Rank of Correlation Coefficient as a Comparable Measure for Biological Significance of Gene Coexpression

Information regarding gene coexpression is useful to predict gene function. Several databases have been constructed for gene coexpression in model organisms based on a large amount of publicly available gene expression data measured by GeneChip platforms. In these databases, Pearson''s correlation coefficients (PCCs) of gene expression patterns are widely used as a measure of gene coexpression. Although the coexpression measure or GeneChip summarization method affects the performance of the gene coexpression database, previous studies for these calculation procedures were tested with only a small number of samples and a particular species. To evaluate the effectiveness of coexpression measures, assessments with large-scale microarray data are required. We first examined characteristics of PCC and found that the optimal PCC threshold to retrieve functionally related genes was affected by the method of gene expression database construction and the target gene function. In addition, we found that this problem could be overcome when we used correlation ranks instead of correlation values. This observation was evaluated by large-scale gene expression data for four species: Arabidopsis, human, mouse and rat.     

Analysis of Gene Coexpression by B-Spline Based CoD Estimation

The gene coexpression study has emerged as a novel holistic approach for microarray data analysis. Different indices have been used in exploring coexpression relationship, but each is associated with certain pitfalls. The Pearson's correlation coefficient, for example, is not capable of uncovering nonlinear pattern and directionality of coexpression. Mutual information can detect nonlinearity but fails to show directionality. The coefficient of determination (CoD) is unique in exploring different patterns of gene coexpression, but so far only applied to discrete data and the conversion of continuous microarray data to the discrete format could lead to information loss. Here, we proposed an effective algorithm, CoexPro, for gene coexpression analysis. The new algorithm is based on B-spline approximation of coexpression between a pair of genes, followed by CoD estimation. The algorithm was justified by simulation studies and by functional semantic similarity analysis. The proposed algorithm is capable of uncovering both linear and a specific class of nonlinear relationships from continuous microarray data. It can also provide suggestions for possible directionality of coexpression to the researchers. The new algorithm presents a novel model for gene coexpression and will be a valuable tool for a variety of gene expression and network studies. The application of the algorithm was demonstrated by an analysis on ligand-receptor coexpression in cancerous and noncancerous cells. The software implementing the algorithm is available upon request to the authors.     

A biologically inspired measure for coexpression analysis

Two genes are said to be coexpressed if their expression levels have a similar spatial or temporal pattern. Ever since the profiling of gene microarrays has been in progress, computational modeling of coexpression has acquired a major focus. As a result, several similarity/distance measures have evolved over time to quantify coexpression similarity/dissimilarity between gene pairs. Of these, correlation coefficient has been established to be a suitable quantifier of pairwise coexpression. In general, correlation coefficient is good for symbolizing linear dependence, but not for nonlinear dependence. In spite of this drawback, it outperforms many other existing measures in modeling the dependency in biological data. In this paper, for the first time, we point out a significant weakness of the existing similarity/distance measures, including the standard correlation coefficient, in modeling pairwise coexpression of genes. A novel measure, called BioSim, which assumes values between -1 and +1 corresponding to negative and positive dependency and 0 for independency, is introduced. The computation of BioSim is based on the aggregation of stepwise relative angular deviation of the expression vectors considered. The proposed measure is analytically suitable for modeling coexpression as it accounts for the features of expression similarity, expression deviation and also the relative dependence. It is demonstrated how the proposed measure is better able to capture the degree of coexpression between a pair of genes as compared to several other existing ones. The efficacy of the measure is statistically analyzed by integrating it with several module-finding algorithms based on coexpression values and then applying it on synthetic and biological data. The annotation results of the coexpressed genes as obtained from gene ontology establish the significance of the introduced measure. By further extending the BioSim measure, it has been shown that one can effectively identify the variability in the expression patterns over multiple phenotypes. We have also extended BioSim to figure out pairwise differential expression pattern and coexpression dynamics. The significance of these studies is shown based on the analysis over several real-life data sets. The computation of the measure by focusing on stepwise time points also makes it effective to identify partially coexpressed genes. On the whole, we put forward a complete framework for coexpression analysis based on the BioSim measure.     

MetaGSCA: A tool for meta-analysis of gene set differential coexpression

Analyses of gene set differential coexpression may shed light on molecular mechanisms underlying phenotypes and diseases. However, differential coexpression analyses of conceptually similar individual studies are often inconsistent and underpowered to provide definitive results. Researchers can greatly benefit from an open-source application facilitating the aggregation of evidence of differential coexpression across studies and the estimation of more robust common effects. We developed Meta Gene Set Coexpression Analysis (MetaGSCA), an analytical tool to systematically assess differential coexpression of an a priori defined gene set by aggregating evidence across studies to provide a definitive result. In the kernel, a nonparametric approach that accounts for the gene-gene correlation structure is used to test whether the gene set is differentially coexpressed between two comparative conditions, from which a permutation test p-statistic is computed for each individual study. A meta-analysis is then performed to combine individual study results with one of two options: a random-intercept logistic regression model or the inverse variance method. We demonstrated MetaGSCA in case studies investigating two human diseases and identified pathways highly relevant to each disease across studies. We further applied MetaGSCA in a pan-cancer analysis with hundreds of major cellular pathways in 11 cancer types. The results indicated that a majority of the pathways identified were dysregulated in the pan-cancer scenario, many of which have been previously reported in the cancer literature. Our analysis with randomly generated gene sets showed excellent specificity, indicating that the significant pathways/gene sets identified by MetaGSCA are unlikely false positives. MetaGSCA is a user-friendly tool implemented in both forms of a Web-based application and an R package “MetaGSCA”. It enables comprehensive meta-analyses of gene set differential coexpression data, with an optional module of post hoc pathway crosstalk network analysis to identify and visualize pathways having similar coexpression profiles.     

Adaptive thresholds to detect differentially expressed genes in microarray data

To detect changes in gene expression data from microarrays, a fixed threshold for fold difference is used widely. However, it is not always guaranteed that a threshold value which is appropriate for highly expressed genes is suitable for lowly expressed genes. In this study, aiming at detecting truly differentially expressed genes from a wide expression range, we proposed an adaptive threshold method (AT). The adaptive thresholds, which have different values for different expression levels, are calculated based on two measurements under the same condition. The sensitivity, specificity and false discovery rate (FDR) of AT were investigated by simulations. The sensitivity and specificity under various noise conditions were greater than 89.7% and 99.32%, respectively. The FDR was smaller than 0.27. These results demonstrated the reliability of the method.     

Missing value estimation for DNA microarray gene expression data: local least squares imputation

MOTIVATION: Gene expression data often contain missing expression values. Effective missing value estimation methods are needed since many algorithms for gene expression data analysis require a complete matrix of gene array values. In this paper, imputation methods based on the least squares formulation are proposed to estimate missing values in the gene expression data, which exploit local similarity structures in the data as well as least squares optimization process. RESULTS: The proposed local least squares imputation method (LLSimpute) represents a target gene that has missing values as a linear combination of similar genes. The similar genes are chosen by k-nearest neighbors or k coherent genes that have large absolute values of Pearson correlation coefficients. Non-parametric missing values estimation method of LLSimpute are designed by introducing an automatic k-value estimator. In our experiments, the proposed LLSimpute method shows competitive results when compared with other imputation methods for missing value estimation on various datasets and percentages of missing values in the data. AVAILABILITY: The software is available at http://www.cs.umn.edu/~hskim/tools.html CONTACT: hpark@cs.umn.edu     

Assessment and integration of publicly available SAGE, cDNA microarray, and oligonucleotide microarray expression data for global coexpression analyses

Large amounts of gene expression data from several different technologies are becoming available to the scientific community. A common practice is to use these data to calculate global gene coexpression for validation or integration of other "omic" data. To assess the utility of publicly available datasets for this purpose we have analyzed Homo sapiens data from 1202 cDNA microarray experiments, 242 SAGE libraries, and 667 Affymetrix oligonucleotide microarray experiments. The three datasets compared demonstrate significant but low levels of global concordance (rc<0.11). Assessment against Gene Ontology (GO) revealed that all three platforms identify more coexpressed gene pairs with common biological processes than expected by chance. As the Pearson correlation for a gene pair increased it was more likely to be confirmed by GO. The Affymetrix dataset performed best individually with gene pairs of correlation 0.9-1.0 confirmed by GO in 74% of cases. However, in all cases, gene pairs confirmed by multiple platforms were more likely to be confirmed by GO. We show that combining results from different expression platforms increases reliability of coexpression. A comparison with other recently published coexpression studies found similar results in terms of performance against GO but with each method producing distinctly different gene pair lists.     

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.     

Quality criteria for finding genes with high mRNA-protein expression correlation and coexpression correlation

mRNA expression is widely used as a proxy for protein expression. However, their true relation is not known and two genes with the same mRNA levels might have different abundances of respective proteins. A related question is whether the coexpression of mRNA for gene pairs is reflected by the corresponding protein pairs. We examined the mRNA-protein correlation for both expression and coexpression. This analysis yielded insights into the relationship between mRNA and protein abundance, and allowed us to identify subsets of greater mRNA-protein coherence. The correlation between mRNA and protein was low for both expression and coexpression, 0.12 and 0.06 respectively. However, applying the best-performing quality measure, high-quality subsets reached a Spearman correlation of 0.31 for expression, 0.34 for coexpression and 0.49 for coexpression when restricted to functionally coupled genes. Our methodology can thus identify subsets for which the mRNA levels are expected to be the strongest correlated with protein levels.     

Ranking analysis of correlation coefficients in gene expressions

Development of statistical methods has become very necessary for large-scale correlation analysis in the current "omic" data. We propose ranking analysis of correlation coefficients (RAC) based on transforming correlation matrix into correlation vector and conducting a "locally ranking" strategy that significantly reduces computational complexity and load. RAC gives estimation of null correlation distribution and an estimator of false discovery rate (FDR) for finding gene pairs of being correlated in expressions obtained by comparison between the ranked observed correlation coefficients and the ranked estimated ones at a given threshold level. The simulated and real data show that the estimated null correlation distribution is exactly the same with the true one and the FDR estimator works well in various scenarios. By applying our RAC, in the null dataset, no gene pairs were found but, in the human cancer dataset, 837 gene pairs were found to have positively correlated expression variations at FDR≤5%. RAC performs well in multiple conditions (classes), each with 3 or more replicate observations.     

Time ordering of gene coexpression

Temporal microarray gene expression profiles allow characterization of gene function through time dynamics of gene coexpression within the same genetic pathway. In this paper, we define and estimate a global time shift characteristic for each gene via least squares, inferred from pairwise curve alignments. These time shift characteristics of individual genes reflect a time ordering that is derived from ob- served temporal gene expression profiles. Once these time shift characteristics are obtained for each gene, they can be entered into further analyses, such as clustering. We illustrate the proposed methodology using Drosophila embryonic development and yeast cell-cycle gene expression profiles, as well as simulations. Feasibility is demonstrated through the successful recovery of time ordering. Estimated time shifts for Drosophila maternal and zygotic genes provide excellent discrimination between these two categories and confirm known genetic pathways through the time order of gene expression. The application to yeast cell-cycle data establishes a natural time order of genes that is in line with cell-cycle phases. The method does not require periodicity of gene expression profiles. Asymptotic justifications are also provided.     

Some comments on instability of false discovery rate estimation

Some extended false discovery rate (FDR) controlling multiple testing procedures rely heavily on empirical estimates of the FDR constructed from gene expression data. Such estimates are also used as performance indicators when comparing different methods for microarray data analysis. The present communication shows that the variance of the proposed estimators may be intolerably high, the correlation structure of microarray data being the main cause of their instability.     

Local coexpression domains of two to four genes in the genome of Arabidopsis

Expression of genes in eukaryotic genomes is known to cluster, but cluster size is generally loosely defined and highly variable. We have here taken a very strict definition of cluster as sets of physically adjacent genes that are highly coexpressed and form so-called local coexpression domains. The Arabidopsis (Arabidopsis thaliana) genome was analyzed for the presence of such local coexpression domains to elucidate its functional characteristics. We used expression data sets that cover different experimental conditions, organs, tissues, and cells from the Massively Parallel Signature Sequencing repository and microarray data (Affymetrix) from a detailed root analysis. With these expression data, we identified 689 and 1,481 local coexpression domains, respectively, consisting of two to four genes with a pairwise Pearson's correlation coefficient larger than 0.7. This number is approximately 1- to 5-fold higher than the numbers expected by chance. A small (5%-10%) yet significant fraction of genes in the Arabidopsis genome is therefore organized into local coexpression domains. These local coexpression domains were distributed over the genome. Genes in such local domains were for the major part not categorized in the same functional category (GOslim). Neither tandemly duplicated genes nor shared promoter sequence nor gene distance explained the occurrence of coexpression of genes in such chromosomal domains. This indicates that other parameters in genes or gene positions are important to establish coexpression in local domains of Arabidopsis chromosomes.