A Robust Statistical Method for Detecting Differentially Expressed Genes

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

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 mixture model approach to detecting differentially expressed genes with microarray data

An exciting biological advancement over the past few years is the use of microarray technologies to measure simultaneously the expression levels of thousands of genes. The bottleneck now is how to extract useful information from the resulting large amounts of data. An important and common task in analyzing microarray data is to identify genes with altered expression under two experimental conditions. We propose a nonparametric statistical approach, called the mixture model method (MMM), to handle the problem when there are a small number of replicates under each experimental condition. Specifically, we propose estimating the distributions of a t -type test statistic and its null statistic using finite normal mixture models. A comparison of these two distributions by means of a likelihood ratio test, or simply using the tail distribution of the null statistic, can identify genes with significantly changed expression. Several methods are proposed to effectively control the false positives. The methodology is applied to a data set containing expression levels of 1,176 genes of rats with and without pneumococcal middle ear infection.     

Genome-wide co-expression based prediction of differential expressions

MOTIVATION: Microarrays have been widely used for medical studies to detect novel disease-related genes. They enable us to study differential gene expressions at a genomic level. They also provide us with informative genome-wide co-expressions. Although many statistical methods have been proposed for identifying differentially expressed genes, genome-wide co-expressions have not been well considered for this issue. Incorporating genome-wide co-expression information in the differential expression analysis may improve the detection of disease-related genes. RESULTS: In this study, we proposed a statistical method for predicting differential expressions through the local regression between differential expression and co-expression measures. The smoother span parameter was determined by optimizing the rank correlation between the observed and predicted differential expression measures. A mixture normal quantile-based method was used to transform data. We used the gene-specific permutation procedure to evaluate the significance of a prediction. Two published microarray data sets were analyzed for applications. For the data set collected for a prostate cancer study, the proposed method identified many genes with weak differential expressions. Several of these genes have been shown in literature to be associated with the disease. For the data set collected for a type 2 diabetes study, no significant genes could be identified by the traditional methods. However, the proposed method identified many genes with significantly low false discovery rates. AVAILABILITY: The R codes are freely available at http://home.gwu.edu/~ylai/research/CoDiff, where the gene lists ranked by our method are also provided as the Supplementary Material.     

Comparative Study of Regulatory Circuits in Two Sea Urchin Species Reveals Tight Control of Timing and High Conservation of Expression Dynamics

Accurate temporal control of gene expression is essential for normal development and must be robust to natural genetic and environmental variation. Studying gene expression variation within and between related species can delineate the level of expression variability that development can tolerate. Here we exploit the comprehensive model of sea urchin gene regulatory networks and generate high-density expression profiles of key regulatory genes of the Mediterranean sea urchin, Paracentrotus lividus (Pl). The high resolution of our studies reveals highly reproducible gene initiation times that have lower variation than those of maximal mRNA levels between different individuals of the same species. This observation supports a threshold behavior of gene activation that is less sensitive to input concentrations. We then compare Mediterranean sea urchin gene expression profiles to those of its Pacific Ocean relative, Strongylocentrotus purpuratus (Sp). These species shared a common ancestor about 40 million years ago and show highly similar embryonic morphologies. Our comparative analyses of five regulatory circuits operating in different embryonic territories reveal a high conservation of the temporal order of gene activation but also some cases of divergence. A linear ratio of 1.3-fold between gene initiation times in Pl and Sp is partially explained by scaling of the developmental rates with temperature. Scaling the developmental rates according to the estimated Sp-Pl ratio and normalizing the expression levels reveals a striking conservation of relative dynamics of gene expression between the species. Overall, our findings demonstrate the ability of biological developmental systems to tightly control the timing of gene activation and relative dynamics and overcome expression noise induced by genetic variation and growth conditions.     

Exploiting the full power of temporal gene expression profiling through a new statistical test: Application to the analysis of muscular dystrophy data

Background  

The identification of biologically interesting genes in a temporal expression profiling dataset is challenging and complicated by high levels of experimental noise. Most statistical methods used in the literature do not fully exploit the temporal ordering in the dataset and are not suited to the case where temporal profiles are measured for a number of different biological conditions. We present a statistical test that makes explicit use of the temporal order in the data by fitting polynomial functions to the temporal profile of each gene and for each biological condition. A Hotelling T ²-statistic is derived to detect the genes for which the parameters of these polynomials are significantly different from each other.     

A Hybrid Approach of Gene Sets and Single Genes for the Prediction of Survival Risks with Gene Expression Data

Accumulated biological knowledge is often encoded as gene sets, collections of genes associated with similar biological functions or pathways. The use of gene sets in the analyses of high-throughput gene expression data has been intensively studied and applied in clinical research. However, the main interest remains in finding modules of biological knowledge, or corresponding gene sets, significantly associated with disease conditions. Risk prediction from censored survival times using gene sets hasn’t been well studied. In this work, we propose a hybrid method that uses both single gene and gene set information together to predict patient survival risks from gene expression profiles. In the proposed method, gene sets provide context-level information that is poorly reflected by single genes. Complementarily, single genes help to supplement incomplete information of gene sets due to our imperfect biomedical knowledge. Through the tests over multiple data sets of cancer and trauma injury, the proposed method showed robust and improved performance compared with the conventional approaches with only single genes or gene sets solely. Additionally, we examined the prediction result in the trauma injury data, and showed that the modules of biological knowledge used in the prediction by the proposed method were highly interpretable in biology. A wide range of survival prediction problems in clinical genomics is expected to benefit from the use of biological knowledge.     

Mining co-regulated gene profiles for the detection of functional associations in gene expression data

MOTIVATION: Association pattern discovery (APD) methods have been successfully applied to gene expression data. They find groups of co-regulated genes in which the genes are either up- or down-regulated throughout the identified conditions. These methods, however, fail to identify similarly expressed genes whose expressions change between up- and down-regulation from one condition to another. In order to discover these hidden patterns, we propose the concept of mining co-regulated gene profiles. Co-regulated gene profiles contain two gene sets such that genes within the same set behave identically (up or down) while genes from different sets display contrary behavior. To reduce and group the large number of similar resulting patterns, we propose a new similarity measure that can be applied together with hierarchical clustering methods. RESULTS: We tested our proposed method on two well-known yeast microarray data sets. Our implementation mined the data effectively and discovered patterns of co-regulated genes that are hidden to traditional APD methods. The high content of biologically relevant information in these patterns is demonstrated by the significant enrichment of co-regulated genes with similar functions. Our experimental results show that the Mining Attribute Profile (MAP) method is an efficient tool for the analysis of gene expression data and competitive with bi-clustering techniques.     

Functional hierarchical models for identifying genes with different time-course expression profiles

Time-course studies of gene expression are essential in biomedical research to understand biological phenomena that evolve in a temporal fashion. We introduce a functional hierarchical model for detecting temporally differentially expressed (TDE) genes between two experimental conditions for cross-sectional designs, where the gene expression profiles are treated as functional data and modeled by basis function expansions. A Monte Carlo EM algorithm was developed for estimating both the gene-specific parameters and the hyperparameters in the second level of modeling. We use a direct posterior probability approach to bound the rate of false discovery at a pre-specified level and evaluate the methods by simulations and application to microarray time-course gene expression data on Caenorhabditis elegans developmental processes. Simulation results suggested that the procedure performs better than the two-way ANOVA in identifying TDE genes, resulting in both higher sensitivity and specificity. Genes identified from the C. elegans developmental data set show clear patterns of changes between the two experimental conditions.     

Evaluation and Validation of Reference Genes for Normalization of Quantitative Real-Time PCR Based Gene Expression Studies in Peanut

The quantitative real-time PCR (qPCR) based techniques have become essential for gene expression studies and high-throughput molecular characterization of transgenic events. Normalizing to reference gene in relative quantification make results from qPCR more reliable when compared to absolute quantification, but requires robust reference genes. Since, ideal reference gene should be species specific, no single internal control gene is universal for use as a reference gene across various plant developmental stages and diverse growth conditions. Here, we present validation studies of multiple stably expressed reference genes in cultivated peanut with minimal variations in temporal and spatial expression when subjected to various biotic and abiotic stresses. Stability in the expression of eight candidate reference genes including ADH3, ACT11, ATPsyn, CYP2, ELF1B, G6PD, LEC and UBC1 was compared in diverse peanut plant samples. The samples were categorized into distinct experimental sets to check the suitability of candidate genes for accurate and reliable normalization of gene expression using qPCR. Stability in expression of the references genes in eight sets of samples was determined by geNorm and NormFinder methods. While three candidate reference genes including ADH3, G6PD and ELF1B were identified to be stably expressed across experiments, LEC was observed to be the least stable, and hence must be avoided for gene expression studies in peanut. Inclusion of the former two genes gave sufficiently reliable results; nonetheless, the addition of the third reference gene ELF1B may be potentially better in a diverse set of tissue samples of peanut.     

Analyzing gene expression data in terms of gene sets: methodological issues

MOTIVATION: Many statistical tests have been proposed in recent years for analyzing gene expression data in terms of gene sets, usually from Gene Ontology. These methods are based on widely different methodological assumptions. Some approaches test differential expression of each gene set against differential expression of the rest of the genes, whereas others test each gene set on its own. Also, some methods are based on a model in which the genes are the sampling units, whereas others treat the subjects as the sampling units. This article aims to clarify the assumptions behind different approaches and to indicate a preferential methodology of gene set testing. RESULTS: We identify some crucial assumptions which are needed by the majority of methods. P-values derived from methods that use a model which takes the genes as the sampling unit are easily misinterpreted, as they are based on a statistical model that does not resemble the biological experiment actually performed. Furthermore, because these models are based on a crucial and unrealistic independence assumption between genes, the P-values derived from such methods can be wildly anti-conservative, as a simulation experiment shows. We also argue that methods that competitively test each gene set against the rest of the genes create an unnecessary rift between single gene testing and gene set testing.     

基因表达谱富集分析方法研究进展

微阵列技术是生物技术变革的核心,允许研究者同时监测成千上万个基因的表达水平,已广泛应用于医学研究。如何挖掘海量基因表达信息中的有用信息并进行生物学专业解释,是基因表达谱数据分析领域所面临的一个重要挑战。不同的研究者提出了各种基于基因集进行富集分析的方法,在此将这些方法大致分为两大类,即bottom-up方法和top-down方法。前者先进行单基因分析,然后根据生物学领域知识注释基因集并进行分析。该方法应用广泛,且结果比单基因分析容易解释。后者先根据生物学领域知识将各基因进行归类,然后进行基因差异表达模式分析。该方法不仅能提高结论的可解释性,而且能达到降维的目的。