Volume 14, Issue 3

The use of fold-change (FC) to prioritize differentially expressed genes (DEGs) for post-hoc characterization is a common technique in the analysis of RNA sequencing datasets. However, the use of FC can overlook certain population of DEGs, such as high copy number transcripts which undergo metabolically expensive changes in expression yet fail to exceed the ratiometric FC cut-off, thereby missing potential important biological information. Here we evaluate an alternative approach to prioritizing RNAseq data based on absolute changes in normalized transcript counts (ΔT) between control and treatment conditions. In five pairwise comparisons with a wide range of effect sizes, rank-ordering of DEGs based on the magnitude of ΔT produced a power curve-like distribution, in which 4.7–5.0% of transcripts were responsible for 36–50% of the cumulative change. Thus, differential gene expression is characterized by the high production-cost expression of a small number of genes (large ΔT genes), while the differential expression of the majority of genes involves a much smaller metabolic investment by the cell. To determine whether the large ΔT datasets are representative of coordinated changes in the transcriptional program, we evaluated large ΔT genes for enrichment of gene ontologies (GOs) and predicted protein interactions. In comparison to randomly selected DEGs, the large ΔT transcripts were significantly enriched for both GOs and predicted protein interactions. Furthermore, enrichments were were consistent with the biological context of each comparison yet distinct from those produced using equal-sized populations of large FC genes, indicating that the large ΔT genes represent an orthagonal transcriptional response. Finally, the composition of the large ΔT gene sets were unique to each pairwise comparison, indicating that they represent coherent and context-specific responses to biological conditions rather than the non-specific upregulation of a family of genes. These findings suggest that the large ΔT genes are not a product of random or stochastic phenomenon, but rather represent biologically meaningful changes in the transcriptional program. They furthermore imply that high abundance transcripts are associated with particularly cellular states, and as cells change in response to internal or external conditions, the relative distribution of the abundant transcripts changes accordingly. Thus, prioritization of DEGs based on the concept of metabolic cost is a simple yet powerful method to identify biologically important transcriptional changes and provide novel insights into cellular behaviors.

A nonparametric estimator of mutual information is proposed and is shown to have asymptotic normality and efficiency, and a bias decaying exponentially in sample size. The asymptotic normality and the rapidly decaying bias together offer a viable inferential tool for assessing mutual information between two random elements on finite alphabets where the maximum likelihood estimator of mutual information greatly inflates the probability of type I error. The proposed estimator is illustrated by three examples in which the association between a pair of genes is assessed based on their expression levels. Several results of simulation study are also provided.

Adaptive transmission disequilibrium test (aTDT) and MAX3 test are two robust-efficient association tests for case-parent family trio data. Both tests incorporate information of common genetic models including recessive, additive and dominant models and are efficient in power and robust to genetic model specifications. The aTDT uses information of departure from Hardy-Weinberg disequilibrium to identify the potential genetic model underlying the data and then applies the corresponding TDT-type test, and the MAX3 test is defined as the maximum of the absolute value of three TDT-type tests under the three common genetic models. In this article, we propose three robust Bayes procedures, the aTDT based Bayes factor, MAX3 based Bayes factor and Bayes model averaging (BMA), for association analysis with case-parent trio design. The asymptotic distributions of aTDT under the null and alternative hypothesis are derived in order to calculate its Bayes factor. Extensive simulations show that the Bayes factors and the p -values of the corresponding tests are generally consistent and these Bayes factors are robust to genetic model specifications, especially so when the priors on the genetic models are equal. When equal priors are used for the underlying genetic models, the Bayes factor method based on aTDT is more powerful than those based on MAX3 and Bayes model averaging. When the prior placed a small (large) probability on the true model, the Bayes factor based on aTDT (BMA) is more powerful. Analysis of a simulation data about RA from GAW15 is presented to illustrate applications of the proposed methods.

In genome-wide association studies (GWAS), it is of interest to identify genetic variants associated with phenotypes. For a given phenotype, the associated genetic variants are usually a sparse subset of all possible variants. Traditional Lasso-type estimation methods can therefore be used to detect important genes. But the relationship between genotypes at one variant and a phenotype may be influenced by other variables, such as sex and life style. Hence it is important to be able to incorporate gene-covariate interactions into the sparse regression model. In addition, because there is biological knowledge on the manner in which genes work together in structured groups, it is desirable to incorporate this information as well. In this paper, we present a novel sparse regression methodology for gene-covariate models in association studies that not only allows such interactions but also considers biological group structure. Simulation results show that our method substantially outperforms another method, in which interaction is considered, but group structure is ignored. Application to data on total plasma immunoglobulin E (IgE) concentrations in the Framingham Heart Study (FHS), using sex and smoking status as covariates, yields several potentially interesting gene-covariate interactions.

Gene Set Enrichment Analysis (GSEA) is a basic tool for genomic data treatment. Its test statistic is based on a cumulated weight function, and its distribution under the null hypothesis is evaluated by Monte-Carlo simulation. Here, it is proposed to subtract to the cumulated weight function its asymptotic expectation, then scale it. Under the null hypothesis, the convergence in distribution of the new test statistic is proved, using the theory of empirical processes. The limiting distribution needs to be computed only once, and can then be used for many different gene sets. This results in large savings in computing time. The test defined in this way has been called Weighted Kolmogorov Smirnov (WKS) test. Using expression data from the GEO repository, tested against the MSig Database C2, a comparison between the classical GSEA test and the new procedure has been conducted. Our conclusion is that, beyond its mathematical and algorithmic advantages, the WKS test could be more informative in many cases, than the classical GSEA test.

Nowadays, there are reliable scientific data highlighting that the probability density function of the gene expression demonstrates a number of universal features commonly observed in the microarray experiments. First of all, these distributions demonstrate the power-law asymptotics and, secondly, the shape of these distributions is inherent for all organisms and tissues. This fact leads to appearance of a number of works where authors investigate various probability distributions for an approximation of the empirical distributions of the gene expression. Nevertheless, all these distributions are not a limit distribution and are not a solution of any equation. These facts, in our opinion, are essential shortcoming of these probability laws. Besides, the expression of the individual gene is not an accidental phenomenon and it depends on the expression of the other genes. This suggests an existence of the genic regulatory net in a cell. The present work describes the class of the fractional-stable distributions. This class of the distributions is a limit distribution of the sums of independent identically distributed random variables. Due to the power-law asymptotics, these distributions are applicable for the approximation of the experimental densities of the gene expression for microarray experiments. The parameters of the fractional stable distributions are statistically estimated by experimental data and the functions of the empirical and theoretical densities are compared. Here we describe algorithms for simulation of the fractional-stable variables and estimation of the parameters of the the fractional stable densities. The results of such a comparison allow to conclude that the empirical densities of the gene expression can be approximated by the fractional-stable distributions.

Here we introduce the causal structure identification (CSI) package, a Gaussian process based approach to inferring gene regulatory networks (GRNs) from multiple time series data. The standard CSI approach infers a single GRN via joint learning from multiple time series datasets; the hierarchical approach (HCSI) infers a separate GRN for each dataset, albeit with the networks constrained to favor similar structures, allowing for the identification of context specific networks. The software is implemented in MATLAB and includes a graphical user interface (GUI) for user friendly inference. Finally the GUI can be connected to high performance computer clusters to facilitate analysis of large genomic datasets.

High-throughput sequencing techniques are increasingly affordable and produce massive amounts of data. Together with other high-throughput technologies, such as microarrays, there are an enormous amount of resources in databases. The collection of these valuable data has been routine for more than a decade. Despite different technologies, many experiments share the same goal. For instance, the aims of RNA-seq studies often coincide with those of differential gene expression experiments based on microarrays. As such, it would be logical to utilize all available data. However, there is a lack of biostatistical tools for the integration of results obtained from different technologies. Although diverse technological platforms produce different raw data, one commonality for experiments with the same goal is that all the outcomes can be transformed into a platform-independent data format – rankings – for the same set of items. Here we present the R package TopKLists , which allows for statistical inference on the lengths of informative (top- k ) partial lists, for stochastic aggregation of full or partial lists, and for graphical exploration of the input and consolidated output. A graphical user interface has also been implemented for providing access to the underlying algorithms. To illustrate the applicability and usefulness of the package, we integrated microRNA data of non-small cell lung cancer across different measurement techniques and draw conclusions. The package can be obtained from CRAN under a LGPL-3 license.