CDS: a fold-change based statistical test for concomitant identification of distinctness and similarity in gene expression analysis

The problem of identifying differential activity such as in gene expression is a major defeat in biostatistics and bioinformatics.Equally important,however much less frequently studied,is the question of similar activity from one biological condition to another.The foldchange,or ratio,is usually considered a relevant criterion for stating difference and similarity between measurements.Importantly,no statistical method for concomitant evaluation of similarity and distinctness currently exists for biological applications.Modem microarray,digital PCR(dPCR),and Next-Generation Sequencing(NGS) technologies frequently provide a means of coefficient of variation estimation for individual measurements.Using fold-change,and by making the assumption that measurements are normally distributed with known variances,we designed a novel statistical test that allows us to detect concomitantly,thus using the same formalism,differentially and similarly expressed genes(http://cds.ihes.fr).Given two sets of gene measurements in different biological conditions,the probabilities of making type I and type II errors in stating that a gene is differentially or similarly expressed from one condition to the other can be calculated.Furthermore,a confidence interval for the fold-change can be delineated.Finally,we demonstrate that the assumption of normality can be relaxed to consider arbitrary distributions numerically.The Concomitant evaluation of Distinctness and Similarity(CDS) statistical test correctly estimates similarities and differences between measurements of gene expression.The implementation,being time and memory efficient,allows the use of the CDS test in high-throughput data analysis such as microarray,dPCR,and NGS experiments.Importantly,the CDS test can be applied to the comparison of single measurements(N:1) provided the variance(or coefficient of variation) of the signals is known,making CDS a valuable tool also in biomedical analysis where typically a single measurement per subject is available.     

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.     

Statistical significance analysis of longitudinal gene expression data

MOTIVATION: Time-course microarray experiments are designed to study biological processes in a temporal fashion. Longitudinal gene expression data arise when biological samples taken from the same subject at different time points are used to measure the gene expression levels. It has been observed that the gene expression patterns of samples of a given tumor measured at different time points are likely to be much more similar to each other than are the expression patterns of tumor samples of the same type taken from different subjects. In statistics, this phenomenon is called the within-subject correlation of repeated measurements on the same subject, and the resulting data are called longitudinal data. It is well known in other applications that valid statistical analyses have to appropriately take account of the possible within-subject correlation in longitudinal data. RESULTS: We apply estimating equation techniques to construct a robust statistic, which is a variant of the robust Wald statistic and accounts for the potential within-subject correlation of longitudinal gene expression data, to detect genes with temporal changes in expression. We associate significance levels to the proposed statistic by either incorporating the idea of the significance analysis of microarrays method or using the mixture model method to identify significant genes. The utility of the statistic is demonstrated by applying it to an important study of osteoblast lineage-specific differentiation. Using simulated data, we also show pitfalls in drawing statistical inference when the within-subject correlation in longitudinal gene expression data is ignored.     

How many differentially expressed genes: A perspective from the comparison of genotypic and phenotypic distances

Identifying differentially expressed genes is critical in microarray data analysis. Many methods have been developed by combining p-value, fold-change, and various statistical models to determine these genes. When using these methods, it is necessary to set up various pre-determined cutoff values. However, many of these cutoff values are somewhat arbitrary and may not have clear connections to biology. In this study, a genetic distance method based on gene expression level was developed to analyze eight sets of microarray data extracted from the GEO database. Since the genes used in distance calculation have been ranked by fold-change, the genetic distance becomes more stable when adding more genes in the calculation, indicating there is an optimal set of genes which are sufficient to characterize the stable difference between samples. This set of genes is differentially expressed genes representing both the genotypic and phenotypic differences between samples.     

Local-pooled-error test for identifying differentially expressed genes with a small number of replicated microarrays

MOTIVATION: In microarray studies gene discovery based on fold-change values is often misleading because error variability for each gene is heterogeneous under different biological conditions and intensity ranges. Several statistical testing methods for differential gene expression have been suggested, but some of these approaches are underpowered and result in high false positive rates because within-gene variance estimates are based on a small number of replicated arrays. RESULTS: We propose to use local-pooled-error (LPE) estimates and robust statistical tests for evaluating significance of each gene's differential expression. Our LPE estimation is based on pooling errors within genes and between replicate arrays for genes in which expression values are similar. We have applied our LPE method to compare gene expression in na?ve and activated CD8+ T-cells. Our results show that the LPE method effectively identifies significant differential-expression patterns with a small number of replicated arrays. AVAILABILITY: The methodology is implemented with S-PLUS and R functions available at http://hesweb1.med.virginia.edu/bioinformatics     

The complexity of gene expression dynamics revealed by permutation entropy

Background

High complexity is considered a hallmark of living systems. Here we investigate the complexity of temporal gene expression patterns using the concept of Permutation Entropy (PE) first introduced in dynamical systems theory. The analysis of gene expression data has so far focused primarily on the identification of differentially expressed genes, or on the elucidation of pathway and regulatory relationships. We aim to study gene expression time series data from the viewpoint of complexity.

Results

Applying the PE complexity metric to abiotic stress response time series data in Arabidopsis thaliana, genes involved in stress response and signaling were found to be associated with the highest complexity not only under stress, but surprisingly, also under reference, non-stress conditions. Genes with house-keeping functions exhibited lower PE complexity. Compared to reference conditions, the PE of temporal gene expression patterns generally increased upon stress exposure. High-complexity genes were found to have longer upstream intergenic regions and more cis-regulatory motifs in their promoter regions indicative of a more complex regulatory apparatus needed to orchestrate their expression, and to be associated with higher correlation network connectivity degree. Arabidopsis genes also present in other plant species were observed to exhibit decreased PE complexity compared to Arabidopsis specific genes.

Conclusions

We show that Permutation Entropy is a simple yet robust and powerful approach to identify temporal gene expression profiles of varying complexity that is equally applicable to other types of molecular profile data.     

Evaluation of DNA microarray results with quantitative gene expression platforms

We have evaluated the performance characteristics of three quantitative gene expression technologies and correlated their expression measurements to those of five commercial microarray platforms, based on the MicroArray Quality Control (MAQC) data set. The limit of detection, assay range, precision, accuracy and fold-change correlations were assessed for 997 TaqMan Gene Expression Assays, 205 Standardized RT (Sta)RT-PCR assays and 244 QuantiGene assays. TaqMan is a registered trademark of Roche Molecular Systems, Inc. We observed high correlation between quantitative gene expression values and microarray platform results and found few discordant measurements among all platforms. The main cause of variability was differences in probe sequence and thus target location. A second source of variability was the limited and variable sensitivity of the different microarray platforms for detecting weakly expressed genes, which affected interplatform and intersite reproducibility of differentially expressed genes. From this analysis, we conclude that the MAQC microarray data set has been validated by alternative quantitative gene expression platforms thus supporting the use of microarray platforms for the quantitative characterization of gene expression.     

Combined static and dynamic analysis for determining the quality of time-series expression profiles

Expression profiling of time-series experiments is widely used to study biological systems. However, determining the quality of the resulting profiles remains a fundamental problem. Because of inadequate sampling rates, the effect of arrest-and-release methods and loss of synchronization, the measurements obtained from a series of time points may not accurately represent the underlying expression profiles. To solve this, we propose an approach that combines time-series and static (average) expression data analysis--for each gene, we determine whether its temporal expression profile can be reconciled with its static expression levels. We show that by combining synchronized and unsynchronized human cell cycle data, we can identify many cycling genes that are missed when using only time-series data. The algorithm also correctly distinguishes cycling genes from genes that specifically react to an environmental stimulus even if they share similar temporal expression profiles. Experimental validation of these results shows the utility of this analytical approach for determining the accuracy of gene expression patterns.     

Dynamic models of gene expression and classification

Powerful new methods, like expression profiles using cDNA arrays, have been used to monitor changes in gene expression levels as a result of a variety of metabolic, xenobiotic or pathogenic challenges. This potentially vast quantity of data enables, in principle, the dissection of the complex genetic networks that control the patterns and rhythms of gene expression in the cell. Here we present a general approach to developing dynamic models for analyzing time series of whole genome expression. In this approach, a self-consistent calculation is performed that involves both linear and non-linear response terms for interrelating gene expression levels. This calculation uses singular value decomposition (SVD) not as a statistical tool but as a means of inverting noisy and near-singular matrices. The linear transition matrix that is determined from this calculation can be used to calculate the underlying network reflected in the data. This suggests a direct method of classifying genes according to their place in the resulting network. In addition to providing a means to model such a large multivariate system this approach can be used to reduce the dimensionality of the problem in a rational and consistent way, and suppress the strong noise amplification effects often encountered with expression profile data. Non-linear and higher-order Markov behavior of the network are also determined in this self-consistent method. In data sets from yeast, we calculate the Markov matrix and the gene classes based on the linear-Markov network. These results compare favorably with previously used methods like cluster analysis. Our dynamic method appears to give a broad and general framework for data analysis and modeling of gene expression arrays. Electronic Publication     

Dynamic modeling of gene expression in prokaryotes: application to glucose-lactose diauxie in Escherichia coli

Coexpression of genes or, more generally, similarity in the expression profiles poses an unsurmountable obstacle to inferring the gene regulatory network (GRN) based solely on data from DNA microarray time series. Clustering of genes with similar expression profiles allows for a course-grained view of the GRN and a probabilistic determination of the connectivity among the clusters. We present a model for the temporal evolution of a gene cluster network which takes into account interactions of gene products with genes and, through a non-constant degradation rate, with other gene products. The number of model parameters is reduced by using polynomial functions to interpolate temporal data points. In this manner, the task of parameter estimation is reduced to a system of linear algebraic equations, thus making the computation time shorter by orders of magnitude. To eliminate irrelevant networks, we test each GRN for stability with respect to parameter variations, and impose restrictions on its behavior near the steady state. We apply our model and methods to DNA microarray time series' data collected on Escherichia coli during glucose-lactose diauxie and infer the most probable cluster network for different phases of the experiment. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1007/s11693-011-9079-2) contains supplementary material, which is available to authorized users.     

Optimal approach for classification of acute leukemia subtypes based on gene expression data

The classification of cancer subtypes, which is critical for successful treatment, has been studied extensively with the use of gene expression profiles from oligonucleotide chips or cDNA microarrays. Various pattern recognition methods have been successfully applied to gene expression data. However, these methods are not optimal, rather they are high-performance classifiers that emphasize only classification accuracy. In this paper, we propose an approach for the construction of the optimal linear classifier using gene expression data. Two linear classification methods, linear discriminant analysis (LDA) and discriminant partial least-squares (DPLS), are applied to distinguish acute leukemia subtypes. These methods are shown to give satisfactory accuracy. Moreover, we determined optimally the number of genes participating in the classification (a remarkably small number compared to previous results) on the basis of the statistical significance test. Thus, the proposed method constructs the optimal classifier that is composed of a small size predictor and provides high accuracy.     

Differential and trajectory methods for time course gene expression data

MOTIVATION: The issue of high dimensionality in microarray data has been, and remains, a hot topic in statistical and computational analysis. Efficient gene filtering and differentiation approaches can reduce the dimensions of data, help to remove redundant genes and noises, and highlight the most relevant genes that are major players in the development of certain diseases or the effect of drug treatment. The purpose of this study is to investigate the efficiency of parametric (including Bayesian and non-Bayesian, linear and non-linear), non-parametric and semi-parametric gene filtering methods through the application of time course microarray data from multiple sclerosis patients being treated with interferon-beta-1a. The analysis of variance with bootstrapping (parametric), class dispersion (semi-parametric) and Pareto (non-parametric) with permutation methods are presented and compared for filtering and finding differentially expressed genes. The Bayesian linear correlated model, the Bayesian non-linear model the and non-Bayesian mixed effects model with bootstrap were also developed to characterize the differential expression patterns. Furthermore, trajectory-clustering approaches were developed in order to investigate the dynamic patterns and inter-dependency of drug treatment effects on gene expression. RESULTS: Results show that the presented methods performed significant differently but all were adequate in capturing a small number of the potentially relevant genes to the disease. The parametric method, such as the mixed model and two Bayesian approaches proved to be more conservative. This may because these methods are based on overall variation in expression across all time points. The semi-parametric (class dispersion) and non-parametric (Pareto) methods were appropriate in capturing variation in expression from time point to time point, thereby making them more suitable for investigating significant monotonic changes and trajectories of changes in gene expressions in time course microarray data. Also, the non-linear Bayesian model proved to be less conservative than linear Bayesian correlated growth models to filter out the redundant genes, although the linear model showed better fit than non-linear model (smaller DIC). We also report the trajectories of significant genes-since we have been able to isolate trajectories of genes whose regulations appear to be inter-dependent.