A pedagogical walkthrough of computational modeling and simulation of Wnt signaling pathway using static causal models in MATLAB

The discrete coefficient of determination (CoD) measures the nonlinear interaction between discrete predictor and target variables and has had far-reaching applications in Genomic Signal Processing. Previous work has addressed the inference of the discrete CoD using classical parametric and nonparametric approaches. In this paper, we introduce a Bayesian framework for the inference of the discrete CoD. We derive analytically the optimal minimum mean-square error (MMSE) CoD estimator, as well as a CoD estimator based on the Optimal Bayesian Predictor (OBP). For the latter estimator, exact expressions for its bias, variance, and root-mean-square (RMS) are given. The accuracy of both Bayesian CoD estimators with non-informative and informative priors, under fixed or random parameters, is studied via analytical and numerical approaches. We also demonstrate the application of the proposed Bayesian approach in the inference of gene regulatory networks, using gene-expression data from a previously published study on metastatic melanoma.     

Identifying set-wise differential co-expression in gene expression microarray data

Background  

Previous differential coexpression analyses focused on identification of differentially coexpressed gene pairs, revealing many insightful biological hypotheses. However, this method could not detect coexpression relationships between pairs of gene sets. Considering the success of many set-wise analysis methods for microarray data, a coexpression analysis based on gene sets may elucidate underlying biological processes provoked by the conditional changes. Here, we propose a differentially coexpressed gene sets (dCoxS) algorithm that identifies the differentially coexpressed gene set pairs between conditions.     

Binary state pattern clustering: a digital paradigm for class and biomarker discovery in gene microarray studies of cancer.

Class and biomarker discovery continue to be among the preeminent goals in gene microarray studies of cancer. We have developed a new data mining technique, which we call Binary State Pattern Clustering (BSPC) that is specifically adapted for these purposes, with cancer and other categorical datasets. BSPC is capable of uncovering statistically significant sample subclasses and associated marker genes in a completely unsupervised manner. This is accomplished through the application of a digital paradigm, where the expression level of each potential marker gene is treated as being representative of its discrete functional state. Multiple genes that divide samples into states along the same boundaries form a kind of gene-cluster that has an associated sample-cluster. BSPC is an extremely fast deterministic algorithm that scales well to large datasets. Here we describe results of its application to three publicly available oligonucleotide microarray datasets. Using an alpha-level of 0.05, clusters reproducing many of the known sample classifications were identified along with associated biomarkers. In addition, a number of simulations were conducted using shuffled versions of each of the original datasets, noise-added datasets, as well as completely artificial datasets. The robustness of BSPC was compared to that of three other publicly available clustering methods: ISIS, CTWC and SAMBA. The simulations demonstrate BSPC's substantially greater noise tolerance and confirm the accuracy of our calculations of statistical significance.     

Drug Repositioning through Systematic Mining of Gene Coexpression Networks in Cancer

Gene coexpression network analysis is a powerful “data-driven” approach essential for understanding cancer biology and mechanisms of tumor development. Yet, despite the completion of thousands of studies on cancer gene expression, there have been few attempts to normalize and integrate co-expression data from scattered sources in a concise “meta-analysis” framework. We generated such a resource by exploring gene coexpression networks in 82 microarray datasets from 9 major human cancer types. The analysis was conducted using an elaborate weighted gene coexpression network (WGCNA) methodology and identified over 3,000 robust gene coexpression modules. The modules covered a range of known tumor features, such as proliferation, extracellular matrix remodeling, hypoxia, inflammation, angiogenesis, tumor differentiation programs, specific signaling pathways, genomic alterations, and biomarkers of individual tumor subtypes. To prioritize genes with respect to those tumor features, we ranked genes within each module by connectivity, leading to identification of module-specific functionally prominent hub genes. To showcase the utility of this network information, we positioned known cancer drug targets within the coexpression networks and predicted that Anakinra, an anti-rheumatoid therapeutic agent, may be promising for development in colorectal cancer. We offer a comprehensive, normalized and well documented collection of >3000 gene coexpression modules in a variety of cancers as a rich data resource to facilitate further progress in cancer research.     

Geometric interpretation of gene coexpression network analysis

THE MERGING OF NETWORK THEORY AND MICROARRAY DATA ANALYSIS TECHNIQUES HAS SPAWNED A NEW FIELD: gene coexpression network analysis. While network methods are increasingly used in biology, the network vocabulary of computational biologists tends to be far more limited than that of, say, social network theorists. Here we review and propose several potentially useful network concepts. We take advantage of the relationship between network theory and the field of microarray data analysis to clarify the meaning of and the relationship among network concepts in gene coexpression networks. Network theory offers a wealth of intuitive concepts for describing the pairwise relationships among genes, which are depicted in cluster trees and heat maps. Conversely, microarray data analysis techniques (singular value decomposition, tests of differential expression) can also be used to address difficult problems in network theory. We describe conditions when a close relationship exists between network analysis and microarray data analysis techniques, and provide a rough dictionary for translating between the two fields. Using the angular interpretation of correlations, we provide a geometric interpretation of network theoretic concepts and derive unexpected relationships among them. We use the singular value decomposition of module expression data to characterize approximately factorizable gene coexpression networks, i.e., adjacency matrices that factor into node specific contributions. High and low level views of coexpression networks allow us to study the relationships among modules and among module genes, respectively. We characterize coexpression networks where hub genes are significant with respect to a microarray sample trait and show that the network concept of intramodular connectivity can be interpreted as a fuzzy measure of module membership. We illustrate our results using human, mouse, and yeast microarray gene expression data. The unification of coexpression network methods with traditional data mining methods can inform the application and development of systems biologic methods.     

MILVA: an interactive tool for the exploration of multidimensional microarray data

MOTIVATION: Clustering techniques such as k-means and hierarchical clustering are commonly used to analyze DNA microarray derived gene expression data. However, the interactions between processes underlying the cell activity suggest that the complexity of the microarray data structure may not be fully represented with discrete clustering methods. RESULTS: A newly developed software tool called MILVA (microarray latent visualization and analysis) is presented here to investigate microarray data without separating gene expression profiles into discrete classes. The underpinning of the MILVA software is the two-dimensional topographic representation of multidimensional microarray data. On this basis, the interactive MILVA functions allow a continuous exploration of microarray data driven by the direct supervision of the biologist in detecting activity patterns of co-regulated genes. AVAILABILITY: The MILVA software is freely available. The software and the related documentation can be downloaded from http://www.ncrg.aston.ac.uk/Projects/milva. User 'surrey' as username and '3245' as password to login. The software is currently available for Windows platform only.     

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.     

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.     

Graph-based consensus clustering for class discovery from gene expression data

MOTIVATION: Consensus clustering, also known as cluster ensemble, is one of the important techniques for microarray data analysis, and is particularly useful for class discovery from microarray data. Compared with traditional clustering algorithms, consensus clustering approaches have the ability to integrate multiple partitions from different cluster solutions to improve the robustness, stability, scalability and parallelization of the clustering algorithms. By consensus clustering, one can discover the underlying classes of the samples in gene expression data. RESULTS: In addition to exploring a graph-based consensus clustering (GCC) algorithm to estimate the underlying classes of the samples in microarray data, we also design a new validation index to determine the number of classes in microarray data. To our knowledge, this is the first time in which GCC is applied to class discovery for microarray data. Given a pre specified maximum number of classes (denoted as K(max) in this article), our algorithm can discover the true number of classes for the samples in microarray data according to a new cluster validation index called the Modified Rand Index. Experiments on gene expression data indicate that our new algorithm can (i) outperform most of the existing algorithms, (ii) identify the number of classes correctly in real cancer datasets, and (iii) discover the classes of samples with biological meaning. AVAILABILITY: Matlab source code for the GCC algorithm is available upon request from Zhiwen Yu.     

Avoiding Spurious Submovement Decompositions II: A Scattershot Algorithm

Evidence for the existence of discrete submovements underlying continuous human movement has motivated many attempts to “extract” them. Although they produce visually convincing results, all of the methodologies that have been employed are prone to produce spurious decompositions. In previous work, a branch-and-bound algorithm for submovement extraction, capable of global nonlinear minimization, and hence, capable of avoiding spurious decompositions, was presented [Rohrer and Hogan (Biol Cybern 39:190–199, 2003)]. Here, we present a scattershot-type global nonlinear minimization algorithm that requires approximately four orders of magnitude less time to compute. A sensitivity analysis reveals that the scattershot algorithm can reliably detect changes in submovement parameters over time, e.g., over the course of neuromotor recovery.     

Fuzzy J-Means and VNS methods for clustering genes from microarray data

MOTIVATION: In the interpretation of gene expression data from a group of microarray experiments that include samples from either different patients or conditions, special consideration must be given to the pleiotropic and epistatic roles of genes, as observed in the variation of gene coexpression patterns. Crisp clustering methods assign each gene to one cluster, thereby omitting information about the multiple roles of genes. RESULTS: Here, we present the application of a local search heuristic, Fuzzy J-Means, embedded into the variable neighborhood search metaheuristic for the clustering of microarray gene expression data. We show that for all the datasets studied this algorithm outperforms the standard Fuzzy C-Means heuristic. Different methods for the utilization of cluster membership information in determining gene coregulation are presented. The clustering and data analyses were performed on simulated datasets as well as experimental cDNA microarray data for breast cancer and human blood from the Stanford Microarray Database. AVAILABILITY: The source code of the clustering software (C programming language) is freely available from Nabil.Belacel@nrc-cnrc.gc.ca     

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.     

Dynamic Bayesian network and nonparametric regression for nonlinear modeling of gene networks from time series gene expression data

We propose a dynamic Bayesian network and nonparametric regression model for constructing a gene network from time series microarray gene expression data. The proposed method can overcome a shortcoming of the Bayesian network model in the sense of the construction of cyclic regulations. The proposed method can analyze the microarray data as a continuous data and can capture even nonlinear relations among genes. It can be expected that this model will give a deeper insight into complicated biological systems. We also derive a new criterion for evaluating an estimated network from Bayes approach. We conduct Monte Carlo experiments to examine the effectiveness of the proposed method. We also demonstrate the proposed method through the analysis of the Saccharomyces cerevisiae gene expression data.     

Variable selection and pattern recognition with gene expression data generated by the microarray technology

Lack of adequate statistical methods for the analysis of microarray data remains the most critical deterrent to uncovering the true potential of these promising techniques in basic and translational biological studies. The popular practice of drawing important biological conclusions from just one replicate (slide) should be discouraged. In this paper, we discuss some modern trends in statistical analysis of microarray data with a special focus on statistical classification (pattern recognition) and variable selection. In addressing these issues we consider the utility of some distances between random vectors and their nonparametric estimates obtained from gene expression data. Performance of the proposed distances is tested by computer simulations and analysis of gene expression data on two different types of human leukemia. In experimental settings, the error rate is estimated by cross-validation, while a control sample is generated in computer simulation experiments aimed at testing the proposed gene selection procedures and associated classification rules.