Identifying Differentially Expressed Genes for Time-course Microarray Data through Functional Data Analysis

Identification of differentially expressed (DE) genes across two conditions is a common task with microarray. Most existing approaches accomplish this goal by examining each gene separately based on a model and then control the false discovery rate over all genes. We took a different approach that employs a uniform platform to simultaneously depict the dynamics of the gene trajectories for all genes and select differently expressed genes. A new Functional Principal Component (FPC) approach is developed for time-course microarray data to borrow strength across genes. The approach is flexible as the temporal trajectory of the gene expressions is modeled nonparametrically through a set of orthogonal basis functions, and often fewer basis functions are needed to capture the shape of the gene expression trajectory than existing nonparametric methods. These basis functions are estimated from the data reflecting major modes of variation in the data. The correlation structure of the gene expressions over time is also incorporated without any parametric assumptions and estimated from all genes such that the information across other genes can be shared to infer one individual gene. Estimation of the parameters is carried out by an efficient hybrid EM algorithm. The performance of the proposed method across different scenarios was compared favorably in simulation to two-way mixed-effects ANOVA and the EDGE method using B-spline basis function. Application to the real data on C. elegans developmental stages also suggested that FPC analysis combined with hybrid EM algorithm provides a computationally fast and efficient method for identifying DE genes based on time-course microarray data.     

A global approach to identify differentially expressed genes in cDNA (two-color) microarray experiments

MOTIVATION: Currently most of the methods for identifying differentially expressed genes fall into the category of so called single-gene-analysis, performing hypothesis testing on a gene-by-gene basis. In a single-gene-analysis approach, estimating the variability of each gene is required to determine whether a gene is differentially expressed or not. Poor accuracy of variability estimation makes it difficult to identify genes with small fold-changes unless a very large number of replicate experiments are performed. RESULTS: We propose a method that can avoid the difficult task of estimating variability for each gene, while reliably identifying a group of differentially expressed genes with low false discovery rates, even when the fold-changes are very small. In this article, a new characterization of differentially expressed genes is established based on a theorem about the distribution of ranks of genes sorted by (log) ratios within each array. This characterization of differentially expressed genes based on rank is an example of all-gene-analysis instead of single gene analysis. We apply the method to a cDNA microarray dataset and many low fold-changed genes (as low as 1.3 fold-changes) are reliably identified without carrying out hypothesis testing on a gene-by-gene basis. The false discovery rate is estimated in two different ways reflecting the variability from all the genes without the complications related to multiple hypothesis testing. We also provide some comparisons between our approach and single-gene-analysis based methods. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.     

Probe rank approaches for gene selection in oligonucleotide arrays with a small number of replicates

MOTIVATION: One major area of interest in analyzing oligonucleotide gene array data is identifying differentially expressed genes. A challenge to biostatisticians is to develop an approach to summarizing probe-level information that adequately reflects the true expression level while accounting for probe variation, chip variation and interaction effects. Various statistical tools, such as MAS and RMA, have been developed to address this issue. In these approaches, the probe level expression data are summarized into gene level data, which are then used for downstream statistical analysis. Since probe variation is often larger than chip variation and there is also a potential interaction effect between probe affinity and treatment effect, strategies such as a gene level analysis, may not be optimal. In this study, we propose a procedure to analyze probe level data for selecting differentially expressed genes under two treatment conditions (groups) with a small number of replicates. The probe level discrepancy between two groups can be measured by a difference of the percentiles of probe perfect-match (PM) ranks or of probe PM weighted ranks. The difference is then compared with a pre-specified threshold to determine differentially expressed genes. The probe level approach takes into account non-homogenous treatment effects and reduces possible cross-hybridization effects across a set of probes. RESULTS: The proposed approach is compared with MAS and RMA using two benchmark gene array datasets. Positive predictivity and sensitivity are used for evaluation. Results show the proposed approach has higher positive predictivity and higher sensitivity. AVAILABILITY: Available on request from the authors. CONTACT: dtchen@uab.edu.     

一种融合表达谱相关性信息的激活子网辨识算法

传统表达谱数据分析方法集中于寻找差异表达基因和共表达基因集合,没有考虑基因表达产物之间已知的相互作用.近年来在系统生物学的研究中发展了将基因表达谱与蛋白质相互作用网络进行整合分析的方法.现有方法未能综合考虑基因表达差异性和相关性信息,容易导致辨识结果中重要功能分子缺失且生物学功能相关度不高.提出一种融合表达谱差异性和相关性信息的激活子网辨识算法,能够在蛋白质相互作用网络中辨识高功能相关度的激活子网.应用到人免疫缺陷病毒HIV-1感染过程的研究,结果表明,该算法可以有效避免仅考虑基因表达差异性所引入的偏差,揭示了高相关性低表达差异基因在相关通路中的关键性作用.     

Genes@Work: an efficient algorithm for pattern discovery and multivariate feature selection in gene expression data

MOTIVATION: Despite the growing literature devoted to finding differentially expressed genes in assays probing different tissues types, little attention has been paid to the combinatorial nature of feature selection inherent to large, high-dimensional gene expression datasets. New flexible data analysis approaches capable of searching relevant subgroups of genes and experiments are needed to understand multivariate associations of gene expression patterns with observed phenotypes. RESULTS: We present in detail a deterministic algorithm to discover patterns of multivariate gene associations in gene expression data. The patterns discovered are differential with respect to a control dataset. The algorithm is exhaustive and efficient, reporting all existent patterns that fit a given input parameter set while avoiding enumeration of the entire pattern space. The value of the pattern discovery approach is demonstrated by finding a set of genes that differentiate between two types of lymphoma. Moreover, these genes are found to behave consistently in an independent dataset produced in a different laboratory using different arrays, thus validating the genes selected using our algorithm. We show that the genes deemed significant in terms of their multivariate statistics will be missed using other methods. AVAILABILITY: Our set of pattern discovery algorithms including a user interface is distributed as a package called Genes@Work. This package is freely available to non-commercial users and can be downloaded from our website (http://www.research.ibm.com/FunGen).     

An empirical Bayesian approach for identifying differential coexpression in high-throughput experiments

A common goal of microarray and related high-throughput genomic experiments is to identify genes that vary across biological condition. Most often this is accomplished by identifying genes with changes in mean expression level, so called differentially expressed (DE) genes, and a number of effective methods for identifying DE genes have been developed. Although useful, these approaches do not accommodate other types of differential regulation. An important example concerns differential coexpression (DC). Investigations of this class of genes are hampered by the large cardinality of the space to be interrogated as well as by influential outliers. As a result, existing DC approaches are often underpowered, exceedingly prone to false discoveries, and/or computationally intractable for even a moderately large number of pairs. To address this, an empirical Bayesian approach for identifying DC gene pairs is developed. The approach provides a false discovery rate controlled list of significant DC gene pairs without sacrificing power. It is applicable within a single study as well as across multiple studies. Computations are greatly facilitated by a modification to the expectation-maximization algorithm and a procedural heuristic. Simulations suggest that the proposed approach outperforms existing methods in far less computational time; and case study results suggest that the approach will likely prove to be a useful complement to current DE methods in high-throughput genomic studies.     

Testing for differentially-expressed genes by maximum-likelihood analysis of microarray data.

Although two-color fluorescent DNA microarrays are now standard equipment in many molecular biology laboratories, methods for identifying differentially expressed genes in microarray data are still evolving. Here, we report a refined test for differentially expressed genes which does not rely on gene expression ratios but directly compares a series of repeated measurements of the two dye intensities for each gene. This test uses a statistical model to describe multiplicative and additive errors influencing an array experiment, where model parameters are estimated from observed intensities for all genes using the method of maximum likelihood. A generalized likelihood ratio test is performed for each gene to determine whether, under the model, these intensities are significantly different. We use this method to identify significant differences in gene expression among yeast cells growing in galactose-stimulating versus non-stimulating conditions and compare our results with current approaches for identifying differentially-expressed genes. The effect of sample size on parameter optimization is also explored, as is the use of the error model to compare the within- and between-slide intensity variation intrinsic to an array experiment.     

PADGE: analysis of heterogeneous patterns of differential gene expression.

We have devised a novel analysis approach, percentile analysis for differential gene expression (PADGE), for identifying genes differentially expressed between two groups of heterogeneous samples. PADGE was designed to compare expression profiles of sample subgroups at a series of percentile cutoffs and to examine the trend of relative expression between sample groups as expression level increases. Simulation studies showed that PADGE has more statistical power than t-statistics, cancer outlier profile analysis (COPA) (Tomlins SA, Rhodes DR, Perner S, Dhanasekaran SM, Mehra R, Sun XW, Varambally S, Cao X, Tchinda J, Kuefer R, Lee C, Montie JE, Shah RB, Pienta KJ, Rubin MA, Chinnaiyan AM. Science 310: 644-648, 2005), and kurtosis (Teschendorff AE, Naderi A, Barbosa-Morais NL, Caldas C. Bioinformatics 22: 2269-2275, 2006). Application of PADGE to microarray data sets in tumor tissues demonstrated its utility in prioritizing cancer genes encoding potential therapeutic targets or diagnostic markers. A web application was developed for researchers to analyze a large gene expression data set from heterogeneous biological samples and identify differentially expressed genes between subsets of sample classes using PADGE and other available approaches. Availability: http://www.cgl.ucsf.edu/Research/genentech/padge/.     

Identification of differentially expressed genes using multi-resolution wavelet transformation analysis combined with SAM

Although many statistical methods have been proposed for identifying differentially expressed genes, the optimal approach has still not been resolved. Therefore, it is necessary to develop more efficient methods of finding differentially expressed genes while accounting for noise and false discovery rate (FDR). We propose a method based on multi-resolution wavelet transformation analysis combined with SAM for identifying differentially expressed genes by adjusting the Δ and computing the FDR. This method was applied to a microarray expression dataset from adenoma patients and normal subjects. The number of differentially expressed genes gradually reduced with an increasing Δ value, and the FDR was reduced after wavelet transformation. At a given Δ value, the FDR was also reduced before and after wavelet transformation. In conclusion, a greater number and quality of differentially expressed genes were detected using the method when compared to non-transformed data, and the FDRs were notably more controlled and reduced.     

Discovering molecular pathways from protein interaction and gene expression data

In this paper, we describe an approach for identifying 'pathways' from gene expression and protein interaction data. Our approach is based on the assumption that many pathways exhibit two properties: their genes exhibit a similar gene expression profile, and the protein products of the genes often interact. Our approach is based on a unified probabilistic model, which is learned from the data using the EM algorithm. We present results on two Saccharomyces cerevisiae gene expression data sets, combined with a binary protein interaction data set. Our results show that our approach is much more successful than other approaches at discovering both coherent functional groups and entire protein complexes.     

Modeling Genome-Wide Dynamic Regulatory Network in Mouse Lungs with Influenza Infection Using High-Dimensional Ordinary Differential Equations

The immune response to viral infection is regulated by an intricate network of many genes and their products. The reverse engineering of gene regulatory networks (GRNs) using mathematical models from time course gene expression data collected after influenza infection is key to our understanding of the mechanisms involved in controlling influenza infection within a host. A five-step pipeline: detection of temporally differentially expressed genes, clustering genes into co-expressed modules, identification of network structure, parameter estimate refinement, and functional enrichment analysis, is developed for reconstructing high-dimensional dynamic GRNs from genome-wide time course gene expression data. Applying the pipeline to the time course gene expression data from influenza-infected mouse lungs, we have identified 20 distinct temporal expression patterns in the differentially expressed genes and constructed a module-based dynamic network using a linear ODE model. Both intra-module and inter-module annotations and regulatory relationships of our inferred network show some interesting findings and are highly consistent with existing knowledge about the immune response in mice after influenza infection. The proposed method is a computationally efficient, data-driven pipeline bridging experimental data, mathematical modeling, and statistical analysis. The application to the influenza infection data elucidates the potentials of our pipeline in providing valuable insights into systematic modeling of complicated biological processes.     

Robust Modeling of Differential Gene Expression Data Using Normal/Independent Distributions: A Bayesian Approach

In this paper, the problem of identifying differentially expressed genes under different conditions using gene expression microarray data, in the presence of outliers, is discussed. For this purpose, the robust modeling of gene expression data using some powerful distributions known as normal/independent distributions is considered. These distributions include the Student’s t and normal distributions which have been used previously, but also include extensions such as the slash, the contaminated normal and the Laplace distributions. The purpose of this paper is to identify differentially expressed genes by considering these distributional assumptions instead of the normal distribution. A Bayesian approach using the Markov Chain Monte Carlo method is adopted for parameter estimation. Two publicly available gene expression data sets are analyzed using the proposed approach. The use of the robust models for detecting differentially expressed genes is investigated. This investigation shows that the choice of model for differentiating gene expression data is very important. This is due to the small number of replicates for each gene and the existence of outlying data. Comparison of the performance of these models is made using different statistical criteria and the ROC curve. The method is illustrated using some simulation studies. We demonstrate the flexibility of these robust models in identifying differentially expressed genes.     

A Regression-Based Differential Expression Detection Algorithm for Microarray Studies with Ultra-Low Sample Size

Global gene expression analysis using microarrays and, more recently, RNA-seq, has allowed investigators to understand biological processes at a system level. However, the identification of differentially expressed genes in experiments with small sample size, high dimensionality, and high variance remains challenging, limiting the usability of these tens of thousands of publicly available, and possibly many more unpublished, gene expression datasets. We propose a novel variable selection algorithm for ultra-low-n microarray studies using generalized linear model-based variable selection with a penalized binomial regression algorithm called penalized Euclidean distance (PED). Our method uses PED to build a classifier on the experimental data to rank genes by importance. In place of cross-validation, which is required by most similar methods but not reliable for experiments with small sample size, we use a simulation-based approach to additively build a list of differentially expressed genes from the rank-ordered list. Our simulation-based approach maintains a low false discovery rate while maximizing the number of differentially expressed genes identified, a feature critical for downstream pathway analysis. We apply our method to microarray data from an experiment perturbing the Notch signaling pathway in Xenopus laevis embryos. This dataset was chosen because it showed very little differential expression according to limma, a powerful and widely-used method for microarray analysis. Our method was able to detect a significant number of differentially expressed genes in this dataset and suggest future directions for investigation. Our method is easily adaptable for analysis of data from RNA-seq and other global expression experiments with low sample size and high dimensionality.     

Identifying differentially expressed genes from microarray experiments via statistic synthesis

MOTIVATION: A common objective of microarray experiments is the detection of differential gene expression between samples obtained under different conditions. The task of identifying differentially expressed genes consists of two aspects: ranking and selection. Numerous statistics have been proposed to rank genes in order of evidence for differential expression. However, no one statistic is universally optimal and there is seldom any basis or guidance that can direct toward a particular statistic of choice. RESULTS: Our new approach, which addresses both ranking and selection of differentially expressed genes, integrates differing statistics via a distance synthesis scheme. Using a set of (Affymetrix) spike-in datasets, in which differentially expressed genes are known, we demonstrate that our method compares favorably with the best individual statistics, while achieving robustness properties lacked by the individual statistics. We further evaluate performance on one other microarray study.     

Mixture models for gene expression experiments with two species

Cross-species research in drug development is novel and challenging. A bivariate mixture model utilizing information across two species was proposed to solve the fundamental problem of identifying differentially expressed genes in microarray experiments in order to potentially improve the understanding of translation between preclinical and clinical studies for drug development. The proposed approach models the joint distribution of treatment effects estimated from independent linear models. The mixture model posits up to nine components, four of which include groups in which genes are differentially expressed in both species. A comprehensive simulation to evaluate the model performance and one application on a real world data set, a mouse and human type II diabetes experiment, suggest that the proposed model, though highly structured, can handle various configurations of differential gene expression and is practically useful on identifying differentially expressed genes, especially when the magnitude of differential expression due to different treatment intervention is weak. In the mouse and human application, the proposed mixture model was able to eliminate unimportant genes and identify a list of genes that were differentially expressed in both species and could be potential gene targets for drug development.     

Codependency and mutual exclusivity for gene community detection from sparse single-cell transcriptome data

Single-cell RNA-seq (scRNA-seq) can be used to characterize cellular heterogeneity in thousands of cells. The reconstruction of a gene network based on coexpression patterns is a fundamental task in scRNA-seq analyses, and the mutual exclusivity of gene expression can be critical for understanding such heterogeneity. Here, we propose an approach for detecting communities from a genetic network constructed on the basis of coexpression properties. The community-based comparison of multiple coexpression networks enables the identification of functionally related gene clusters that cannot be fully captured through differential gene expression-based analysis. We also developed a novel metric referred to as the exclusively expressed index (EEI) that identifies mutually exclusive gene pairs from sparse scRNA-seq data. EEI quantifies and ranks the exclusive expression levels of all gene pairs from binary expression patterns while maintaining robustness against a low sequencing depth. We applied our methods to glioblastoma scRNA-seq data and found that gene communities were partially conserved after serum stimulation despite a considerable number of differentially expressed genes. We also demonstrate that the identification of mutually exclusive gene sets with EEI can improve the sensitivity of capturing cellular heterogeneity. Our methods complement existing approaches and provide new biological insights, even for a large, sparse dataset, in the single-cell analysis field.     

Bayesian Joint Analysis of Gene Expression Data and Gene Functional Annotations

Identifying which genes and which gene sets are differentially expressed (DE) under two experimental conditions are both key questions in microarray analysis. Although closely related and seemingly similar, they cannot replace each other, due to their own importance and merits in scientific discoveries. Existing approaches have been developed to address only one of the two questions. Further, most of the methods for detecting DE genes purely rely on gene expression analysis, without using the information about gene functional grouping. Methods for detecting altered gene sets often use a two-step procedure, of which the first step conducts differential expression analysis using expression data only, and the second step takes results from the first step and tries to examine whether each predefined gene set is overrepresented by DE genes through some testing procedure. Such a sequential manner in analysis might cause information loss by just focusing on summary results without using the entire expression data in the second step. Here, we propose a Bayesian joint modeling approach to address the two key questions in parallel, which incorporates the information of functional annotations into expression data analysis and meanwhile infer the enrichment of functional groups. Simulation results and analysis of experimental data obtained for E.?coli show improved statistical power of our integrated approach in both identifying DE genes and altered gene sets, when compared to conventional methods.