Comparative evaluation of reverse engineering gene regulatory networks with relevance networks, graphical gaussian models and bayesian networks

MOTIVATION: An important problem in systems biology is the inference of biochemical pathways and regulatory networks from postgenomic data. Various reverse engineering methods have been proposed in the literature, and it is important to understand their relative merits and shortcomings. In the present paper, we compare the accuracy of reconstructing gene regulatory networks with three different modelling and inference paradigms: (1) Relevance networks (RNs): pairwise association scores independent of the remaining network; (2) graphical Gaussian models (GGMs): undirected graphical models with constraint-based inference, and (3) Bayesian networks (BNs): directed graphical models with score-based inference. The evaluation is carried out on the Raf pathway, a cellular signalling network describing the interaction of 11 phosphorylated proteins and phospholipids in human immune system cells. We use both laboratory data from cytometry experiments as well as data simulated from the gold-standard network. We also compare passive observations with active interventions. RESULTS: On Gaussian observational data, BNs and GGMs were found to outperform RNs. The difference in performance was not significant for the non-linear simulated data and the cytoflow data, though. Also, we did not observe a significant difference between BNs and GGMs on observational data in general. However, for interventional data, BNs outperform GGMs and RNs, especially when taking the edge directions rather than just the skeletons of the graphs into account. This suggests that the higher computational costs of inference with BNs over GGMs and RNs are not justified when using only passive observations, but that active interventions in the form of gene knockouts and over-expressions are required to exploit the full potential of BNs. AVAILABILITY: Data, software and supplementary material are available from http://www.bioss.sari.ac.uk/staff/adriano/research.html     

Gradient directed regularization for sparse Gaussian concentration graphs, with applications to inference of genetic networks

Large-scale microarray gene expression data provide the possibility of constructing genetic networks or biological pathways. Gaussian graphical models have been suggested to provide an effective method for constructing such genetic networks. However, most of the available methods for constructing Gaussian graphs do not account for the sparsity of the networks and are computationally more demanding or infeasible, especially in the settings of high dimension and low sample size. We introduce a threshold gradient descent (TGD) regularization procedure for estimating the sparse precision matrix in the setting of Gaussian graphical models and demonstrate its application to identifying genetic networks. Such a procedure is computationally feasible and can easily incorporate prior biological knowledge about the network structure. Simulation results indicate that the proposed method yields a better estimate of the precision matrix than the procedures that fail to account for the sparsity of the graphs. We also present the results on inference of a gene network for isoprenoid biosynthesis in Arabidopsis thaliana. These results demonstrate that the proposed procedure can indeed identify biologically meaningful genetic networks based on microarray gene expression data.     

Inferring gene networks from time series microarray data using dynamic Bayesian networks

Dynamic Bayesian networks (DBNs) are considered as a promising model for inferring gene networks from time series microarray data. DBNs have overtaken Bayesian networks (BNs) as DBNs can construct cyclic regulations using time delay information. In this paper, a general framework for DBN modelling is outlined. Both discrete and continuous DBN models are constructed systematically and criteria for learning network structures are introduced from a Bayesian statistical viewpoint. This paper reviews the applications of DBNs over the past years. Real data applications for Saccharomyces cerevisiae time series gene expression data are also shown.     

Network-Based Inference of Cancer Progression from Microarray Data

Cancer cells exhibit a common phenotype of uncontrolled cell growth, but this phenotype may arise from many different combinations of mutations. By inferring how cells evolve in individual tumors, a process called cancer progression, we may be able to identify important mutational events for different tumor types, potentially leading to new therapeutics and diagnostics. Prior work has shown that it is possible to infer frequent progression pathways by using gene expression profiles to estimate ldquodistancesrdquo between tumors. Here, we apply gene network models to improve these estimates of evolutionary distance by controlling for correlations among coregulated genes. We test three variants of this approach: one using an optimized best-fit network, another using sampling to infer a high-confidence subnetwork, and one using a modular network inferred from clusters of similarly expressed genes. Application to lung cancer and breast cancer microarray data sets shows small improvements in phylogenies when correcting from the optimized network and more substantial improvements when correcting from the sampled or modular networks. Our results suggest that a network correction approach improves estimates of tumor similarity, but sophisticated network models are needed to control for the large hypothesis space and sparse data currently available.     

Superiority of network motifs over optimal networks and an application to the revelation of gene network evolution

MOTIVATION: Estimating the network of regulative interactions between genes from gene expression measurements is a major challenge. Recently, we have shown that for gene networks of up to around 35 genes, optimal network models can be computed. However, even optimal gene network models will in general contain false edges, since the expression data will not unambiguously point to a single network. RESULTS: In order to overcome this problem, we present a computational method to enumerate the most likely m networks and to extract a widely common subgraph (denoted as gene network motif) from these. We apply the method to bacterial gene expression data and extensively compare estimation results to knowledge. Our results reveal that gene network motifs are in significantly better agreement to biological knowledge than optimal network models. We also confirm this observation in a series of estimations using synthetic microarray data and compare estimations by our method with previous estimations for yeast. Furthermore, we use our method to estimate similarities and differences of the gene networks that regulate tryptophan metabolism in two related species and thereby demonstrate the analysis of gene network evolution. AVAILABILITY: Commercial license negotiable with Gene Networks Inc. (cherkis@gene-networks.com) CONTACT: sascha-ott@gmx.net     

Reconstruction of molecular network evolution from cross‐sectional omics data

Cross‐sectional studies may shed light on the evolution of a disease like cancer through the comparison of patient traits among disease stages. This problem is especially challenging when a gene–gene interaction network needs to be reconstructed from omics data, and, in addition, the patients of each stage need not form a homogeneous group. Here, the problem is operationalized as the estimation of stage‐wise mixtures of Gaussian graphical models (GGMs) from high‐dimensional data. These mixtures are fitted by a (fused) ridge penalized EM algorithm. The fused ridge penalty shrinks GGMs of contiguous stages. The (fused) ridge penalty parameters are chosen through cross‐validation. The proposed estimation procedures are shown to be consistent and their performance in other respects is studied in simulation. The down‐stream exploitation of the fitted GGMs is outlined. In a data illustration the methodology is employed to identify gene–gene interaction network changes in the transition from normal to cancer prostate tissue.     

A scale-free structure prior for graphical models with applications in functional genomics

The problem of reconstructing large-scale, gene regulatory networks from gene expression data has garnered considerable attention in bioinformatics over the past decade with the graphical modeling paradigm having emerged as a popular framework for inference. Analysis in a full Bayesian setting is contingent upon the assignment of a so-called structure prior-a probability distribution on networks, encoding a priori biological knowledge either in the form of supplemental data or high-level topological features. A key topological consideration is that a wide range of cellular networks are approximately scale-free, meaning that the fraction, , of nodes in a network with degree is roughly described by a power-law with exponent between and . The standard practice, however, is to utilize a random structure prior, which favors networks with binomially distributed degree distributions. In this paper, we introduce a scale-free structure prior for graphical models based on the formula for the probability of a network under a simple scale-free network model. Unlike the random structure prior, its scale-free counterpart requires a node labeling as a parameter. In order to use this prior for large-scale network inference, we design a novel Metropolis-Hastings sampler for graphical models that includes a node labeling as a state space variable. In a simulation study, we demonstrate that the scale-free structure prior outperforms the random structure prior at recovering scale-free networks while at the same time retains the ability to recover random networks. We then estimate a gene association network from gene expression data taken from a breast cancer tumor study, showing that scale-free structure prior recovers hubs, including the previously unknown hub SLC39A6, which is a zinc transporter that has been implicated with the spread of breast cancer to the lymph nodes. Our analysis of the breast cancer expression data underscores the value of the scale-free structure prior as an instrument to aid in the identification of candidate hub genes with the potential to direct the hypotheses of molecular biologists, and thus drive future experiments.     

A Markov-blanket-based model for gene regulatory network inference

An efficient two-step Markov blanket method for modeling and inferring complex regulatory networks from large-scale microarray data sets is presented. The inferred gene regulatory network (GRN) is based on the time series gene expression data capturing the underlying gene interactions. For constructing a highly accurate GRN, the proposed method performs: 1) discovery of a gene's Markov Blanket (MB), 2) formulation of a flexible measure to determine the network's quality, 3) efficient searching with the aid of a guided genetic algorithm, and 4) pruning to obtain a minimal set of correct interactions. Investigations are carried out using both synthetic as well as yeast cell cycle gene expression data sets. The realistic synthetic data sets validate the robustness of the method by varying topology, sample size, time delay, noise, vertex in-degree, and the presence of hidden nodes. It is shown that the proposed approach has excellent inferential capabilities and high accuracy even in the presence of noise. The gene network inferred from yeast cell cycle data is investigated for its biological relevance using well-known interactions, sequence analysis, motif patterns, and GO data. Further, novel interactions are predicted for the unknown genes of the network and their influence on other genes is also discussed.     

Uncovering Gene Regulatory Networks from Time-Series Microarray Data with Variational Bayesian Structural Expectation Maximization

We investigate in this paper reverse engineering of gene regulatory networks from time-series microarray data. We apply dynamic Bayesian networks (DBNs) for modeling cell cycle regulations. In developing a network inference algorithm, we focus on soft solutions that can provide a posteriori probability (APP) of network topology. In particular, we propose a variational Bayesian structural expectation maximization algorithm that can learn the posterior distribution of the network model parameters and topology jointly. We also show how the obtained APPs of the network topology can be used in a Bayesian data integration strategy to integrate two different microarray data sets. The proposed VBSEM algorithm has been tested on yeast cell cycle data sets. To evaluate the confidence of the inferred networks, we apply a moving block bootstrap method. The inferred network is validated by comparing it to the KEGG pathway map.     

Shortest path analysis using partial correlations for classifying gene functions from gene expression data

MOTIVATION: Gaussian graphical models (GGMs) are a popular tool for representing gene association structures. We propose using estimated partial correlations from these models to attach lengths to the edges of the GGM, where the length of an edge is inversely related to the partial correlation between the gene pair. Graphical lasso is used to fit the GGMs and obtain partial correlations. The shortest paths between pairs of genes are found. Where terminal genes have the same biological function intermediate genes on the path are classified as having the same function. We validate the method using genes of known function using the Rosetta Compendium of yeast (Saccharomyces Cerevisiae) gene expression profiles. We also compare our results with those obtained using a graph constructed using correlations. RESULTS: Using a partial correlation graph, we are able to classify approximately twice as many genes to the same level of accuracy as when using a correlation graph. More importantly when both methods are tuned to classify a similar number of genes, the partial correlation approach can increase the accuracy of the classifications.     

Inferring gene regulatory relationships by combining target-target pattern recognition and regulator-specific motif examination

Although microarray data have been successfully used for gene clustering and classification, the use of time series microarray data for constructing gene regulatory networks remains a particularly difficult task. The challenge lies in reliably inferring regulatory relationships from datasets that normally possess a large number of genes and a limited number of time points. In addition to the numerical challenge, the enormous complexity and dynamic properties of gene expression regulation also impede the progress of inferring gene regulatory relationships. Based on the accepted model of the relationship between regulator and target genes, we developed a new approach for inferring gene regulatory relationships by combining target-target pattern recognition and examination of regulator-specific binding sites in the promoter regions of putative target genes. Pattern recognition was accomplished in two steps: A first algorithm was used to search for the genes that share expression profile similarities with known target genes (KTGs) of each investigated regulator. The selected genes were further filtered by examining for the presence of regulator-specific binding sites in their promoter regions. As we implemented our approach to 18 yeast regulator genes and their known target genes, we discovered 267 new regulatory relationships, among which 15% are rediscovered, experimentally validated ones. Of the discovered target genes, 36.1% have the same or similar functions to a KTG of the regulator. An even larger number of inferred genes fall in the biological context and regulatory scope of their regulators. Since the regulatory relationships are inferred from pattern recognition between target-target genes, the method we present is especially suitable for inferring gene regulatory relationships in which there is a time delay between the expression of regulating and target genes.