourceforge.net/).For visualization, sample groups were averaged using the mean prior to high level mean and variance normalization using the freely available software J-Express 2012 (# Title Agilent-014850 Whole Human Genome Microarray 4x44K G4112F# tissue: benign prostate tissue (N)# 12# tissue: localised prostate cancer (T)# 49# tissue: metastatic castrate resistant prostate cancer (WA)# 27.Testset: Grasso 1 Platform GPL6480# Title Agilent-012391 Whole Human Genome Oligo Microarray G4112A# tissue: benign prostate tissue (N)# 16# tissue: localised prostate cancer (T)# 10# tissue: metastatic castrate resistant prostate cancer (WA)# 8.Training data: Grasso 2 Platform GPL6848http://www.ncbi.nlm.nih.gov/geo/query/acc.cgi?acc=GSE35988.To evaluate the prediction performance 33 gene signature we analysed data from a microarray experiment of Grasso et al as available from GEO (GSE35988) The dataset includes measurements on two different microarray platforms GPL6480 and GPL6848 and includes three different tissue types .We used the samples typed on platform GPL6848 as trainings data to derive the weights of the genes in the multi-gene signature. First, we replaced missing values using the k nearest neighbor algorithm as implemented in the R package impute. The gene PCA3 was not measured on the microarray and the gene CRISP3 was not observed in more than half of these samples. Thus, these two genes were excluded from the signature. We estimated the weights of each gene using an L2 regularized logit regression model  with theThen we used the samples typed on platform GPL6480 as test data to evaluate the prediction performance of the gene-signature. Per sample we computed one score as the weighted average over the 31 proposed genes where the weights were defined by the independent training data. Finally, we computed ROC statistics and report the area under the curve (AUC) of the ROC curve (R package ROCR). The AUC indicates the ability of a marker to distinguish between two groups, where a value 0.5 is random and a value of 1 represents a perfect distinction between the groups. Additionally, we were looking at the AUC of specific genes, in particular KLK3, ERG and AR.et al. about a decade ago and consisting of a small number of whole tissue sections [Seesection).In order to define our starting signatures, we selected a dataset published by Varambally sections . This cosection – ‘’). In addition, we assessed the information content in gene ontology terms associated with clusters generated using each method by calculating Shannon Entropy bit values (section - ‘’). Shannon entropy and coefficient of variation are well known in a great many application domains, from theoretical physics to computational chemistry to materials science. They have been applied in bioinformatics as well, most notably in statistical genetics and molecular biology. Shannon entropy is derived from information theory [A number of different correlation or dissimilarity metrics have been employed when constructing co-expression networks. To determine the correlation between the genes we used a Pearson correlation coefficient to construct a dissimilarity matrix across all affected samples in the prostate tumour progression dataset and all genes identified in the preliminary analysis. We then used hierarchical clustering to group the genes. There are a number of available agglomeration methods available each producing their own clustering structure. To determine the best agglomeration method to apply in constructing our expression modules, we clustered our prostate tumour progression signature using single, average, complete, the Ward  minimum n theory . Most ren theory , to accen theory . By theshttp://david.abcc.ncifcrf.gov/) to determine whether KEGG pathways were enriched within these signatures, we identified focal adhesions  (Table −6) in signature 1 are listed in Table Four large gene signatures were generated at the least stringent cut-point consisting of 1334 genes referred to as signature 1  and the enrichment arose from the overexpression of a total of 36 genes linked to this process in the metastatic cases versus benign tissue. The genes are listed in Table By contrast, signatures 3 and 4 contained genes that predominantly discriminated between metastatic cases and benign tissue samples. The dominant pathway for signature 3 was cell cycle regulation   Table . The fouet al., and also The Cancer Genome Atlas (TCGA) data recently generated using high-throughput transcript sequencing of prostate cancers [http://cancergenome.nih.gov/). MYC and GLYATL1 remain significantly overexpressed features (>1.3 fold) within these signatures in both datasets , myocardin (MYOCD), and myosin, light chain 9, regulatory (MYL9)thus accounting for the pathway enrichment for vascular smooth muscle contraction. As prostate cancer progresses to more advanced stages there is a depletion of stromal cells from the tissue and this perhaps explains the dominant contribution from downregulated muscle-associated genes to the signature and also other features of pathway enrichments particularly of the focal adhesion classification . In orde cancers  , MYC, distal-less homeobox 1 (DLX1), homeobox C6 (HOXC6) and v-ets avian erythroblastosis virus E26 oncogene homolog (ERG)).c-Myc is a well-established oncogenic transcription factor, which is overexpressed through chromosomal amplification on 8q24 but also through post-translational events, which may include glycosylation of the N-terminal transactivation and concomitant antagonism of proteasomal degradation ,31,32. Eet al. and a transcriptomic dataset generated for prostate cancer through high-throughput sequencing by the The Cancer Genome Atlas (TCGA)  Figure . In both) Figure . SecondlCurrently prostate-specific antigen (PSA)/kallikrein 3 (KLK3) is the most widely used protein biomarker for prostate cancer. The androgen receptor (AR) is the most significant transcription factor driving prostate cancer, but is also expressed at high levels in untransformed luminal epithelial cells and therefore is predominantly used as a transcript biomarker associated with metastatic disease and concomitant copy-number amplification . Gene fuet al., and consisting of benign tissue, localised prostate cancer and metastatic cases [To assess the performance of the 33-gene signature in comparison to KLK3/PSA, AR and ERG we interrogated an additional independent expression array dataset generated by Grasso ic cases . This daic cases . KLK3/PSic cases -46. In oet al. ROC curves reveal that the signature exceeds the performance of ERG, KLK3 or the AR as a classifier. Intriguingly, one third of these genes are glycosylating enzymes and transcription factors. PCa is significantly driven by a transcription factor, the AR, but there is increasing evidence of contributions by others and of interplays between them and indeed our signature does not include the AR itself. However, it includes both established examples (MYC and ERG) but also others that have so far been less studied . Mechanistically, future work will investigate this transcriptional co-dependency in more detail and clinically these signatures will be further evaluated in clinical cohorts.In conclusion, in this study we have used a multi-step approach to refine gene signatures derived from diverse transcript detection platforms and sample types in order to arrive at a robust gene signature able to discriminate between PCa and benign tissue Figure . This is


The HLR approach inherits some fascinating characteristics from L1/2 (sparsity) and L2 (grouping effect where highly correlated variables are in or out a model together) penalties. We also proposed a novel univariate HLR thresholding approach to update the estimated coefficients and developed the coordinate descent algorithm for the HLR penalized logistic regression model. The empirical results and simulations indicate that the proposed method is highly competitive amongst several state-of-the-art methods.Cancer classification and feature (gene) selection plays an important role in knowledge discovery in genomic data. Although logistic regression is one of the most popular classification methods, it does not induce feature selection. In this paper, we presented a new hybrid L With advances in high-throughput molecular techniques, the researchers can study the expression of tens of thousands of genes simultaneously. Cancer classification based on gene expression levels is one of the central problems in genome research. Logistic regression is a popular classification method and has an explicit statistical interpretation which can obtain probabilities of classification regarding the cancer phenotype. However, in most gene expression studies, the number of genes typically far exceeds the number of the sample size. This situation is called high-dimensional and low sample size problem, and the normal logistic regression method cannot be directly used to estimate the regression parameters.1 penalty .To further evaluate the effectiveness of our proposed method, in this section, we used several publicly available datasets: Prostate, DLBCL and Lung cancer. The prostate and DLBCL datasets were both downloaded from More information on these datasets is given in et al. [This dataset was originally proposed by Singh et al. ; it is cet al. [This dataset  containAs RNA- sequencing (RNA-seq) technique widely used, therefore, it is important to test the proposed method whether it has the ability to handle the RNA-seq data. To verify it, one dataset that used the next-generation sequencing was involved in our analysis. This dataset  containsWe evaluate the performance of the HLR penalized logistic regression models using the random partition. This means that we divide the datasets at random such that approximate 75% of the datasets becomes the training samples and the other 25% as the test samples. The optimal tuning parameters were found by using the 10-fold cross-validation in the training set. Then, the classification model was built by the sparse logistic regression with the estimated tuning parameters. Finally, application of the classifier to the test set provides the prediction characteristics such as classification accuracy, AUC under the receiver operating characteristic (ROC) analysis. The above procedures were repeated 500 times with different random dataset partitions. The mean number of the selected genes, the training and the testing classification accuracies, were summarized in 1/2, SCAD − L2 and Elastic net methods give the average 10-fold CV accuracy of 96.22%, 96.13%, 95.99%, 96.28% and the average test accuracy of 92.4%, 92.18%, 91.33%, 91.35% with 13.7, 8.2, 22 and 15.2 genes selected respectively. For lymphoma datasets, it can be seen that the HLR method also achieves the best classification performances with the highest accuracy rates in the training and test sets. For lung cancer, our method gained the best training accuracy. The testing performance of Elastic net was slightly better than our method. However, the HLR method achieved its success using only about 15.6 predictors (genes), compared to 28.9 genes for the Elastic net method. Although the Lasso or L1/2 methods gained the sparsest solutions, the classification performance of these two approaches were worse than the HLR method. This is an important consideration for screening and diagnostic applications, where the goal is often to develop an accurate test using as few features as possible in order to control cost.As showed in As showed in We summarized the top 10 ranked (most frequently) genes selected by the five regularization methods for the lung cancer gene expression dataset in To further verify the biomarkers selected by our method, we had collected two independent lung cancer datasets for validation. The GSE19804  containsWe used the support vector machine (SVM) approach to build the classifiers based on the first two, first five and first ten genes selected by the different regularization approaches from the lung cancer dataset , and wer2, for GSE32863, was calculated to be 92.24% that was worse than the classifier with the genes selected by our HLR method, 96.55%. The results indicate that the sparse logistic regression with the HLR approach can select powerful discriminatory genes.It is known that the obtained prediction models may be only applicable to samples from the same platform, cell type, environmental conditions and experimental procedure. However, interestingly, as demonstrated in 1/2, SCAD − L2 and Elastic net techniques, we also make a comparison with the results of other methods for datasets prostate and lymphoma published in the literature. Note that we only considered methods using the CV approach for evaluation, since approaches based on a mere training/test set partition are now widely known as unreliable [In addition to comparing with the Lasso, Lreliable . Table 61/2 (sparsity) and L2 (grouping effect where highly correlated variables are in or out a model together) penalties. We also proposed a novel univariate HLR thresholding function to update the estimated coefficients and developed the coordinate descent algorithm for the HLR penalized logistic regression model.In this paper, we have proposed the HLR function, a new shrinkage and selection method. The HLR approach is inherited some valuable characteristics from the L1/2, SCAD − L2 and Elastic net in analyzing high dimensional and low sample sizes data (microarray and RNA-seq data). Thus, logistic regression with the HLR approach is the promising tool for feature selection in the classification problem. Source code of sparse logistic regression with the HLR approach was provided in The empirical results and simulations show the HLR method was highly competitive amongst Lasso, LS1 File(PDF)Click here for additional data file.S2 FileTop-10 ranked genes selected by all the methods for prostate and lymphoma datasets.(PDF)Click here for additional data file.S3 FileMATLAB code of sparse logistic regression with the HLR approach.(RAR)Click here for additional data file.


High-throughput RNA Sequencing has made splice variant profiling practical. However, its true merit in quantifying splicing isoforms and isoform-specific exon expressions is not well explored in inferring gene networks. This study demonstrates SpliceNet, a method to infer isoform-specific co-expression networks from exon-level RNA-Seq data, using large dimensional trace. It goes beyond differentially expressed genes and infers splicing isoform network changes between normal and diseased samples. It eases the sample size bottleneck; evaluations on simulated data and lung cancer-specific ERBB2 and MAPK signaling pathways, with varying number of samples, evince the merit in handling high exon to sample size ratio datasets. Inferred network rewiring of well established Bcl-x and EGFR centered networks from lung adenocarcinoma expression data is in good agreement with literature. Gene level evaluations demonstrate a substantial performance of SpliceNet over canonical correlation analysis, a method that is currently applied to exon level RNA-Seq data. SpliceNet can also be applied to exon array data. SpliceNet is distributed as an R package available at  Cancer is a complex biological phenomenon where the dynamic interplay between various tumor associated genes and their splice variants (isoforms) are curtailed in determining cell fate . With thTraditionally, DNA microarrays are used to quantify gene expression patterns . SeveralWith the recent advances in next-generation sequencing, RNA Sequencing (RNA-Seq) is gaining popularity in accurately quantifying gene expression. RNA-Seq with its high sensitivity, low background noise and a larger range of coverage, is more robust when compared to traditional microarrays . In RNA-Traditional gene network inference methods such as correlation or mutual information based methods, covariance selection, sparse graphical models and partial correlation methods are based on overall gene expressions . HoweverIt is also important to account for isoform-specific exon expressions, as an exon can be shared by multiple isoforms with different expressions. Unfortunately, none of the current methods consider isoform-specific exon expressions. In lieu of above, there is a strong need to develop efficient computational methods for RNA-Seq expression data analysis that can account isoform-specific exon expressions and are least affected by the exons to sample size ratio . This sthttp://www.jjwanglab.org/SpliceNet/. Although this study demonstrates the application of SpliceNet to cancer genomic data, it can be applied to any exon level RNA-Seq data or exon array data. A detailed explanation of the proposed approach is given in the ‘Materials and Methods’ section.The networks recovered by the proposed method perceive isoform co-expressions. This study goes beyond differentially expressed genes and comprehends diseases by inferring isoform network differences, and can be used in understanding the molecular mechanisms of cancer and other diseases . FurtherExon-level (level 3) RNA-Seq data of lung, kidney and liver cancers are downloaded from TCGA data portal. In total 49 lung adenocarcinoma (LUAD), 45 lung squamous cell carcinoma (LUSC), 50 liver hepatocellular carcinoma (LIHC) and 72 kidney renal cell carcinoma (KIRC) matched samples are used in this study. An in-depth description of RNA-Seq data is published elsewhere . Cancer-p × n, where p is the number of exons mapped to the isoform and n is the number of samples (RNA-Seq) as illustrated in Figure G is mapped to its isoforms and then to their corresponding exon boundaries according to the coordinates of HG-19 (UCSC genome browser) reference genome. Secondly, exon boundaries of each isoform from 1,.., m of gene G are matched to exon-positions of each level 3 RNA-Seq sample and corresponding exon-expression values are extracted. An exon is considered only if it is expressed in at least 50% of the samples, as any inference with half of the data missing (no expression) is not reliable. Considering sequencing errors an error margin of ±5 nt positions is allowed in mapping exon boundaries. The error margin of ±5 nt is a reasonable tradeoff between the acceptable sequencing errors and the smallest human exon of 15 nt }]. Sample wise exon-level expressions and isoform expressions are downloaded from TCGA data portal.Every isoform of a gene in the interest list is represented as an exon-expression matrix (multivariate random variable) of order of 15 nt  and can of 15 nt ,18. MoreX1)( and X2)( with p and q number of exons respectively. Exon-level expressions of the sample are represented as ith exon in X1)( and X2)( and the sample size is n. Suppose that the exon-expression matrix p + q)-dimensional normal distribution N, where μ is the mean vector and Σ is the population covariance matrix of X.Σ11 and Σ22 are the variance matrices of X1)( and X2)( and X2) is small while the sample size is sufficiently large ,18. HoweΣ12 = 0 identifies a zero correlation and independence between the two multivariate random variables, X1)( and X2) is represented as follows:Σij areH0, we use the LDT statistic defined as follows:tr denotes the trace of a matrix. The elements on the main diagonal of nL converges to a normal distribution and is close to zero. A co-expression edge is drawn between any two isoforms/genes based on accepting or rejecting the null hypothesis by comparing the observed value of test statistic, T to the critical value Z at significance level α. If the null hypothesis is rejected, an edge is inferred connecting corresponding isoforms. The critical value for testing the hypothesis is computed by deriving an asymptotic distribution of the statistic . When the ratios of dimension to sample size p/n and q/n are not small enough , from recent high-dimensinonal statistic literature, we knew that standard estimation is not consistent. Therefore, test procedure based on CCA is not reliable. Experiments in the results section clearly show that SpliceNet significantly outperforms CCA.In contrast, the CCA criterion is based on standard consistent estimate of population CCA, provided that the dimensions The method described in the previous section can essentially infer isoform-specific co-expression networks from cancer and normal samples (RNA-Seq data) respectively. Nevertheless, to systematically understand the cause, prognosis and to identify confident therapeutic targets it is very important to distinguish cancer and normal samples. Differentially expressed genes are often identified as disease causing/target genes. The limitation of discounting relationships among genes in such studies advocates the need of new approaches. This study goes beyond differentially expressed genes and theorizes genes as networks to thoroughly comprehend a disease by inferring differential cancer co-expression networks.P-values. According to Figure I1,1 of gene G1 is co-expressed with isoforms I2,1 and I2,3 of gene G2, and I1,2 of G1 with I2,3 of G2. On the other hand, in cancer samples  and I1,1– I2,3 (red).A differential cancer co-expression network is defined as a network with co-expression edges that are either observed only in cancer or in normal samples. Firstly, two independent co-expression networks are inferred using the proposed methods from tumor-matched and normal-matched RNA-Seq samples respectively. Then, a graph comparison operation is performed to remove all common edges. The remainder, differential co-expression edges can be ranked based on the corresponding s Figure , I1,1 ofk Figure  has two F-scores reported in Table The key merit of SpliceNet is in handling large dimensional data, where the number of exons per gene is large and comparable to sample size i.e. when the ratio of number of exons per gene to sample size is large. Firstly, to thoroughly evaluate the performance and stability of SpliceNet, simulations are performed by varying number of exons (dimensions) and samples. The performance of existing R package, RNASeqNet is also evaluated on the same data. The results summarized in Table P-value is ≤0.05. For independent gene pair (no co-expression), random sample Z = (1 Z2Z)T is drawn from population following multivariate normal distribution N of sample size n, where i = 1,2 and p is the number of exons. For dependent gene pairs (co-expressed), sample X = (1 XX2)T is drawn such thatc0 is a constant that is inversely proportional to the distance between null and alternative hypothesis. The performance and stability of SpliceNet is demonstrated by simulating each experimental setup with three different 0c values, 0.2, 0.4 and 0.6. A measure of accuracy, F-score . In contrast the performance of SpliceNet is extremely stable between 0c values 0.6 and 0.4, and adequately stable between 0.4 and 0.2. The overall performance drop of SpliceNet is <10%, verifying the stability of SpliceNet. Secondly, number of exons and sample size are also found to influence the performance of respective methods. A general trend of increasing performance is observed as the sample size increases from 25 to 100 for both RNASeqNet and SpliceNet. However, the performance of SpliceNet is quite significant when compared to RNASeqNet even with smaller sample size and stabilizes quickly . This demonstrates the suitability of SpliceNet even to smaller datasets, which is a major bottleneck for the current methods. Efficiently handling smaller sample size is one of the prime requirements of any analytical tool in biological domain, as it is not always practical to have large number of samples of a specific cancer/disease/condition, small number of available tumor and normal matched RNA-Seq samples support this argument. The F-scores of SpliceNet on different exon combinations 5-5 (low), 20-20 (high) and 20-5 (high-low) are quite comparable, with maximum at 5-5 followed by 20-20 and 20-5. This suggests the merit of SpliceNet in handling genes with both small and large number of exons. It is important to note that SpliceNet has effectively handled high dimensional cases (20-20), especially when the total number of exons  as the sample size increased from 25 to 100. This phenomenon suggests the influence of dimensions to sample size ratio than just the sample size on the performance of CCA based RNASeqNet. In contrast, an increasing trend of performance is observed for other combinations (5-5 and 20-20). It is speculated that a square matrix structure, when the sample size (0c = 0.4), and the results are summarized in Table Simulations are performed by varying number of exons per gene (dimensions) and samples to analyze the influence of the same on the performance of SpliceNet. For gene pair G1–G2, number of exons are set to 5-5 (low), 20-20 (high) and 20-5 (high-low), and number of sample to 25, 50, 75 and 100 i.e. in total there are 12 experimental setups. For every setup, 100 000 replications are performed at 5% significance level i.e. a dependency is considered statistically significant if the  F-score  is reporof exons  is great0c = 0.6), raising consistency concerns on the performance of CCA. Over all, it is evident from Table The performance of RNASeqNet Table  dropped To draw a parallel, SpliceNet is evaluated on the same non-small cell lung cancer-specific pathway used by RNASeqNet . Cancer-To comprehend the advantages and the applications of isoform-specific Differential Cancer Networks, a detailed work out of SpliceNet on Bcl-x and EGFR centered network is demonstrated here. Bcl-x gene is well established to be involved in majority of non-small cell lung cancers . It has Another small network including EGFR (four isoforms) and two other well-established cancer related genes viz. CD44 , eight iF-scores reported in Table To demonstrate the practical applicability, SpliceNet is also evaluated on real RNA-Seq data from three different tissues viz., lung, kidney and liver. Only normal-matched RNA-Seq samples are used for the following evaluation. A total of 49 lung adenocarcinoma (LUAD), 50 LIHC and 72 KIRC samples are downloaded from TCGA data portal. Due to the lack of adequate experimental evidence for isoform co-expression networks, evaluation is performed at gene level. Firstly, tissue-specific gene lists and gene expressions are downloaded from tissue-specific gene expression and regulation, TiGER database , and EnsNetwork inference is the first step towards understanding any complex biological phenomenon ,43,44. TThis study demonstrates a novel method to infer isoform-specific co-expression networks from exon-level RNA-Seq data using LDT. The proposed method, SpliceNet abstracts expressions of genes as multivariate random variables with different number of dimensions (exons) and tests the corresponding dependencies by approximating an empirical distribution. Isoform-specific exon expressions are computed from sample-wise isoform expression data, which was estimated by TCGA project team using RSEM algorithm . HoweverSupplementary Data are available at NAR Online.


Muscle type of pyruvate kinase (PKM) is one of the key mediators of the Warburg effect and tumor metabolism. Due to alternative splicing, there are at least 12 known isoforms of the PKM gene, of which PKM1 and PKM2 are two major isoforms with only a 23 amino acid sequenced difference but quite different characteristics and functions. It was previously thought the isoform switch from PKM1 to PKM2 resulted in high PKM2 expression in tumors, providing a great advantage to tumor cells. However, this traditional view was challenged by two recent studies; one study claimed that this isoform switch does not occur during the Warburg effect; the other study asserted that the isoform switch is tissue-specific. Here, we re-analyzed the RNA sequencing data of 25 types of human tumors from The Cancer Genome Atlas Data Portal, and confirmed that PKM2 was the major isoform in the tumors and was highly elevated in addition to the entire PKM gene. We further demonstrated that the expression level of PKM1 significantly declined even though there was substantially increased expression of the entire PKM gene. The proportion of PKM1 in total transcript variants also significantly declined in tumors but the proportion of PKM2 did not change accordingly. Therefore, we conclude that the isoform switch of PKM1 does indeed occur, but it switches to other isoforms rather than PKM2. Considering the change in the expression levels of PKM1, PKM2 and the entire PKM gene, we propose that the upregulation of PKM2 is primarily due to elevated transcriptional levels of the entire PKM gene, instead of the isoform switch. Numerous metabolic changes during tumorigenesis have received increased attention in recent years. The best known and probably most central change is the unusually high rate of glycolysis and lactate production, which was originally described by Otto Warburg in the 1920s, and was subsequently termed the Warburg effect. Although the mechanisms underlying the Warburg effect are not completely understood, it is widely thought that muscle type of pyruvate kinase (PKM) plays a key role.http://genome.ucsc.edu), but their characteristics, functions, and expression have received little attention and remain unclear.The PKM gene produces two major alternatively spliced isoforms, PKM1, which is constitutively active, and PKM2, which can switch between an active tetrameric and more common inactive dimerform. PKM2 is highly upregulated in cancer cells, and the dynamic tuning of its activity causes the transition from aerobic respiration to glycolysis. This transition is customarily believed to result in the accumulation of phosphoenolpyruvate and other glycolytic intermediates, and consequently, the redirection of glucose for macromolecule iosynthesis rather than ATP production, which provides a great advantage for the growth and division of cancer cells. Currently, there are 10 other isoforms of the PKM gene recorded in the University of California Santa Cruz (UCSC) Genome Bioinformatics database , and included 618 human normal samples and 7,290 tumor samples from 25 tissue types (http://www.ncbi.nlm.nih.gov/gene) using BLAST to determine the transcriptional patterns of these 14 transcript variants. Finally, we assigned uc002atw.1 and uc002atx.1 to PKM1, and uc002aty.1 to PKM2. RNA-Seq by expectation maximization (RSEM) values were used to represent the expression levels of these transcript variants. Data were presented as mean ± standard error of mean (SEM).Level 3 RNA sequencing (RNA-Seq) V2 data , which was released by TCGA before April 15, 2014, were downloaded from the TCGA data portal . Student’s To study the expression profiles of PKM and its isoforms in human tumors, we analyzed TCGA Level 3 expression data from samples that were profiled using RNA-Seq technology, and identified 14 transcript variants of PKM. PKM1, PKM2, and 10 other known isoforms are translated from these transcript variants. The transcriptional patterns of these transcript variants are shown in In Desai et al. , the autThe RSEM value of each transcript variant was calculated, and the results are summarized in As shown in As shown in As shown in As shown in In this study, we examined the mRNA profile of PKM in many types of human tumors based on TCGA data. We discovered that the expression level of PKM1 significantly declined even though there was substantially increased expression of the entire PKM gene in most human tumors. Both the expression and proportion of PKM1 declined, indicating that the PKM1 isoform switch did indeed occur. However, the proportion of PKM2 did not increase as PKM1 levels decreased. We found that the isoforms whose proportions were most increased were uc002atr.1 and uc002ats.1  Tables, et al. [et al. [et al. [et al [et al. [Previous studies reported that PKM1 dominated in normal tissues and its dominance was replaced by PKM2 in cancer development . In factet al.  discover [et al. , the aut. [et al . Due to  [et al.  might noet al. [In the study by Desai et al. , the autWe noticed that prostate adenocarcinoma was the only cancer type in which PKM significantly decreased compared with the normal controls, perhaps due to the slow growing nature of this cancer . In addiWe observed that many other glycolytic enzymes, such as hexokinase 2 (HK2), phosphoglycerate kinase 1 (PGK1), glyceraldehyde-3-phosphate dehydrogenase (GAPDH), and lactate dehydrogenase A (LDHA) were increased in most tumors in the TCGA data portal ., consisFor the past few years, PKM2 was found to not only act as a key enzyme of glycolysis in cytoplasm, but also can be translocated into the nucleus of tumor cells via many different mechanisms ,37. The de novo transcript assembly. Using this technique, transcript levels are usually normalized by RSEM or reads per kilobases per million mapped reads (RPKM), which ideally facilitate the transparent comparison between multiple genes and samples [In recent years, RNA-Seq has emerged as a popular and powerful tool for high throughput whole genome analysis, including transcript quantification, differential expression testing, reference-based gene annotation, and  samples ,49. As sS1 Fig(TIF)Click here for additional data file.S2 Fig(TIF)Click here for additional data file.S1 TableTranscript variants uc002atw.1 and uc002atx.1 are translated to M1; uc002aty.1 is translated to M2. Data are presented by mean and SEM.(DOC)Click here for additional data file.S2 Table(DOC)Click here for additional data file.S3 Table(DOC)Click here for additional data file.


A method is developed that builds upon the widely used two-sample t-statistic approach and uses analysis in Hilbert space to decompose the nonidentified gene vector into two components that are correlated and uncorrelated with the identified set. In the application to data derived from a widely studied prostate cancer database, the proposed method outperforms some of the most highly regarded approaches published to date. Algorithms in MATLAB and in R are available for public download.Accurate differential analysis of microarray data strongly depends on effective treatment of intergene correlation. Such dependence is ordinarily accounted for in terms of its effect on significance cutoffs. In this paper, it is shown that correlation can, in fact, be exploited to share information across tests and reorder expression differentials for increased statistical power, regardless of the threshold. Significantly improved differential analysis is the result of two simple measures: (i) adjusting test statistics to exploit information from identifiable genes (the large subset of genes represented on a microarray that can be classified  In some fields of investigation, especially, perhaps, research in early states of knowledge , there is an equally obvious drawback in using real data—that the “correct answers are not known,” making it difficult to ultimately interpret differences in performance as anything but differences.In certain ways, this paper represents a departure from current trends in scientific publishing. The Worldwide Web has made available extraordinary resources in the form of databases for comparative analysis of methods in bioinformatics and numerous other disciplines. The benefits of using Lest the reader be preparing for an argument promoting classic simulation studies, we hasten to state at the outset that this argument is not forthcoming. Before the age of the internet, simulation studies using reasonably justified data models  were a time-honored standard in all areas of math, science, and engineering. The ready availability of rich data resources makes it irrational to advocate to a return to “pure simulation” using models that are untested against these existing data sets. The authors of this paper in no way promote a return to such methods and appeal to the reader to recognize that “models detached from reality” are not used in any way in this paper.modus operandi is to accept uncertainty in the performance results with the benefit of authenticity in the data generation. The authors hope that this question might engender some debate and research.This research centers on some rather straightforward adjustments to classic hypothesis-testing procedures for use in differential analysis of microarray expression data. The salient result is a “reranking” of the order in which gene expression data are considered for “truly differential” status. In an effort to objectively compare these modified methods with the performance of established algorithms, it was decided to create a database of microarray expression simulations in which the data retained as much second-order statistical character as possible relative to a widely used prostate cancer database. The up- and downregulations of gene expressions were indeed synthetically modulated onto a carefully constructed baseline. The consequence is a set of comparative performance results that are objectively based on data that were “guided by nature” but which were, quite openly stated, synthesized with this natural guidance. Rather than dismissing these results as “simulations,” the reader is urged to consider whether there is merit in moving the uncertainty to the data generation side (if that uncertainty can be intelligently controlled), if it permits objective results on the data analysis side. The current Using the testing approach employing “nature-guided simulation,” the results for the reranking method presented here are remarkably good relative to two established methods developed by respected authorities. Many people have reviewed these results, including some very eminent statisticians and bioinformaticians. Reactions have ranged from encouragement and amazement to deep skepticism. The comment “too good to be true” has been used at least twice, including, once, in a constructive criticism, by a distinguished editor of this journal. We understand this response: unfortunately , no one has been able to find a flaw in the methods. We suggest two possibilities. (1) Some aspect of the simulation procedure is creating a bias toward the developed detection method. (2) Authors with a somewhat different perspective  were able to see some relatively simple algorithmic adjustments that eluded researchers focusing on deeper issues.ISRN Journal of Bioinformatics for the opportunity to bring these ideas to the attention of the research community.Rather than viewing the results of this paper as a claim of superiority of the new method over respected algorithms, the authors appeal to the reader to accept the report in the spirit it is offered: interesting, potentially useful, results that raise many questions, and possibilities for further research. The “intelligent stimulation” approach in itself may offer some grounds for innovation in the field. Attempts to verify that the present results are, indeed, “too good to be true” may reveal technical information benefiting differential expression detection methods. This is the classical way in which research moves forward. We are grateful to the Nature Genetics article entitled “Array of hope” )t-statistic approach with a decomposition of the expression vectors into subspaces of correlated and uncorrelated components.This paper is focused exclusively on the differential expression problem. Research in this area has largely focused on understanding harmful correlation effects on the choice of the threshold demarcating the statistical boundary between differential and nondifferential expression. In fact, however, the nominally confounding correlation can be used to advantage in increasing statistical power of microarray studies. This paper presents a differential analysis method that exploits identifiability and uses a gene expression reranking criterion that accounts for intergene correlation. The framework is readily generalizable for use in studies with multiple or continuous covariates, as well as to other multiple comparison applications. An example method presented here builds upon the widely used two-sample G genes are measured on M microarrays, resulting in a gene expression matrix, say X ∈ ℝG×M, with  element xgm. Each of the M microarray experiments takes place under one of two conditions (indexed by k = 1   or   2) such as control and treatment. These two subsets of the data are called treatment groups in the paper.Suppose that expression data for X, we seek to identify a “small” number, G∗ ≪ G, of genes that are significantly differentially expressed between the two groups. One widely used strategy , say 𝔉, or, equivalently, the FDR, defined as G∗ with the allowable 𝔉 or Based on the gene expression matrix, y e.g., , 32) is  is X, we¯ e.g., , 33–36).–36.X, weX matrix, there may be significantly fewer tail-area null counts than expected, whereas for an “underpowered” X, the situation can worsen with an excessive number of tail-area null counts. It is important to note that techniques for estimating the FDR change the numbers of genes in reported lists, not the gene rankings. The present research was motivated by the hypothesis that, for an “underpowered” X, it would be possible to exploit correlation across t scores to establish a gene ranking with more statistical power than the raw t-based ranking. The method that resulted from an exploration of this question indeed seems to improve the statistical power of all X matrices.As discussed in , 11, fort-statistics,t, to output a substantially revised version of t, denoted τ, the entries of which provide an improved gene ranking. For expediency, we will refer to the procedure that produces τ from t as correlation adjusted reranking, or simply reranking. The essence of reranking is embodied in some fundamental data conditioning procedures to effect the two outcomes mentioned in the introduction—exploiting identifiability, and nullifying the effects of intergene correlation between identified and non-identified genes.The new method uses a vector of In the following sections, we develop the theoretical basis for the reranking process. The performance of reranking is then compared with that of state-of-the-art methods on data derived from real expression experiments. Results of some judiciously developed simulation studies are also reported for their value in understanding certain aspects of the performance.t statistics introduced above. t will be viewed as a random vector with mean vector μ ∈ ℝG and covariance matrix Σ ∈ ℝG×G. Henceforth, we write t ~ . This is a theoretical model only, as μ and Σ are generally unknown. No further distribution information is required.Let us first supply the details surrounding the vector of g, g in treatment condition k. Then, the (unpaired) t-statistic for gene g is computed assg is the pooled within-group sample standard deviation of gene g. If g ∈ ℍ0, then we expect tg ~ , where ν is the number of degrees of freedom, obtained from either the unpaired t-test theory or the permutation null calculations ~t, we seek a revised vector, t1) are uncorrelated with those of the identified set . There are many ways to derive the desired result, each with its own interpretation, but all, of course, ultimately equivalent. Whatever the approach is, it is expedient to remove the mean from the vector t1 and work with the centered vector τ, will be denoted μ1 will be returned to the result at the end. Recall that the mean of the vector t0 is μ0 = 0G0×1, so that “centering” is unnecessary for t0  in the Cartesian space ℝI×J).Conditioned upon the random vector G1 ≥ G0, or p0 ≤ 0.5. If the converse is true, simply reverse the roles of the ℝG1 and ℝG0 spaces in this development). ℝG1 as a Hilbert space, ℋ, with inner product v, w ∈ ℝG1. The inner product induces a norm on ℋ given by 𝒮 be a closed subset of ℝG1. Given some v ∈ ℝG1, we wish to find closest element of 𝒮, say v, in the sense thatd is the metric in .To derive the desired expression for s e.g., –44). Let. Lett~1,a metricd=detc1 into components that are correlated, and uncorrelated, with t0. Vector tc1 resides in the space ℝG1. We seek a vector in a G0-dimensional subspace of ℝG1 (because G0 is the dimension of t0) that is close to tc1 (this will be the component of tc1 that is correlated with t0). The problem at hand is only subtly different from one described in the generalities above. The difference is that we are not given a subspace “𝒮” in which to find an optimal vector; rather we are given only a vector t0 which may reside in an uncountable number of subspaces of dimension G0. The goal will be to perform a linear operation on the given vector to “make it close” to tc1. In the process, we will inherently construct the subspace in which the optimal result resides. The subspace and resulting vector will be of dimension G0 because they are merely different representations of t0 and its implicit initial subspace ℝG0.The Hilbert-space formulation provides the structure in which to achieve the desired decomposition of the random vector t0, let us conceptualize a G0-dimensional subspace of ℝG1, 𝒮, consisting of all the (random) vectors {v : v = Ft0, F : ℝG0 ↦ ℝG1}. F represents some (yet unknown) linear operator of dimensions G1 × G0 and of rank G0. According to the Hilbert projection theorem, for a fixed t0, there is a unique vector d2 with respect to F T} = Σ10 and ℰ{t0(t0)T} = Σ00, the solution becomesGiven .g., see ),(10)∇F  ℰ{tc1tc1 as is possible in the G0-dimensional subspace of ℝG1 that is spanned by the G0 columns of operator tc1 is, say,G1 × G1, it is clearly singular (rank G0) reflecting the inability of tc1 in the subspace 𝒮⊥. In fact t1 that embodies the potentially destructive correlation of the identified genes with the candidate genes. The decorrelated version of tc1 that we seek is therefore𝒮⊥ and therefore to be orthogonal, hence uncorrelated, with t0. Finally, reinserting the mean value, μ1, of the candidate vector, we haveNow the random vector tg and tg′ when g, g′ ∉ ℍ0.Estimates of the elements of Σ are required. For this purpose, we make several observations that are easily verified through simulation. Note that  does notγ and ρ denote the scalar covariance and correlation, respectively, between real, scalar random variables, u and v:Let g, g′ ∈ ℍ0, then [ If 0, then , 4(17)γg ∈ ℍ0 and g′ ∉ ℍ0 (or conversely), thenIf y), thenγy), thenγEquation . M1 ≈ M2 (true for most microarray studies), then :gth gene measured on the mth microarray after subtracting the average response within the treatment group to which xgm belongs (k = 1 or 2). The scale factor ν/(ν − 2) cancels when the terms (Σ00)−1 and Σ01 are multiplied in , then  simplifiquations  and 19)M1 ≈ M2plied in , so thatestimate of  In the light of , 15) ta ta15) tat~1=t1−R^t-statistics . Then, X is converted to g is ranked more highly than gene g′ if gth element of G∗ genes in the reranked list are reported as differentially expressed.In order to nullify any genuine treatment differences, equation ). The elM ≪ G, so that the sample correlation matrix is severely rank deficient. A small quantity  is added to the diagonal entries of  Ordinarily, s0 = Pt0 is much faster than explicitly computing the matrix inverse linsolve with appropriate settings, which, in turn, uses the highly optimized routines of LAPACK (http://www.netlib.org/lapack/).If implemented in a näive way, the matrix inversion to compute 00)-1 in  would be00)-1 in , P^t0, bG = 12625 genes and M = 102 samples. For these data, the algorithm above implemented using MATLAB version R2006b on a computer with a 2.2 GHz dual-core AMD Opteron processor and 8 GB of RAM required ~40 seconds to report the final gene list. Similar implementation with explicit matrix inversions requires ~10 minutes. These times clearly indicate the relative benefit of avoiding the explicit matrix inversion, but the faster reporting time of ~40 sec should certainly not be interpreted as a lower bound for a problem of this scale. Indeed, workstations with 32 GB or more of RAM and with faster processors with eight or more processing cores are commercially available at modest costs. Of course, MATLAB is designed for modularity and ease of use, not computational efficiency. Dedicated, lower-level coding of the reranking steps, implemented on a faster machine with more parallelism could reduce the reranking time significantly. The prostate cancer data  used in s0 to the pooled sample standard deviation when computing the two-sample t-statistic:t/F-test [t/F-test [a posteriori probability approach [𝔉, and the corresponding FDR values,  The reranking method developed above is compared with two leading techniques, SAM  and EDGding SAM , the t/Ft/F-test , 50, thet/F-test , the empt/F-test , and theapproach . It is nG = 12625 genes on M = 102 oligonucleotide microarrays, comparing M1 = 50 healthy males with M2 = 52 prostate cancer patients. The purpose of the Singh study is to identify genes that might anticipate the clinical behavior of prostate cancer. The  .CEL files for the prostate study are publicly available at http://www-genome.wi.mit.edu/MPR/prostate. The general purpose of the present experiments is to compare performance of the reranking algorithm with the published state-of-the-art methods EDGE and SAM. The software RMAExpress [X by the log of its expression level.The primary experiments reported in this paper are based on the prostate cancer data from the work of Singh et al. . This daAExpress  was usedAExpress , each gea priori. Of course, in the nascent field of genomics, such knowledge is not available, and it is the very purpose of techniques like those discussed in this paper to seek such information. We approached this circular problem by using the prostate database to create test expression data with intergene correlation in X resembling that in the real microarray data. This was accomplished by first row standardizing the expression matrix from the prostate database. In particular, the true prostate matrix X was transformed to k = 1, then for k = 2) and for each g:g, m) element of matrix X. Normalizing within-group sample mean squares to unity is not implemented in the reranking algorithm. The normalization is done here prior to any processing as a first step in creating an expression matrix with known differentiation of expression across groups for each gene, but with realistic  intergene correlation.Comparative algorithm performance and insight into the inner workings of the reranking method required expression matrices for which truly differentially expressed genes were known M1 = 50 and M2 = 52. Next, G+ (G−) genes were randomly chosen for up- (down-) regulation by adding a positive (negative) offset x+ (x−) to the corresponding entries in group 2. The total number of truly differentially expressed genes is denoted :truly differentially expressed genes, and, for future purposes, the ratio of the size of the desired gene-discovery list to the number of truly-differential genes, To generate a test data set from statex.r from the EDGE software package (http://www.genomine.org/edge/) and samr.r from the SAMR package (http://www-stat.stanford.edu/~tibs/SAM/), respectively. Both routines computed their native gene summary statistics given the matrix X and corresponding column labels. These statistics, in turn, were used to determine the top G∗ genes. Results based on reranking proceed from the steps outlined in G∗ values corresponding to the largest In all experiments, results for the existing EDGE and SAM methods were obtained using the subroutines pδ, to represent typical conditions of two general classes of gene-discovery problems. The third case was carried out to test robustness of the technique to small sample size.Three experiments (cases) involving the prostate data are reported here. The first two cases were designed, by choice of the proportion of truly differential genes, pδ is small, pδ ~ 0.01–0.05, meaning that there are relatively few truly differentially expressed genes. The smaller pδ is consistent with microarray investigations seeking genes that distinguish subtypes of cancer or diabetes, for example. The complete simulation parameter set for x± = ±0.1 means that x+ = +0.1 and x− = −0.1. For numerical simplicity, we based the experiments on G = 12,000 of Singh's [Gδ = pδG = 300. Two sets of experiment parameters are used in  In the first case,  Singh's  gene expSubcase 1.1 . In the first experiment, the parameter set isG∗ = 100, is significantly smaller than Gδ = 300, or pδ∗ = G∗/Gδ = 1/3. In practice, a relatively small G∗ would be chosen to identify high-quality, class-distinguishing features for expression-profiling-based clinical diagnosis and prognosis, in which the goal is to build accurate classifiers and predictors. Whereas Singh et al. [h et al.  build a 𝒫δ1, 𝒫e1) of Subcase 1.1. Remarkably, for 36 of 40 X matrices, the reranking procedure reports gene lists with no false discoveries at all, while the other techniques fail to obtain a single gene list with pδ” experiments carried out with an array of parameter sets. In particular, the quality of the results notwithstanding  or decreasing the “signal” magnitudes of either up-( x+) or down-(x−) regulation, all create increasing probabilistic risk of false discoveries, 𝔉. As G∗ was allowed to approach Gδ in 𝔉, yet the reranking approach remained consistently superior to the others according to this measure. “Better,” however, does not always mean “good.” For illustration, we report a second In any rational detection algorithm built around a parametrized stochastic framework, it is possible to find regions of the parameter space in which performance deteriorates. In the “small Subcase 1.2 . In this variation of G∗ = Gδ = 300. This is still a “small pδ” situation, but with a “greedy” approach to gene discovery, an attempt to identify “all” genes (estimated to be) differentially expressed, pδ∗ = 1. Such a strategy would be employed in a microarray study designed to liberally identify a set of genes to be explored further—experimentally or computationally—to gain better understanding of underlying gene networks.𝔉, over 40 data sets for Subcase 1.2 experiment. The corresponding FDR, pδ∗ = 1 and with relatively weak differential expression “signals” (x± = ±0.1), identifying a good gene lists is not an easy task, as evident from the results. Among all methods only reranking achieved sufficiently low values of X matrices, but, clearly, even reranking would not provide scientifically useful or reliable gene lists in this high-risk environment.pδ ~ 0.1, typical of studies comparing healthy versus diseased cell activities. Simulation parameters for this case arepδ∗. This is akin to an increased prior probability of a differentially expressed gene in a Bayesian detection strategy. To further challenge the algorithms in the light of the “increased prior,” the up/downregulation of expression was made considerably weaker in  The second case employs a larger Subcase 2.1 . In the first 𝒫δ2, 𝒫e2) represents a large pδ proportion, but relatively small pδ∗ = 300/1200 = 0.25. The experimental results for this case over 40 trials are shown in pδ, small pδ∗, experiment of Subcase 1.1. EDGE and SAM consistently report a very large proportion of false discoveries .Subcase 2.2 . A second pδ∗ ratios. The parameters  remain identical to those in Subcase 2.1 experiment, except that G∗ = 1200, so pδ∗ = 1. Results are shown in pδ∗ experiment in Subcase 1.2, the reranking approach significantly outperforms EDGE and SAM, with typically 𝔉 and pδ throughout the range 0 < pδ∗ ≤ 1. At some application-dependent point in this range, reranking, although “better,” is not sufficiently “good” at producing reliable discoveries. Clearly, in the present experiment in which pδ∗ = 1, the reranking result of typically M, is ordinarily quite small compared with the number of genes investigated, G. The gene discovery operation is therefore required to draw conclusions from a sparse sampling of the gene expressions. To gain some insight into the robustness of the gene-discovery methods to small sample sizes, variations on pδ) experiments were repeated with the further stressor of a significant reduction in the sample space. M1 and M2 were each reduced to 20. So that observations could be more attributable to the sample size, M, the signal levels were increased back to x± = ±0.1. The simulation parameters used in 𝒫δ3, are identical to 𝒫δ2 of (G∗ = 300 or pδ∗ = 0.25 and the second (Subcase 3.2) with a “greedy” gene discovery list of size G∗ = 1200 or pδ∗ = 1. The number of microarray chips available to a study, 𝒫δ2 of . As in tX. The data generation process (including row standardization) detailed in 𝔉 and pδ∗ experiment of panel (b) does not mean that the results are necessarily reliable or useful. Nevertheless, these results suggest that the reranking procedure increases power in the analysis of small sample data sets.To create the data set for Before devising the test data setup of xm the mth column of a simulated expression matrix X. We assume that the random vector xm is multivariate Gaussian with (stationary with index m) mean 0G×1 and covariance matrix Λ. Each such column represents G = 3226 genes, which, in their null expressions, are modeled by a covariance matrix Λ that introduces roughly the same amount of linear dependence as found in the BRCA data of [G∗ = 50 (pδ∗ = 0.5) and G∗ = 100 (pδ∗ = 1).Let us denote by  data of . We chos𝔉 and G∗ = 50 and G∗ = 100, respectively. With a smaller M, preeminence of the reranking method scales down. Nevertheless, for 26 out of 40 simulated X realizations, reranking achieves an FDR Figures X realizations for G∗ = 100  more prominent. SAM mitigates this issue in some measure by using the exchangeability factor s0 to adjust the effective pooled variance [It is notable that, with a smaller variance .In most microarray data, there are at least three resources that can be used to advantage: (i) identifiability, (ii) parallel structure, and (iii) intergene correlation itself. Analysis in papers by Efron , 57 suggLimited time and resources often require biomedical researchers to work on only a small number of “hot (gene) prospects.” Even under such highly conservative conditions, however, misleading results can occur, as is evident in the results of Figures a priori as nondifferential—to reduce the correlation in the expression data for the remaining gene candidates. When applied to the widely used two-sample t-statistic approach, this viewpoint yielded a simple differential analysis technique which requires as inputs only a gene expression matrix, related two-sample labels, and the size of desired output gene-list G∗. The method was tested on data constructed from the prostate cancer database of Singh et al. [t-statistic approach itself, reranking shows substantial improvement in statistical power. As is the case with all published techniques, the reranking process' power tends to increase considerably with an increase in the number of microarray samples. However, even for small sample sizes, performance was significantly better than the alternatives in the experiments conducted here.In summary, this paper has reported the development and testing of a novel framework for the detection of differential gene expression. The framework exploits identifiability—the fact that in most microarray data sets, a large proportion of genes can be identified h et al.  and someh et al. , EDGE [1h et al. , and the


Brain-wide mRNA mappings offer a great potential for neuroscience research as they can provide information about system proteomics. In a previous work we have correlated mRNA maps with the binding patterns of radioligands targeting specific molecular systems and imaged with positron emission tomography (PET) in unrelated control groups. This approach is potentially applicable to any imaging modality as long as an efficient procedure of imaging-genomic matching is provided. In the original work we considered mRNA brain maps of the whole human genome derived from the Allen human brain database (ABA) and we performed the analysis with a specific region-based segmentation with a resolution that was limited by the PET data parcellation. There we identified the need for a platform for imaging-genomic integration that should be usable with any imaging modalities and fully exploit the high resolution mapping of ABA dataset.In this work we present MENGA , a software platform that allows the investigation of the correlation patterns between neuroimaging data of any sort  with mRNA gene expression profiles derived from the ABA database at high resolution.We applied MENGA to six different imaging datasets from three modalities  targeting the dopamine and serotonin receptor systems and the myelin molecular structure. We further investigated imaging-genomic correlations in the case of mismatch between selected proteins and imaging targets. For example, these patterns have been correlated with the binding patterns of radioligands targeting specific molecular systems and imaged with positron emission tomography (PET) in unrelated control groups CUMI  and [11C]WAY100635 PET tracers, which target the 5HT1A receptors (as agonist and antagonist respectively) FDOPA PET and [123I]FP-CIT SPET templates were used as markers of the dopamine synthesis capacity  and the dopamine transporter (DAT) respectively. The templates are freely available at the NITRC website (http://www.nitrc.org/projects/spmtemplates/) [11C]Raclopride PET data was obtained by averaging healthy subjects data that have been previously published WAY100635 was somewhat higher than the one of the agonist [11C]CUMI (on average R2 = 0.892±0.048 and R2 = 0.828±0.059 respectively). On the contrary, the myelin water content template showed the smallest image auto-correlation (R2 = 0.664±0.123). This indicates limited spatial homogeneity, since a slight difference in the ABA coordinates of the genomic sampling across the donors leads to different image sample values that are then reflected by a small auto-correlation.The results of MENGA analysis in the matched studies are reported in 2 > 0.75) with the only exception of the dopamine transporter . Myelin and dopamine data showed comparable univariate cross-correlations between imaging and mRNA templates (R2 between 0.320±0.156 and 0.458±0.175) but lower for the SPET-DAT (R2 = 0.193±0.157).Univariate and multivariate cross-correlations are reported in Multivariate cross-correlation values showed the same trend as univariate results, but the coefficient of determination values obtained was generally higher , Fig 5. In addition to comparing imaging data with the corresponding target mRNA expression levels, we also applied MENGA to a series of mismatched image-genomic cases. Three image templates were correlated to mRNA data of unrelated biological system. This was done to exclude the possibility that MENGA returns correlation values induced by spurious confounding factors.11C]CUMI template with the dopamine D2 receptor gene, the dopamine SPET data with the 5HT1A serotonin receptor gene and the myelin template with the dopamine synthesis capacity mRNA. Results for the mismatched analysis are reported in We tested the serotonin FP-CIT-5HT1A match to 25% for the myelin water content-DDC match), indicating a high probability for Moreover, the chance likelihood of the multivariate correlation was high , see a priori hypotheses. The highest cross-correlation was found for the serotonin system (the receptor 5HT1A) where no post-translational modifications have been reported [11C]CUMI compared to the antagonist [11C]WAY100635 for the same site, confirming our previous results [The results obtained by MENGA on the paradigmatic set of images were consistent with our reported . For thi results .Cross-correlation results for myelin and dopamine systems were comparable with the only exception of DAT data that also presented the smallest genomic auto-correlation. This may be expected as mRNA levels are better predictors of concentrations for structural than functional proteins ,6.The lack of correlation found in the integration of imaging data and mismatched information eliminates the possibility that the similarities found in the spatial patterns are due to spurious correlations. The image auto-correlation analysis among the modalities highlights the different impact of the image re-sampling in donors’ space.In ABA database, only 30% of the genes are represented by a single probe, 51% of the genes are described by two probes and 19% of the genes by three or more. The presence of multiple probes is not necessarily an advantage, as ABA includes the probes with varying specificity or sensitivity to the target. The presence of probes with very inconsistent expression profiles for the same gene may prevent the possibility of simply considering the mean mRNA expression as representative of the true mean transcript expression. It follows that it is fundamental for any type of application to select only the probe that best describes the real transcript profile and discard the remaining ones.In this work we implemented a data-driven method for the probe selection. The approach accounts for between-donor consistency and probe information content to retain the representative expression profile for a given gene, which in turn is used for MENGA integration analysis; please refer to the Appendix for a detailed discussion. Note that the processed version of ABA database included in MENGA also contains all the probe profiles in log2 intensity prior the normalization in z-score, so that the expert user has the freedom to apply the software to the raw data implementing his/her criteria of choice for the probe selection.MENGA returns the imaging-genomic cross-correlation values to give a quantitative assessment of the amount of the variability in the image phenotype that can be explained by spatial mRNA expression patterns. High values of cross-correlation indicate a good correspondence of image data and mRNA information. In presence of low cross-correlation values, it is necessary to distinguish between univariate and multivariate results. In particular, low average values of univariate cross-correlations  can indicate high variability in the biological gene process under study, which is likely to also lead to low genomic auto-correlation estimates.In this case the interpretation of multivariate results must be considered with care due to the presence of the PCA step in the analysis. The presence of the PCA step is not a problem in the presence of high genomic auto-correlation. In this case, the process is characterized by low variability and all the donors carry similar mRNA information and PCA will return few components (even one component could be enough to account for 95% of the data variability) all similarly correlated with the image data with no risk of overfitting. On the other hand, in the presence of a highly variable biological process, a larger number of highly non collinear principal components will be required to describe the genomic data. As a consequence, the multivariate correlation could be only driven by the component the most correlated with the image and overestimate the true correlation present in the data.MENGA is an integrated system that allows the comparison of genomic and imaging data. The software uses mRNA brain maps of the whole human genome derived from the Allen human brain atlas and it has can be used in conjunction with any imaging modality. Specifically, it explores the similarities between the spatial patterns of genomic expressions of a pre-selected list of genes and brain imaging data of unrelated subjects.http://human.brain-map.org/static/download. The datasets contained the probe expression values normalized across all brains using the normalization process described in the technical white paper, Microarray Data Normalization presented in the same website. For each donor, ABA makes available all normalized microarray samples for all probes in log2 value as well as probe and sample metadata necessary for the processing analysis.The original ABA dataset consisted in the complete microarray datasets for the full complement of six brains that were downloaded from The dataset is derived from 6 healthy donors  and contains 29’177 gene expression profiles sampled throughout the brain. The number of probes was consistent between genes (on average 2.0 ± 1.4 probes per gene). In particular, 51% of the genes had 2 probes, 30% and 13% of genes had 1 and 3 probes respectively and only 6% of genes had more than 3 probes. On average, 617 ± 242 samples were collected for each donor to represent all the brain structures proportionally to their volume. For two out of the six brains, samples were collected from both hemispheres. For the remaining four, tissue samples for microarray analysis were limited to the left hemisphere. Full details about the procedures for the tissue collection and processing, the microarray experimental design and execution, and the data quality control up to the integration of the data into the online resource are reported in the supplementary data of [The first step of our processing of ABA database consisted in the organization of the dataset in gene folders each containing all the probes for a given gene. For each donor, samples data for all probes were converted in z-score  which were then used for all the analyses. Note that the different number of samples per donor causes negligible impact on the z-score calculation because the number of samples is such to allow a valid normalization (more than 400 samples per donor). Finally, we defined a unique mRNA profile for each gene by selecting the probe that best the gene expression profile, evaluating the data from all donors at the same time. One probe was retained as representative of the particular gene transcript and it was the same for all donors. We chose to select the probe on the basis of the distribution of the expression values in z-score for all donors. In this approach data from all donors are combined together creating a unique vector on which the distribution analysis is performed: the probe with the most symmetric and least skewed distribution is chosen as representative of the gene profile. Specifically, we created the histogram of the distribution for each probe and then we located its maximum: we selected the one with the peak located utmost on the right or, if all the probes presented the maximum in the same bin, we chose the probe with the lowest peak. This approach is different than the one presented in , where tSince the number of probes varies across the genes, we considered two different cases:one probe: the probe is necessarily selected;two or more probes: we evaluated the distribution of the expression values and chose the one with the most symmetric and least skewed profile to avoid the non-linearity effect on the microarray measures.The probe selected was then selected as unique gene profile and stored in the processed version of ABA database. This is available in MENGA distribution package.overlapping samples with a certain window size) and on the percentage of image samples eliminated when using the MNI mask (boundary samples). The minimum distance between two different genomic samples was 1 mm (i.e. there were adjacent samples) but these represented less than 0.1% of the total number of samples on average across the donors (mean ± SD: 0.03% ± 0.02%) (We assessed the impact of using different window sizes on the percentage of pairs of samples that would be included in the same image sample (± 0.02%) . Even whThe size of the window had a greater impact on the percentage of voxels eliminated when using the MNI whole brain mask. This percentage varied across donors as consequence of the different sampling of ABA (in the whole brain for the first two donors and only in the left hemisphere for the other four donors) . In geneWe also evaluated the number of samples available for each region of the simplified coarse list in the best scenario of having all the samples available (i.e. MNI whole brain mask) and a representative set of regions. The number of samples was consistent across donors and each regions was well represented (between donors mean and SD: 35 ± 27 samples per region) . To noteS1 TableThe ABA labels and the corresponding names of the ROIs for the coarse level and the simplified coarse level of resolution included in MENGA are reported.(DOCX)Click here for additional data file.S2 Tableoverlapping samples) for a certain window size is reported for various size values (from 1 to 11 mm) for each donor. The mean, standard deviation, minimum and maximum across donors are also reported.The percentage of pairs of samples that would be included in the same window ((DOCX)Click here for additional data file.S3 Tableboundary samples), is reported for various size values (from 1 to 11 mm) for each donor. The mean, standard deviation, minimum and maximum across donors are also reported.The percentage of samples eliminated because including NaN elements, i.e. elements outside the MNI whole brain mask ((DOCX)Click here for additional data file.S4 Tablesimplified coarse list of ROIs) is reported for each donor. The mean, standard deviation, minimum and maximum across regions are also reported. The MNI whole brain mask was used to include all the available samples. In fact the number of samples for the first two donors  is at least twice the number of samples of the four remaining donor.The number of samples included in the regions listed ((DOCX)Click here for additional data file.


We report and model a previously undescribed systematic error causing spurious excess correlations that depend on the distance between probes on Affymetrix® microarrays. The phenomenon affects pairs of features with large chip separations, up to over 100 probes apart. The effect may have a significant impact on analysis of correlations in large collections of expression data, where the systematic experimental errors are repeated in many data sets. Examples of such studies include analysis of functions and interactions in groups of genes, as well as global properties of genomes. We find that the average correlations between probes on Affymetrix microarrays are larger for smaller chip distances, which points out to a previously undescribed positional artifact. The magnitude of the artifact depends on the design of the chip, and we find it to be especially high for the yeast S98 microarray, where spurious excess correlations reach 0.1 at a distance of 50 probes. We have designed an algorithm to correct this bias and provide new data sets with the corrected expression values. This algorithm was successfully implemented to remove the positional artifact from the S98 chip data while preserving the integrity of the data. DNA microarrays provide a means of measuring the concentrations of thousands of genetic sequences in one experiment, and are used in many fields ranging from basic biological research to medical applications123456891011This technology has produced thousands of experimental data sets that are available through online databases such as the Gene Expression Omnibus (GEO)1415161718192425Saccharomyces cerevisiae. In order to investigate systematic position effects, we analyzed the expression data available in the Gene Expression Omnibus database. We observed that the data collected for experiments done using the S98 chip display long-range excess correlations strongly dependent on the distance between the probes on the chip. Although the effects are similar in appearance to the ones observed in spotted microarrays, the physical nature of the positional artifact in Affymetrix chips must be different because the Affymetrix chips are fabricated using in situ synthesis of the probes.In this paper we consider the Affymetrix microarray platforms, specifically the Yeast Genome S98 Array, a popular whole genome platform for Systematic excess correlations may bias the inference of functional gene relationships from large numbers of experiments. To describe and correct these effects, we modeled this artifact in S98 chips and designed an algorithm to correct for it by reconstructing the unbiased expression values. Our model is derived based on a large collection of array data and allows the removal of spurious correlations from any set of experiments that use the same chip.L and H); see definition in Methods below. Therefore, if no positional effects were present, one would expect this correlation map to be flat and only random oscillations around the average correlation in the genome would be observed; a small positive number, depending on the collection of experiments used in the analysis.The Affymetrix Yeast Genome S98 Array contains 9335 probe sets with a total of 285,156 probes. To characterize the dependence of the correlations between different probe sets on their physical location on the chip, we computed a map of average correlation as a function of probe separation along the x-axis (dx) and along the y-axis (dy). Every pixel in this correlation map represents the average of all pairs of probes with a given separation on the chip  probes are typically lower than in the perfect match (PM) probes, the effect is expected to result in PM signal overflowing into the MM probes in their vicinity.We measured this phenomenon using data from the Yeast2 microarray. Based on our model of the artifact, we predicted the intensity of the spurious signal in each of the mismatch probes, and compared it with the measured MM signal. We binned the observed MM intensities vs. the predicted ones in the logarithmic scale and computed the average in each respective bin. The correlation coefficient between predicted spurious signal and the average MM measurement is 0.949, with a p-value of 2.5e-7 see . This noThe positional artifact in the microarray data extends over large distances on the chip, which means that it originates via a long-range process. Elucidating the physical mechanism behind this effect is beyond the scope of this paper, but possibilities include the diffusion of fluorophores during the washing stage of the experiment, diffusion of light while scanning the array, or a combination thereof. In spotted microarrays, several methods have been suggested to correct for similar positional artifacts, either by correcting the expression values for all probesHere, we modeled the effect as partial diffusion of the signal in two dimensions. Based on this assumption, the original, unaffected expression values can be reconstructed from the data by using a deconvolution procedure with a two-component model kernel designed to remove any possible diffusive effects (see Methods for detailed discussion). To this end, we implemented an algorithm for optimizing the shape of the model kernel to best reconstruct the true expression values, and used the corrected expression values to compute the corrected correlation chip map, Creating special software to model and remove the effect has been necessary because existing preprocessing packages Unlike other deconvolution methods previously used2425Saccharomyces cerevisiae. The targets of many TFs are expected to share a mode of regulation and they exhibit correlations in their expression profiles. There are several published lists of Yeast TF's with their targets. The assignments of the targets of TF in these are based on different experimental and computational techniques. Here we considered two different sets of data, YEASTRACTThe positional artifact in the microarray data may influence the interpretation of results based on the analysis of a large number of genes such as gene annotation or network inference. In such studies the repeated systematic effects become significant even at low magnitude. In order to test the effects of these corrections on our understanding of gene regulation, we analyzed the expression of target genes of transcription factors (TFs) in http://moment.utmb.edu/S98/. Our model kernel can be used with no change to correct the expression values in any experiment done with the S98 platform. The computer program for performing the deconvolution is also available on the website. Similar artifacts are also present in other Affymetrix platforms, including the Yeast2 array and the mouse arrays MOE430A and MOE430B. However, the way this artifact manifests depends strongly on the design of the array, especially on the relative positions of probes within a probe set. Specifically, the excess correlations in the Yeast2, MOE430A and MOE430B arrays are an order of magnitude lower than in the yeast S98 microarrays. We expect that our approach, with little or no modification, can detect, quantify and correct positional artifacts in different platforms. In the future we intend to investigate the underlying physical mechanisms of this positional artifact.The analysis of hundreds of expression microarray experiments using the Affymetrix S98 yeast genome chip has led us to uncover a systematic error that manifests in the form of excess correlations between nearby probes on the chip. These spurious correlations depend strongly on the distance between probes. This positional artifact may interfere with interpretation of whole-genome gene expression studies. Removing this artifact is a necessary step in inferring gene relationships from large-scale data sets. We designed a computational method that removes the spurious correlations by correcting the measured expression levels. Our method is based on the assumption that the effect is consistent with a diffusion effect that may be taking place either during the washing or the scanning stage of a microarray experiment. Thus, the measured expression level of each probe is convolved by contributions from the diffused signal. We reconstructed the true expression levels by applying deconvolution with a model kernel, and show that this successfully removes the positional bias. This method was implemented using the CUDA GPU computing technology, which allowed a 480-fold speed up of computations. The corrected data are provided online at The primary sources of data for this work are the microarray datasets available from the GEO website for the Affymetrix Yeast Genome S98 Array. To describe and parameterize the positional effect, we utilized 1383 available data sets in the GPL90 platform family (the list is available on the supporting webpage). We used the probe set data according to the GPL90 platform description file provided by Affymetrix©. The final result of this work, data corrected for the artifact, has been created for 1494 samples. Affymetrix Yeast2 Array was based on 670 samples of GPL2529 GEO platform. Two mouse arrays were also analyzed: Affymetrix MOE430A and MOE430B. The analysis was based on 4277 data sets of the GPL339 platform for the Affymetrix MOE430A and 959 data sets for the GPL340 platform for the Affymetrix MOE430B array.The positional artifact was detected through calculating the average correlation between probes at a given separation on the chip. These data sets were first normalized as the different samples come from many different experiments in a wide range of conditions. To this end we scaled the expression values in each sample by dividing them by the sample mean.To calculate the average correlation between probes at a given separation on the chip, we calculated the Pearson correlation coefficient of the expression values across 1,383 arrays for all pairs of genes, and then computed the arithmetic mean for all pairs of probes with each given chip separation . When characterizing the positional artifact, we omitted genes with both neighboring chromosomal and neighboring chip locations, as these often share a regulatory sequence.Repeatedly computing the correlation coefficients for all pairs of probes over many experiments is CPU-intensive. However, this problem is suitable for parallelization and scales very well on a large number of computing cores. Rather than parallelizing these calculations on a cluster of CPUs, we opted to run our calculations on a single graphics processing unit (GPU). The computational power of GPUs has surpassed that of CPUs and they come with a large number of cores at a much lower price per core. All cores on the GPU share one global memory, which also cuts the communication time between them significantly.We used the CUDA (Compute Unified Device Architecture) programming interface from NVIDIA. In this work, we executed our algorithm on the NVIDIA GeForce GTX 275 that has 30 multiprocessors with 240 computing cores and 869 MB of memory. The most time-consuming step in our approach is the repeated calculation of the correlation coefficients between all probe-sets. One such cycle takes typically about 80 minutes on a single Intel® Xeon® W3540 CPU core, and has been a bottleneck in our optimization algorithm. The same calculation can be performed in approximately 10 seconds on the GeForce GTX 275 GPU using CUDA programming scheme (in single precision).oE, for each probe is expressed asx,y) is the position of the probe and K is a kernel function that convolves the true expression value, tE. L and H denote the dimensions of the chip.We propose that the artifact results from a process in which a fraction of the signal overflows to other probes on the microarray, and can be described mathematically as convolution. Thus, the observed expression value, K, consists of two components: a Dirac delta corresponding to the signal remaining in its original position and a Gaussian component describing the diffusion effect: The integration assumes tE = 0 for  outside of the chip.The kernel, A is the density amplitude of the Delta function  and σ denotes the width of the Gaussian distribution. In practice, we use measurements binned onto pixels on the chip, corresponding to integer values of the position coordinates x and y. In this case, the Dirac delta is defined as δ = 1 for  =  and δ = 0 elsewhere. We optimized the shape of K in order to find such values of the parameters A and σ, for which deconvolution will remove the positional artifact without destroying the original data.oE which is obtained for each sample by converting the expression values into a two-dimensional spatial matrix. The positions of the individual probes were used as indices for such matrix where each matrix has 285156 entries (number of probes). The deconvolution was performed in Fourier space and implemented on the GPU using the Fast Fourier Transform. The deconvolution process was applied to all 1383 samples. Finally, the corrected expression levels were rescaled to preserve their original distribution.Deconvolution using the model given in x,y) in chip coordinates is defined as:pqn is the number of probe pairs ,  with a given separation and PCC is the Pearson correlation coefficient between deconvolved signal at two positions, computed over 1383 experiments. We characterized the flatness of the correlation map using an objective function based on the square of the first spatial moment of the average correlation:We optimized the parameters of the kernel function in order to obtain a possibly flat average correlation map. The average correlation between probes separated by a vector  for all experiments available in the GEO database.We optimized the parameters of