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A spline function approach for detecting differentially expressed genes in microarray data analysis.

MOTIVATION: A primary objective of microarray studies is to determine genes which are differentially expressed under various conditions. Parametric tests, such as two-sample t-tests, may be used to identify differentially expressed genes, but they require some assumptions that are not realistic for many practical problems. Non-parametric tests, such as empirical Bayes methods and mixture normal approaches, have been proposed, but the inferences are complicated and the tests may not have as much power as parametric models. RESULTS: We propose a weakly parametric method to model the distributions of summary statistics that are used to detect differentially expressed genes. Standard maximum likelihood methods can be employed to make inferences. For illustration purposes the proposed method is applied to the leukemia data (training part) discussed elsewhere. A simulation study is conducted to evaluate the performance of the proposed method.

Algorithms↗

Normalization of microarray data using a spatial mixed model analysis which includes splines.

MOTIVATION: Microarray experiments with thousands of genes on a slide and multiple slides used in any experimental set represent a large body of data with many sources of variation. The identification of such sources of variation within microarray experimental sets is critical for correct deciphering of desired gene expression differences. RESULTS: We describe new methods for the normalization using spatial mixed models which include splines and analysis of two-colour spotted microarrays for within slide variation and for a series of slides. The model typically explains 45-85% of the variation on a slide with only approximately 1% of the total degrees of freedom. The results from our methods compare favourably with those from intensity dependent normalization loess methods where we accounted for twice as much uncontrolled and unwanted variation on the slides. We have also developed an index for each EST that combines the various measures of the differential response into a single value that researchers can use to rapidly assess the genes of interest.

Algorithms↗

GeneNetwork: an interactive tool for reconstruction of genetic networks using microarray data.

UNLABELLED: Inferring genetic network architecture from time series data generated from high-throughput experimental technologies, such as cDNA microarray, can help us to understand the system behavior of living organisms. We have developed an interactive tool, GeneNetwork, which provides four reverse engineering models and three data interpolation approaches to infer relationships between genes. GeneNetwork enables a user to readily reconstruct genetic networks based on microarray data without having intimate knowledge of the mathematical models. A simple graphical user interface enables rapid, intuitive mapping and analysis of the reconstructed network allowing biologists to explore gene relationships at the system level. AVAILABILITY: Download from http://genenetwork.sbl.bc.sinica.edu.tw/. SUPPLEMENTARY INFORMATION: Supplement documentation of algorithms for the four approaches is downloadable at the above location.

Algorithms↗

Weighted analysis of microarray gene expression using maximum-likelihood.

MOTIVATION: The numerical values of gene expression measured using microarrays are usually presented to the biological end-user as summary statistics of spot pixel data, such as the spot mean, median and mode. Much of the subsequent data analysis reported in the literature, however, uses only one of these spot statistics. This results in sub-optimal estimates of gene expression levels and a need for improvement in quantitative spot variation surveillance. RESULTS: This paper develops a maximum-likelihood method for estimating gene expression using spot mean, variance and pixel number values available from typical microarray scanners. It employs a hierarchical model of variation between and within microarray spots. The hierarchical maximum-likelihood estimate (MLE) is shown to be a more efficient estimator of the mean than the 'conventional' estimate using solely the spot mean values (i.e. without spot variance data). Furthermore, under the assumptions of our model, the spot mean and spot variance are shown to be sufficient statistics that do not require the use of all pixel data. The hierarchical MLE method is applied to data from both Monte Carlo (MC) simulations and a two-channel dye-swapped spotted microarray experiment. The MC simulations show that the hierarchical MLE method leads to improved detection of differential gene expression particularly when 'outlier' spots are present on the arrays. Compared with the conventional method, the MLE method applied to data from the microarray experiment leads to an increase in the number of differentially expressed genes detected for low cut-off P-values of interest.

Algorithms↗

Relational patterns of gene expression via non-metric multidimensional scaling analysis.

MOTIVATION: Microarray experiments result in large-scale data sets that require extensive mining and refining to extract useful information. We demonstrate the usefulness of (non-metric) multidimensional scaling (MDS) method in analyzing a large number of genes. Applying MDS to the microarray data is certainly not new, but the existing works are all on small numbers (< 100) of points to be analyzed. We have been developing an efficient novel algorithm for non-metric MDS (nMDS) analysis for very large data sets as a maximally unsupervised data mining device. We wish to demonstrate its usefulness in the context of bioinformatics (unraveling relational patterns among genes from time series data in this paper). RESULTS: The Pearson correlation coefficient with its sign flipped is used to measure the dissimilarity of the gene activities in transcriptional response of cell-cycle-synchronized human fibroblasts to serum. These dissimilarity data have been analyzed with our nMDS algorithm to produce an almost circular relational pattern of the genes. The obtained pattern expresses a temporal order in the data in this example; the temporal expression pattern of the genes rotates along this circular arrangement and is related to the cell cycle. For the data we analyze in this paper we observe the following. If an appropriate preparation procedure is applied to the original data set, linear methods such as the principal component analysis (PCA) could achieve reasonable results, but without data preprocessing linear methods such as PCA cannot achieve a useful picture. Furthermore, even with an appropriate data preprocessing, the outcomes of linear procedures are not as clear-cut as those by nMDS without preprocessing.

Algorithms↗

Normalization of two-channel microarray experiments: a semiparametric approach.

MOTIVATION: An important underlying assumption of any experiment is that the experimental subjects are similar across levels of the treatment variable, so that changes in the response variable can be attributed to exposure to the treatment under study. This assumption is often not valid in the analysis of a microarray experiment due to systematic biases in the measured expression levels related to experimental factors such as spot location (often referred to as a print-tip effect), arrays, dyes, and various interactions of these effects. Thus, normalization is a critical initial step in the analysis of a microarray experiment, where the objective is to balance the individual signal intensity levels across the experimental factors, while maintaining the effect due to the treatment under investigation. RESULTS: Various normalization strategies have been developed including log-median centering, analysis of variance modeling, and local regression smoothing methods for removing linear and/or intensity-dependent systematic effects in two-channel microarray experiments. We describe a method that incorporates many of these into a single strategy, referred to as two-channel fastlo, and is derived from a normalization procedure that was developed for single-channel arrays. The proposed normalization procedure is applied to a two-channel dose-response experiment.

Algorithms↗

Validation of alternative methods of data normalization in gene co-expression studies.

MOTIVATION: Clusters of genes encoding proteins with related functions, or in the same regulatory network, often exhibit expression patterns that are correlated over a large number of conditions. Protein associations and gene regulatory networks can be modelled from expression data. We address the question of which of several normalization methods is optimal prior to computing the correlation of the expression profiles between every pair of genes. RESULTS: We use gene expression data from five experiments with a total of 78 hybridizations and 23 diverse conditions. Nine methods of data normalization are explored based on all possible combinations of normalization techniques according to between and within gene and experiment variation. We compare the resulting empirical distribution of gene x gene correlations with the expectations and apply cross-validation to test the performance of each method in predicting accurate functional annotation. We conclude that normalization methods based on mixed-model equations are optimal.

Algorithms↗

Boosting proportional hazards models using smoothing splines, with applications to high-dimensional microarray data.

MOTIVATION: An important area of research in the postgenomics era is to relate high-dimensional genetic or genomic data to various clinical phenotypes of patients. Due to large variability in time to certain clinical events among patients, studying possibly censored survival phenotypes can be more informative than treating the phenotypes as categorical variables. Due to high dimensionality and censoring, building a predictive model for time to event is more difficult than the classification/linear regression problem. We propose to develop a boosting procedure using smoothing splines for estimating the general proportional hazards models. Such a procedure can potentially be used for identifying non-linear effects of genes on the risk of developing an event. RESULTS: Our empirical simulation studies showed that the procedure can indeed recover the true functional forms of the covariates and can identify important variables that are related to the risk of an event. Results from predicting survival after chemotherapy for patients with diffuse large B-cell lymphoma demonstrate that the proposed method can be used for identifying important genes that are related to time to death due to cancer and for building a parsimonious model for predicting the survival of future patients. In addition, there is clear evidence of non-linear effects of some genes on survival time.

Algorithms↗

A two-stage normalization method for partially degraded mRNA microarray data.

MOTIVATION: The goal of the study is to obtain genetic information from exfoliated colonocytes in the fecal stream rather than directly from mucosa cells within the colon. The latter is obtained through invasive procedures. The difficulties encountered by this procedure are that certain probe information may be compromised due to partially degraded mRNA. Proper normalization is essential to obtaining useful information from these fecal array data. RESULTS: We propose a new two-stage semiparametric normalization method motivated by the features observed in fecal microarray data. A location-scale transformation and a robust inclusion step were used to roughly align arrays within the same treatment. A non-parametric estimated non-linear transformation was then used to remove the potential intensity-based biases. We compared the performance of the new method in analyzing a fecal microarray dataset with those achieved by two existing normalization approaches: global median transformation and quantile normalization. The new method favorably compared with the global median and quantile normalization methods. AVAILABILITY: The R codes implementing the two-stage method may be obtained from the corresponding author.

Algorithms↗

An expression index for Affymetrix GeneChips based on the generalized logarithm.

MOTIVATION: Affymetrix GeneChip high-density oligonucleotide arrays interrogate a single transcript using multiple short 25mer probes. Usually, a necessary step in the analysis of experiments using these GeneChips is to summarize each of these probe sets into a single expression index that can then be used for determining differential expression, for classification, for clustering, and for other analyses. In this paper, we propose a new expression index that is competitive with the best existing methods, and superior in many cases. We call this expression index method GLA, for GLog Average, since after normalization at the probe level, we take the mean generalized logarithm of perfect match probes. RESULTS: In this paper, we use Affycomp as the primary tool to assess the weaknesses and strengths of GLA. Comparisons are made between GLA and most widely used summary methods (RMA, MAS5.0 and MBEI) in great detail. The substantial reduction in variability and increased ability to detect differential expression, together with the simplicity of implementation, make GLA a plausible candidate for analysis of Affymetrix GeneChip data.

Algorithms↗

Maximum significance clustering of oligonucleotide microarrays.

MOTIVATION: Affymetrix high-density oligonucleotide microarrays measure the expression of DNA transcripts using probesets, i.e. multiple probes per transcript. Usually, these multiple measurements are transformed into a single probeset expression level before data analysis proceeds; any information on variability is lost. In this paper we demonstrate how individual probe measurements can be used in a statistic for differential expression. Furthermore, we show how this statistic can serve as a criterion for clustering microarrays. RESULTS: A novel clustering algorithm using this maximum significance criterion is demonstrated to be more efficient with the measured data than competing techniques for dealing with repeated measurements, especially when the sample size is small.

Algorithms↗

Polynomial model approach for resynchronization analysis of cell-cycle gene expression data.

MOTIVATION: Identification of genes expressed in a cell-cycle-specific periodical manner is of great interest to understand cyclic systems which play a critical role in many biological processes. However, identification of cell-cycle regulated genes by raw microarray gene expression data directly is complicated by the factor of synchronization loss, thus remains a challenging problem. Decomposing the expression measurements and extracting synchronized expression will allow to better represent the single-cell behavior and improve the accuracy in identifying periodically expressed genes. RESULTS: In this paper, we propose a resynchronization-based algorithm for identifying cell-cycle-related genes. We introduce a synchronization loss model by modeling the gene expression measurements as a superposition of different cell populations growing at different rates. The underlying expression profile is then reconstructed through resynchronization and is further fitted to the measurements in order to identify periodically expressed genes. Results from both simulations and real microarray data show that the proposed scheme is promising for identifying cyclic genes and revealing underlying gene expression profiles. AVAILABILITY: Contact the authors. SUPPLEMENTARY INFORMATION: Supplementary data are available at: http://dsplab.eng.umd.edu/~genomics/syn/

Algorithms↗

Eigengene-based linear discriminant model for tumor classification using gene expression microarray data.

MOTIVATION: The nearest shrunken centroids classifier has become a popular algorithm in tumor classification problems using gene expression microarray data. Feature selection is an embedded part of the method to select top-ranking genes based on a univariate distance statistic calculated for each gene individually. The univariate statistics summarize gene expression profiles outside of the gene co-regulation network context, leading to redundant information being included in the selection procedure. RESULTS: We propose an Eigengene-based Linear Discriminant Analysis (ELDA) to address gene selection in a multivariate framework. The algorithm uses a modified rotated Spectral Decomposition (SpD) technique to select 'hub' genes that associate with the most important eigenvectors. Using three benchmark cancer microarray datasets, we show that ELDA selects the most characteristic genes, leading to substantially smaller classifiers than the univariate feature selection based analogues. The resulting de-correlated expression profiles make the gene-wise independence assumption more realistic and applicable for the shrunken centroids classifier and other diagonal linear discriminant type of models. Our algorithm further incorporates a misclassification cost matrix, allowing differential penalization of one type of error over another. In the breast cancer data, we show false negative prognosis can be controlled via a cost-adjusted discriminant function. AVAILABILITY: R code for the ELDA algorithm is available from author upon request.

Artificial Intelligence↗

Mosclust: a software library for discovering significant structures in bio-molecular data.

UNLABELLED: The R package mosclust (model order selection for clustering problems) implements algorithms based on the concept of stability for discovering significant structures in bio-molecular data. The software library provides stability indices obtained through different data perturbations methods (resampling, random projections, noise injection), as well as statistical tests to assess the significance of multi-level structures singled out from the data. AVAILABILITY: http://homes.dsi.unimi.it/~valenti/SW/mosclust/download/mosclust_1.0.tar.gz. SUPPLEMENTARY INFORMATION: http://homes.dsi.unimi.it/~valenti/SW/mosclust.

Algorithms↗

Clustering threshold gradient descent regularization: with applications to microarray studies.

MOTIVATION: An important goal of microarray studies is to discover genes that are associated with clinical outcomes, such as disease status and patient survival. While a typical experiment surveys gene expressions on a global scale, there may be only a small number of genes that have significant influence on a clinical outcome. Moreover, expression data have cluster structures and the genes within a cluster have correlated expressions and coordinated functions, but the effects of individual genes in the same cluster may be different. Accordingly, we seek to build statistical models with the following properties. First, the model is sparse in the sense that only a subset of the parameter vector is non-zero. Second, the cluster structures of gene expressions are properly accounted for. RESULTS: For gene expression data without pathway information, we divide genes into clusters using commonly used methods, such as K-means or hierarchical approaches. The optimal number of clusters is determined using the Gap statistic. We propose a clustering threshold gradient descent regularization (CTGDR) method, for simultaneous cluster selection and within cluster gene selection. We apply this method to binary classification and censored survival analysis. Compared to the standard TGDR and other regularization methods, the CTGDR takes into account the cluster structure and carries out feature selection at both the cluster level and within-cluster gene level. We demonstrate the CTGDR on two studies of cancer classification and two studies correlating survival of lymphoma patients with microarray expressions. AVAILABILITY: R code is available upon request. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Algorithms↗

Comprehensive whole genome array CGH profiling of mantle cell lymphoma model genomes.

Mantle cell lymphoma (MCL) is an aggressive non-Hodgkin's lymphoma with median patient survival times of approximately 3 years. Although the characteristic t(11;14)(q13;q32) is found in virtually all cases, experimental evidence suggests that this event alone is insufficient to result in lymphoma and secondary genomic alterations are required. Using a newly developed DNA microarray of 32 433 overlapping genomic segments spanning the entire human genome, we can for the first time move beyond marker based analysis and comprehensively search for secondary genomic alterations concomitant with the t(11;14) in eight commonly used cell models of MCL (Granta-519, HBL-2, NCEB-1, Rec-1, SP49, UPN-1, Z138C and JVM-2). Examining these genomes at tiling resolution identified an unexpected average of 35 genetic alterations per cell line, with equal numbers of amplifications and deletions. Recurrent high-level amplifications were identified at 18q21 containing BCL2, and at 13q31 containing GPC5. In addition, a recurrent homozygous deletion was identified at 9p21 containing p15 and p16. Alignment of these profiles revealed 14 recurrent losses and 21 recurrent gains as small as 130 kb. Remarkably, even the intra immunoglobulin gene deletions at 2p11 and 22q11 were detected, demonstrating the power of combining the detection sensitivity of array comparative genomic hybridization (CGH) with the resolution of an overlapping whole genome tiling-set. These alterations not only coincided with previously described aberrations in MCL, but also defined 13 novel regions. Further characterization of such minimally altered genomic regions identified using whole genome array CGH will define novel dominant oncogenes and tumor suppressor genes that play important roles in the pathogenesis of MCL.

Chromosomes↗

Label-free DNA sensors using ultrasensitive diamond field-effect transistors in solution.

Charge detection biosensors have recently become the focal point of biosensor research, especially field-effect-transistors (FETs) that combine compactness, low cost, high input, and low output impedances, to realize simple and stable in vivo diagnostic systems. However, critical evaluation of the possibility and limitations of charge detection of label-free DNA hybridization using silicon-based ion-sensitive FETs (ISFETs) has been introduced recently. The channel surface of these devices must be covered by relatively thick insulating layers ( SiO2, Si3N4, Al2O3, or Ta2O5) to protect against the invasion of ions from solution. These thick insulating layers are not suitable for charge detection of DNA and miniaturization, as the small capacitance of thick insulating layers restricts translation of the negative DNA charge from the electrolyte to the channel surface. To overcome these difficulties, thin-gate-insulator FET sensors should be developed. Here, we report diamond solution-gate FETs (SGFETs), where the DNA-immobilized channels are exposed directly to the electrolyte solution without gate insulator. These SGFETs operate stably within the large potential window of diamond (>3.0 V). Thus, the channel surface does not need to be covered by thick insulating layers, and DNA is immobilized directly through amine sites, which is a factor of 30 more sensitive than existing Si-ISFET DNA sensors. Diamond SGFETs can rapidly detect complementary, 3-mer mismatched (10 pM) and has a potential for the detection of single-base mismatched oligonucleotide DNA, without biological degradation by cyclically repeated hybridization and denature.

Biosensing Techniques↗

Clustering of microarray data reveals transcript patterns associated with somatic embryogenesis in soybean.

Globular somatic embryos can be induced from immature cotyledons of soybean (Glycine max L. Merr. cv Jack) placed on high levels of the auxin 2,4-dichlorophenoxyacetic acid (2,4-D). Somatic embryos develop from the adaxial side of the cotyledon, whereas the abaxial side evolves into a callus. Using a 9,280-cDNA clone array, we have compared steady-state RNA from the adaxial side from which embryos develop and from the abaxial callus at five time points over the course of the 4 weeks necessary for the development of globular embryos. In a second set of experiments, we have profiled the expression of each clone in the adaxial side during the same period. A total of 495 genes differentially expressed in at least one of these experiments were grouped according to the similarity of their expression profiles using a nonhierarchical clustering algorithm. Our results indicate that the appearance of somatic embryos is preceded by dedifferentiation of the cotyledon during the first 2 weeks on auxin. Changes in mRNA abundance of genes characteristic of oxidative stress and genes indicative of cell division in the adaxial side of the cotyledons suggest that the arrangement of the new cells into organized structures might depend on a genetically controlled balance between cell proliferation and cell death. Our data also suggest that the formation of somatic globular embryos is accompanied by the transcription of storage proteins and the synthesis of gibberellic acid.

2,4-Dichlorophenoxyacetic Acid↗