Integrative analysis of genetical genomics data incorporating network structures

In a living organism, tens of thousands of genes are expressed and interact with each other to achieve necessary cellular functions. Gene regulatory networks contain information on regulatory mechanisms and the functions of gene expressions. Thus, incorporating network structures, discerned either through biological experiments or statistical estimations, could potentially increase the selection and estimation accuracy of genes associated with a phenotype of interest. Here, we considered a gene selection problem using gene expression data and the graphical structures found in gene networks. Because gene expression measurements are intermediate phenotypes between a trait and its associated genes, we adopted an instrumental variable regression approach. We treated genetic variants as instrumental variables to address the endogeneity issue. We proposed a two‐step estimation procedure. In the first step, we applied the LASSO algorithm to estimate the effects of genetic variants on gene expression measurements. In the second step, the projected expression measurements obtained from the first step were treated as input variables. A graph‐constrained regularization method was adopted to improve the efficiency of gene selection and estimation. We theoretically showed the selection consistency of the estimation method and derived the bound of the estimates. Simulation and real data analyses were conducted to demonstrate the effectiveness of our method and to compare it with its counterparts.     

Bayesian network and nonparametric heteroscedastic regression for nonlinear modeling of genetic network

We propose a new statistical method for constructing a genetic network from microarray gene expression data by using a Bayesian network. An essential point of Bayesian network construction is the estimation of the conditional distribution of each random variable. We consider fitting nonparametric regression models with heterogeneous error variances to the microarray gene expression data to capture the nonlinear structures between genes. Selecting the optimal graph, which gives the best representation of the system among genes, is still a problem to be solved. We theoretically derive a new graph selection criterion from Bayes approach in general situations. The proposed method includes previous methods based on Bayesian networks. We demonstrate the effectiveness of the proposed method through the analysis of Saccharomyces cerevisiae gene expression data newly obtained by disrupting 100 genes.     

Efficient reverse-engineering of a developmental gene regulatory network

Understanding the complex regulatory networks underlying development and evolution of multi-cellular organisms is a major problem in biology. Computational models can be used as tools to extract the regulatory structure and dynamics of such networks from gene expression data. This approach is called reverse engineering. It has been successfully applied to many gene networks in various biological systems. However, to reconstitute the structure and non-linear dynamics of a developmental gene network in its spatial context remains a considerable challenge. Here, we address this challenge using a case study: the gap gene network involved in segment determination during early development of Drosophila melanogaster. A major problem for reverse-engineering pattern-forming networks is the significant amount of time and effort required to acquire and quantify spatial gene expression data. We have developed a simplified data processing pipeline that considerably increases the throughput of the method, but results in data of reduced accuracy compared to those previously used for gap gene network inference. We demonstrate that we can infer the correct network structure using our reduced data set, and investigate minimal data requirements for successful reverse engineering. Our results show that timing and position of expression domain boundaries are the crucial features for determining regulatory network structure from data, while it is less important to precisely measure expression levels. Based on this, we define minimal data requirements for gap gene network inference. Our results demonstrate the feasibility of reverse-engineering with much reduced experimental effort. This enables more widespread use of the method in different developmental contexts and organisms. Such systematic application of data-driven models to real-world networks has enormous potential. Only the quantitative investigation of a large number of developmental gene regulatory networks will allow us to discover whether there are rules or regularities governing development and evolution of complex multi-cellular organisms.     

Hub-centered gene network reconstruction using automatic relevance determination

Network inference deals with the reconstruction of biological networks from experimental data. A variety of different reverse engineering techniques are available; they differ in the underlying assumptions and mathematical models used. One common problem for all approaches stems from the complexity of the task, due to the combinatorial explosion of different network topologies for increasing network size. To handle this problem, constraints are frequently used, for example on the node degree, number of edges, or constraints on regulation functions between network components. We propose to exploit topological considerations in the inference of gene regulatory networks. Such systems are often controlled by a small number of hub genes, while most other genes have only limited influence on the network's dynamic. We model gene regulation using a Bayesian network with discrete, Boolean nodes. A hierarchical prior is employed to identify hub genes. The first layer of the prior is used to regularize weights on edges emanating from one specific node. A second prior on hyperparameters controls the magnitude of the former regularization for different nodes. The net effect is that central nodes tend to form in reconstructed networks. Network reconstruction is then performed by maximization of or sampling from the posterior distribution. We evaluate our approach on simulated and real experimental data, indicating that we can reconstruct main regulatory interactions from the data. We furthermore compare our approach to other state-of-the art methods, showing superior performance in identifying hubs. Using a large publicly available dataset of over 800 cell cycle regulated genes, we are able to identify several main hub genes. Our method may thus provide a valuable tool to identify interesting candidate genes for further study. Furthermore, the approach presented may stimulate further developments in regularization methods for network reconstruction from data.     

Annotating gene function by combining expression data with a modular gene network

MOTIVATION: A promising and reliable approach to annotate gene function is clustering genes not only by using gene expression data but also literature information, especially gene networks. RESULTS: We present a systematic method for gene clustering by combining these totally different two types of data, particularly focusing on network modularity, a global feature of gene networks. Our method is based on learning a probabilistic model, which we call a hidden modular random field in which the relation between hidden variables directly represents a given gene network. Our learning algorithm which minimizes an energy function considering the network modularity is practically time-efficient, regardless of using the global network property. We evaluated our method by using a metabolic network and microarray expression data, changing with microarray datasets, parameters of our model and gold standard clusters. Experimental results showed that our method outperformed other four competing methods, including k-means and existing graph partitioning methods, being statistically significant in all cases. Further detailed analysis showed that our method could group a set of genes into a cluster which corresponds to the folate metabolic pathway while other methods could not. From these results, we can say that our method is highly effective for gene clustering and annotating gene function.     

High-confidence discovery of genetic network regulators in expression quantitative trait loci data

Expression QTL (eQTL) studies involve the collection of microarray gene expression data and genetic marker data from segregating individuals in a population to search for genetic determinants of differential gene expression. Previous studies have found large numbers of trans-regulated genes (regulated by unlinked genetic loci) that link to a single locus or eQTL "hotspot," and it would be desirable to find the mechanism of coregulation for these gene groups. However, many difficulties exist with current network reconstruction algorithms such as low power and high computational cost. A common observation for biological networks is that they have a scale-free or power-law architecture. In such an architecture, highly influential nodes exist that have many connections to other nodes. If we assume that this type of architecture applies to genetic networks, then we can simplify the problem of genetic network reconstruction by focusing on discovery of the key regulatory genes at the top of the network. We introduce the concept of "shielding" in which a specific gene expression variable (the shielder) renders a set of other gene expression variables (the shielded genes) independent of the eQTL. We iteratively build networks from the eQTL to the shielder down using tests of conditional independence. We have proposed a novel test for controlling the shielder false-positive rate at a predetermined level by requiring a threshold number of shielded genes per shielder. Using simulation, we have demonstrated that we can control the shielder false-positive rate as well as obtain high shielder and edge specificity. In addition, we have shown our method to be robust to violation of the latent variable assumption, an important feature in the practical application of our method. We have applied our method to a yeast expression QTL data set in which microarray and marker data were collected from the progeny of a backcross of two species of Saccharomyces cerevisiae (Brem et al. 2002). Seven genetic networks have been discovered, and bioinformatic analysis of the discovered regulators and corresponding regulated genes has generated plausible hypotheses for mechanisms of regulation that can be tested in future experiments.     

Genes under weaker stabilizing selection increase network evolvability and rapid regulatory adaptation to an environmental shift

Regulatory networks play a central role in the modulation of gene expression, the control of cellular differentiation, and the emergence of complex phenotypes. Regulatory networks could constrain or facilitate evolutionary adaptation in gene expression levels. Here, we model the adaptation of regulatory networks and gene expression levels to a shift in the environment that alters the optimal expression level of a single gene. Our analyses show signatures of natural selection on regulatory networks that both constrain and facilitate rapid evolution of gene expression level towards new optima. The analyses are interpreted from the standpoint of neutral expectations and illustrate the challenge to making inferences about network adaptation. Furthermore, we examine the consequence of variable stabilizing selection across genes on the strength and direction of interactions in regulatory networks and in their subsequent adaptation. We observe that directional selection on a highly constrained gene previously under strong stabilizing selection was more efficient when the gene was embedded within a network of partners under relaxed stabilizing selection pressure. The observation leads to the expectation that evolutionarily resilient regulatory networks will contain optimal ratios of genes whose expression is under weak and strong stabilizing selection. Altogether, our results suggest that the variable strengths of stabilizing selection across genes within regulatory networks might itself contribute to the long‐term adaptation of complex phenotypes.     

Co-clustering of biological networks and gene expression data

MOTIVATION: Large scale gene expression data are often analysed by clustering genes based on gene expression data alone, though a priori knowledge in the form of biological networks is available. The use of this additional information promises to improve exploratory analysis considerably. RESULTS: We propose constructing a distance function which combines information from expression data and biological networks. Based on this function, we compute a joint clustering of genes and vertices of the network. This general approach is elaborated for metabolic networks. We define a graph distance function on such networks and combine it with a correlation-based distance function for gene expression measurements. A hierarchical clustering and an associated statistical measure is computed to arrive at a reasonable number of clusters. Our method is validated using expression data of the yeast diauxic shift. The resulting clusters are easily interpretable in terms of the biochemical network and the gene expression data and suggest that our method is able to automatically identify processes that are relevant under the measured conditions.     

Inference of biological pathway from gene expression profiles by time delay boolean networks

One great challenge of genomic research is to efficiently and accurately identify complex gene regulatory networks. The development of high-throughput technologies provides numerous experimental data such as DNA sequences, protein sequence, and RNA expression profiles makes it possible to study interactions and regulations among genes or other substance in an organism. However, it is crucial to make inference of genetic regulatory networks from gene expression profiles and protein interaction data for systems biology. This study will develop a new approach to reconstruct time delay Boolean networks as a tool for exploring biological pathways. In the inference strategy, we will compare all pairs of input genes in those basic relationships by their corresponding [Formula: see text]-scores for every output gene. Then, we will combine those consistent relationships to reveal the most probable relationship and reconstruct the genetic network. Specifically, we will prove that [Formula: see text] state transition pairs are sufficient and necessary to reconstruct the time delay Boolean network of [Formula: see text] nodes with high accuracy if the number of input genes to each gene is bounded. We also have implemented this method on simulated and empirical yeast gene expression data sets. The test results show that this proposed method is extensible for realistic networks.     

Gene expression network reconstruction by convex feature selection when incorporating genetic perturbations

Cellular gene expression measurements contain regulatory information that can be used to discover novel network relationships. Here, we present a new algorithm for network reconstruction powered by the adaptive lasso, a theoretically and empirically well-behaved method for selecting the regulatory features of a network. Any algorithms designed for network discovery that make use of directed probabilistic graphs require perturbations, produced by either experiments or naturally occurring genetic variation, to successfully infer unique regulatory relationships from gene expression data. Our approach makes use of appropriately selected cis-expression Quantitative Trait Loci (cis-eQTL), which provide a sufficient set of independent perturbations for maximum network resolution. We compare the performance of our network reconstruction algorithm to four other approaches: the PC-algorithm, QTLnet, the QDG algorithm, and the NEO algorithm, all of which have been used to reconstruct directed networks among phenotypes leveraging QTL. We show that the adaptive lasso can outperform these algorithms for networks of ten genes and ten cis-eQTL, and is competitive with the QDG algorithm for networks with thirty genes and thirty cis-eQTL, with rich topologies and hundreds of samples. Using this novel approach, we identify unique sets of directed relationships in Saccharomyces cerevisiae when analyzing genome-wide gene expression data for an intercross between a wild strain and a lab strain. We recover novel putative network relationships between a tyrosine biosynthesis gene (TYR1), and genes involved in endocytosis (RCY1), the spindle checkpoint (BUB2), sulfonate catabolism (JLP1), and cell-cell communication (PRM7). Our algorithm provides a synthesis of feature selection methods and graphical model theory that has the potential to reveal new directed regulatory relationships from the analysis of population level genetic and gene expression data.     

Differential network expression during drug and stress response

MOTIVATION: The application of microarray chip technology has led to an explosion of data concerning the expression levels of the genes in an organism under a plethora of conditions. One of the major challenges of systems biology today is to devise generally applicable methods of interpreting this data in a way that will shed light on the complex relationships between multiple genes and their products. The importance of such information is clear, not only as an aid to areas of research like drug design, but also as a contribution to our understanding of the mechanisms behind an organism's ability to react to its environment. RESULTS: We detail one computational approach for using gene expression data to identify response networks in an organism. The method is based on the construction of biological networks given different sets of interaction information and the reduction of the said networks to important response sub-networks via the integration of the gene expression data. As an application, the expression data of known stress responders and DNA repair genes in Mycobacterium tuberculosis is used to construct a generic stress response sub-network. This is compared to similar networks constructed from data obtained from subjecting M.tuberculosis to various drugs; we are thus able to distinguish between generic stress response and specific drug response. We anticipate that this approach will be able to accelerate target identification and drug development for tuberculosis in the future. CONTACT: chris@lanl.gov SUPPLEMENTARY INFORMATION: Supplementary Figures 1 through 6 on drug response networks and differential network analyses on cerulenin, chlorpromazine, ethionamide, ofloxacin, thiolactomycin and triclosan. Supplementary Tables 1 to 3 on predicted protein interactions. http://www.santafe.edu/~chris/DifferentialNW.     

Modeling Genome-Wide Dynamic Regulatory Network in Mouse Lungs with Influenza Infection Using High-Dimensional Ordinary Differential Equations

The immune response to viral infection is regulated by an intricate network of many genes and their products. The reverse engineering of gene regulatory networks (GRNs) using mathematical models from time course gene expression data collected after influenza infection is key to our understanding of the mechanisms involved in controlling influenza infection within a host. A five-step pipeline: detection of temporally differentially expressed genes, clustering genes into co-expressed modules, identification of network structure, parameter estimate refinement, and functional enrichment analysis, is developed for reconstructing high-dimensional dynamic GRNs from genome-wide time course gene expression data. Applying the pipeline to the time course gene expression data from influenza-infected mouse lungs, we have identified 20 distinct temporal expression patterns in the differentially expressed genes and constructed a module-based dynamic network using a linear ODE model. Both intra-module and inter-module annotations and regulatory relationships of our inferred network show some interesting findings and are highly consistent with existing knowledge about the immune response in mice after influenza infection. The proposed method is a computationally efficient, data-driven pipeline bridging experimental data, mathematical modeling, and statistical analysis. The application to the influenza infection data elucidates the potentials of our pipeline in providing valuable insights into systematic modeling of complicated biological processes.     

Gene regulatory network modeling via global optimization of high-order dynamic Bayesian network

ABSTRACT: BACKGROUND: Dynamic Bayesian network (DBN) is among the mainstream approaches for modeling various biological networks, including the gene regulatory network (GRN). Most current methods for learning DBN employ either local search such as hill-climbing, or a meta stochastic global optimization framework such as genetic algorithm or simulated annealing, which are only able to locate sub-optimal solutions. Further, current DBN applications have essentially been limited to small sized networks. RESULTS: To overcome the above difficulties, we introduce here a deterministic global optimization based DBN approach for reverse engineering genetic networks from time course gene expression data. For such DBN models that consist only of inter time slice arcs, we show that there exists a polynomial time algorithm for learning the globally optimal network structure. The proposed approach, named GlobalMIT+, employs the recently proposed information theoretic scoring metric named mutual information test (MIT). GlobalMIT+ is able to learn high-order time delayed genetic interactions, which are common to most biological systems. Evaluation of the approach using both synthetic and real data sets, including a 733 cyanobacterial gene expression data set, shows significantly improved performance over other techniques. CONCLUSIONS: Our studies demonstrate that deterministic global optimization approaches can infer large scale genetic networks.     

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.