An empirical Bayes approach to inferring large-scale gene association networks

MOTIVATION: Genetic networks are often described statistically using graphical models (e.g. Bayesian networks). However, inferring the network structure offers a serious challenge in microarray analysis where the sample size is small compared to the number of considered genes. This renders many standard algorithms for graphical models inapplicable, and inferring genetic networks an 'ill-posed' inverse problem. METHODS: We introduce a novel framework for small-sample inference of graphical models from gene expression data. Specifically, we focus on the so-called graphical Gaussian models (GGMs) that are now frequently used to describe gene association networks and to detect conditionally dependent genes. Our new approach is based on (1) improved (regularized) small-sample point estimates of partial correlation, (2) an exact test of edge inclusion with adaptive estimation of the degree of freedom and (3) a heuristic network search based on false discovery rate multiple testing. Steps (2) and (3) correspond to an empirical Bayes estimate of the network topology. RESULTS: Using computer simulations, we investigate the sensitivity (power) and specificity (true negative rate) of the proposed framework to estimate GGMs from microarray data. This shows that it is possible to recover the true network topology with high accuracy even for small-sample datasets. Subsequently, we analyze gene expression data from a breast cancer tumor study and illustrate our approach by inferring a corresponding large-scale gene association network for 3883 genes.     

Boolean networks using the chi-square test for inferring large-scale gene regulatory networks

Background  

Boolean network (BN) modeling is a commonly used method for constructing gene regulatory networks from time series microarray data. However, its major drawback is that its computation time is very high or often impractical to construct large-scale gene networks. We propose a variable selection method that are not only reduces BN computation times significantly but also obtains optimal network constructions by using chi-square statistics for testing the independence in contingency tables.     

Recursive regularization for inferring gene networks from time-course gene expression profiles

Background  

Inferring gene networks from time-course microarray experiments with vector autoregressive (VAR) model is the process of identifying functional associations between genes through multivariate time series. This problem can be cast as a variable selection problem in Statistics. One of the promising methods for variable selection is the elastic net proposed by Zou and Hastie (2005). However, VAR modeling with the elastic net succeeds in increasing the number of true positives while it also results in increasing the number of false positives.     

Regularized estimation of large-scale gene association networks using graphical Gaussian models

Background  

Graphical Gaussian models are popular tools for the estimation of (undirected) gene association networks from microarray data. A key issue when the number of variables greatly exceeds the number of samples is the estimation of the matrix of partial correlations. Since the (Moore-Penrose) inverse of the sample covariance matrix leads to poor estimates in this scenario, standard methods are inappropriate and adequate regularization techniques are needed. Popular approaches include biased estimates of the covariance matrix and high-dimensional regression schemes, such as the Lasso and Partial Least Squares.     

Stochastic models for inferring genetic regulation from microarray gene expression data

Microarray expression profiles are inherently noisy and many different sources of variation exist in microarray experiments. It is still a significant challenge to develop stochastic models to realize noise in microarray expression profiles, which has profound influence on the reverse engineering of genetic regulation. Using the target genes of the tumour suppressor gene p53 as the test problem, we developed stochastic differential equation models and established the relationship between the noise strength of stochastic models and parameters of an error model for describing the distribution of the microarray measurements. Numerical results indicate that the simulated variance from stochastic models with a stochastic degradation process can be represented by a monomial in terms of the hybridization intensity and the order of the monomial depends on the type of stochastic process. The developed stochastic models with multiple stochastic processes generated simulations whose variance is consistent with the prediction of the error model. This work also established a general method to develop stochastic models from experimental information.     

An approach to inferring transcriptional regulation among genes from large-scale expression data

The use of DNA microarrays opens up the possibility of measuring the expression levels of thousands of genes simultaneously under different conditions. Time-course experiments allow researchers to study the dynamics of gene interactions. The inference of genetic networks from such measures can give important insights for the understanding of a variety of biological problems. Most of the existing methods for genetic network reconstruction require many experimental data points, or can only be applied to the reconstruction of small subnetworks. Here we present a method that reduces the dimensionality of the dataset and then extracts the significant dynamic correlations among genes. The method requires a number of points achievable in common time-course experiments.     

Method for inferring and extracting reliable genetic interactions from time-series profile of gene expression

Recent advances in technologies such as DNA microarrays have provided an abundance of gene expression data on the genomic scale. One of the most important projects in the post-genome-era is the systemic identification of gene expression networks. However, inferring internal gene expression structure from experimentally observed time-series data are an inverse problem. We have therefore developed a system for inferring network candidates based on experimental observations. Moreover, we have proposed an analytical method for extracting common core binomial genetic interactions from various network candidates. Common core binomial genetic interactions are reliable interactions with a higher possibility of existence, and are important for understanding the dynamic behavior of gene expression networks. Here, we discuss an efficient method for inferring genetic interactions that combines a Step-by-step strategy (Y. Maki, Y. Takahashi, Y. Arikawa, S. Watanabe, K. Aoshima, Y. Eguchi, T. Ueda, S. Aburatani, S. Kuhara, M. Okamoto, An integrated comprehensive workbench for inferring genetic networks: Voyagene, Journal of Bioinformatics and Computational Biology 2(3) (2004) 533.) with an analysis method for extracting common core binomial genetic interactions.     

A semi-parametric statistical model for integrating gene expression profiles across different platforms

Determining differentially expressed genes (DEGs) between biological samples is the key to understand how genotype gives rise to phenotype. RNA-seq and microarray are two main technologies for profiling gene expression levels. However, considerable discrepancy has been found between DEGs detected using the two technologies. Integration data across these two platforms has the potential to improve the power and reliability of DEG detection. We propose a rank-based semi-parametric model to determine DEGs using information across different sources and apply it to the integration of RNA-seq and microarray data. By incorporating both the significance of differential expression and the consistency across platforms, our method effectively detects DEGs with moderate but consistent signals. We demonstrate the effectiveness of our method using simulation studies, MAQC/SEQC data and a synthetic microRNA dataset. Our integration method is not only robust to noise and heterogeneity in the data, but also adaptive to the structure of data. In our simulations and real data studies, our approach shows a higher discriminate power and identifies more biologically relevant DEGs than eBayes, DEseq and some commonly used meta-analysis methods.     

A continuous optimization approach for inferring parameters in mathematical models of regulatory networks

Background

The advances of systems biology have raised a large number of sophisticated mathematical models for describing the dynamic property of complex biological systems. One of the major steps in developing mathematical models is to estimate unknown parameters of the model based on experimentally measured quantities. However, experimental conditions limit the amount of data that is available for mathematical modelling. The number of unknown parameters in mathematical models may be larger than the number of observation data. The imbalance between the number of experimental data and number of unknown parameters makes reverse-engineering problems particularly challenging.

Results

To address the issue of inadequate experimental data, we propose a continuous optimization approach for making reliable inference of model parameters. This approach first uses a spline interpolation to generate continuous functions of system dynamics as well as the first and second order derivatives of continuous functions. The expanded dataset is the basis to infer unknown model parameters using various continuous optimization criteria, including the error of simulation only, error of both simulation and the first derivative, or error of simulation as well as the first and second derivatives. We use three case studies to demonstrate the accuracy and reliability of the proposed new approach. Compared with the corresponding discrete criteria using experimental data at the measurement time points only, numerical results of the ERK kinase activation module show that the continuous absolute-error criteria using both function and high order derivatives generate estimates with better accuracy. This result is also supported by the second and third case studies for the G1/S transition network and the MAP kinase pathway, respectively. This suggests that the continuous absolute-error criteria lead to more accurate estimates than the corresponding discrete criteria. We also study the robustness property of these three models to examine the reliability of estimates. Simulation results show that the models with estimated parameters using continuous fitness functions have better robustness properties than those using the corresponding discrete fitness functions.

Conclusions

The inference studies and robustness analysis suggest that the proposed continuous optimization criteria are effective and robust for estimating unknown parameters in mathematical models.

Electronic supplementary material

The online version of this article (doi:10.1186/1471-2105-15-256) contains supplementary material, which is available to authorized users.     

A Bayesian model comparison approach to inferring positive selection

A popular approach to detecting positive selection is to estimate the parameters of a probabilistic model of codon evolution and perform inference based on its maximum likelihood parameter values. This approach has been evaluated intensively in a number of simulation studies and found to be robust when the available data set is large. However, uncertainties in the estimated parameter values can lead to errors in the inference, especially when the data set is small or there is insufficient divergence between the sequences. We introduce a Bayesian model comparison approach to infer whether the sequence as a whole contains sites at which the rate of nonsynonymous substitution is greater than the rate of synonymous substitution. We incorporated this probabilistic model comparison into a Bayesian approach to site-specific inference of positive selection. Using simulated sequences, we compared this approach to the commonly used empirical Bayes approach and investigated the effect of tree length on the performance of both methods. We found that the Bayesian approach outperforms the empirical Bayes method when the amount of sequence divergence is small and is less prone to false-positive inference when the sequences are saturated, while the results are indistinguishable for intermediate levels of sequence divergence.     

CyNetworkBMA: a Cytoscape app for inferring gene regulatory networks

Background

Inference of gene networks from expression data is an important problem in computational biology. Many algorithms have been proposed for solving the problem efficiently. However, many of the available implementations are programming libraries that require users to write code, which limits their accessibility.

Results

We have developed a tool called CyNetworkBMA for inferring gene networks from expression data that integrates with Cytoscape. Our application offers a graphical user interface for networkBMA, an efficient implementation of Bayesian Model Averaging methods for network construction. The client-server architecture of CyNetworkBMA makes it possible to distribute or centralize computation depending on user needs.

Conclusions

CyNetworkBMA is an easy-to-use tool that makes network inference accessible to non-programmers through seamless integration with Cytoscape. CyNetworkBMA is available on the Cytoscape App Store at http://apps.cytoscape.org/apps/cynetworkbma.

     

HiNO: an approach for inferring hierarchical organization from regulatory networks

Background

Gene expression as governed by the interplay of the components of regulatory networks is indeed one of the most complex fundamental processes in biological systems. Although several methods have been published to unravel the hierarchical structure of regulatory networks, weaknesses such as the incorrect or inconsistent assignment of elements to their hierarchical levels, the incapability to cope with cyclic dependencies within the networks or the need for a manual curation to retrieve non-overlapping levels remain unsolved.

Methodology/Results

We developed HiNO as a significant improvement of the so-called breadth-first-search (BFS) method. While BFS is capable of determining the overall hierarchical structures from gene regulatory networks, it especially has problems solving feed-forward type of loops leading to conflicts within the level assignments. We resolved these problems by adding a recursive correction approach consisting of two steps. First each vertex is placed on the lowest level that this vertex and its regulating vertices are assigned to (downgrade procedure). Second, vertices are assigned to the next higher level (upgrade procedure) if they have successors with the same level assignment and have themselves no regulators. We evaluated HiNO by comparing it with the BFS method by applying them to the regulatory networks from Saccharomyces cerevisiae and Escherichia coli, respectively. The comparison shows clearly how conflicts in level assignment are resolved in HiNO in order to produce correct hierarchical structures even on the local levels in an automated fashion.

Conclusions

We showed that the resolution of conflicting assignments clearly improves the BFS-method. While we restricted our analysis to gene regulatory networks, our approach is suitable to deal with any directed hierarchical networks structure such as the interaction of microRNAs or the action of non-coding RNAs in general. Furthermore we provide a user-friendly web-interface for HiNO that enables the extraction of the hierarchical structure of any directed regulatory network.

Availability

HiNO is freely accessible at http://mips.helmholtz-muenchen.de/hino/.     

A multivariate approach for integrating genome-wide expression data and biological knowledge

MOTIVATION: Several statistical methods that combine analysis of differential gene expression with biological knowledge databases have been proposed for a more rapid interpretation of expression data. However, most such methods are based on a series of univariate statistical tests and do not properly account for the complex structure of gene interactions. RESULTS: We present a simple yet effective multivariate statistical procedure for assessing the correlation between a subspace defined by a group of genes and a binary phenotype. A subspace is deemed significant if the samples corresponding to different phenotypes are well separated in that subspace. The separation is measured using Hotelling's T(2) statistic, which captures the covariance structure of the subspace. When the dimension of the subspace is larger than that of the sample space, we project the original data to a smaller orthonormal subspace. We use this method to search through functional pathway subspaces defined by Reactome, KEGG, BioCarta and Gene Ontology. To demonstrate its performance, we apply this method to the data from two published studies, and visualize the results in the principal component space.     

A service-oriented architecture for integrating the modeling and formal verification of genetic regulatory networks

Background  

The study of biological networks has led to the development of increasingly large and detailed models. Computer tools are essential for the simulation of the dynamical behavior of the networks from the model. However, as the size of the models grows, it becomes infeasible to manually verify the predictions against experimental data or identify interesting features in a large number of simulation traces. Formal verification based on temporal logic and model checking provides promising methods to automate and scale the analysis of the models. However, a framework that tightly integrates modeling and simulation tools with model checkers is currently missing, on both the conceptual and the implementational level.     

Deducing corticotropin-releasing hormone receptor type 1 signaling networks from gene expression data by usage of genetic algorithms and graphical Gaussian models

Background  

Dysregulation of the hypothalamic-pituitary-adrenal (HPA) axis is a hallmark of complex and multifactorial psychiatric diseases such as anxiety and mood disorders. About 50-60% of patients with major depression show HPA axis dysfunction, i.e. hyperactivity and impaired negative feedback regulation. The neuropeptide corticotropin-releasing hormone (CRH) and its receptor type 1 (CRHR1) are key regulators of this neuroendocrine stress axis. Therefore, we analyzed CRH/CRHR1-dependent gene expression data obtained from the pituitary corticotrope cell line AtT-20, a well-established in vitro model for CRHR1-mediated signal transduction. To extract significantly regulated genes from a genome-wide microarray data set and to deduce underlying CRHR1-dependent signaling networks, we combined supervised and unsupervised algorithms.     

Application of Bayesian networks for inferring cause-effect relations from gene expression profiles of cancer versus normal cells

The paper is devoted to two questions: whether distinction of causes versus effects of neoplasia leaves a signature in the cancer versus normal gene expression profiles and whether roles of genes, "causes" or "effects", can be inferred from repeated measurements of gene expressions. We model joint probability distributions of logarithms of gene expressions with the use of Bayesian networks (BN). Fitting our models to real data confirms that our BN models have the ability to explain some aspects of observational evidence from DNA microarray experiments. Effects of neoplastic transformation are well seen among genes with the highest power to differentiate between normal and cancer cells. Likelihoods of BNs depend on the biological role of selected genes, defined by Gene Ontology. Also predictions of our BN models are coherent with the set of putative causes and effects constructed based on our data set of papillary thyroid cancer.     

A publish-subscribe model of genetic networks

We present a simple model of genetic regulatory networks in which regulatory connections among genes are mediated by a limited number of signaling molecules. Each gene in our model produces (publishes) a single gene product, which regulates the expression of other genes by binding to regulatory regions that correspond (subscribe) to that product. We explore the consequences of this publish-subscribe model of regulation for the properties of single networks and for the evolution of populations of networks. Degree distributions of randomly constructed networks, particularly multimodal in-degree distributions, which depend on the length of the regulatory sequences and the number of possible gene products, differed from simpler Boolean NK models. In simulated evolution of populations of networks, single mutations in regulatory or coding regions resulted in multiple changes in regulatory connections among genes, or alternatively in neutral change that had no effect on phenotype. This resulted in remarkable evolvability in both number and length of attractors, leading to evolved networks far beyond the expectation of these measures based on random distributions. Surprisingly, this rapid evolution was not accompanied by changes in degree distribution; degree distribution in the evolved networks was not substantially different from that of randomly generated networks. The publish-subscribe model also allows exogenous gene products to create an environment, which may be noisy or stable, in which dynamic behavior occurs. In simulations, networks were able to evolve moderate levels of both mutational and environmental robustness.