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.     

A multiorganism based method for Bayesian gene network estimation

The primary goal of this article is to infer genetic interactions based on gene expression data. A new method for multiorganism Bayesian gene network estimation is presented based on multitask learning. When the input datasets are sparse, as is the case in microarray gene expression data, it becomes difficult to separate random correlations from true correlations that would lead to actual edges when modeling the gene interactions as a Bayesian network. Multitask learning takes advantage of the similarity between related tasks, in order to construct a more accurate model of the underlying relationships represented by the Bayesian networks. The proposed method is tested on synthetic data to illustrate its validity. Then it is iteratively applied on real gene expression data to learn the genetic regulatory networks of two organisms with homologous genes.     

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.     

A Bayesian Approach to Pathway Analysis by Integrating Gene–Gene Functional Directions and Microarray Data

Many statistical methods have been developed to screen for differentially expressed genes associated with specific phenotypes in the microarray data. However, it remains a major challenge to synthesize the observed expression patterns with abundant biological knowledge for more complete understanding of the biological functions among genes. Various methods including clustering analysis on genes, neural network, Bayesian network and pathway analysis have been developed toward this goal. In most of these procedures, the activation and inhibition relationships among genes have hardly been utilized in the modeling steps. We propose two novel Bayesian models to integrate the microarray data with the putative pathway structures obtained from the KEGG database and the directional gene–gene interactions in the medical literature. We define the symmetric Kullback–Leibler divergence of a pathway, and use it to identify the pathway(s) most supported by the microarray data. Monte Carlo Markov Chain sampling algorithm is given for posterior computation in the hierarchical model. The proposed method is shown to select the most supported pathway in an illustrative example. Finally, we apply the methodology to a real microarray data set to understand the gene expression profile of osteoblast lineage at defined stages of differentiation. We observe that our method correctly identifies the pathways that are reported to play essential roles in modulating bone mass.     

Combining microarrays and biological knowledge for estimating gene networks via bayesian networks

We propose a statistical method for estimating a gene network based on Bayesian networks from microarray gene expression data together with biological knowledge including protein-protein interactions, protein-DNA interactions, binding site information, existing literature and so on. Microarray data do not contain enough information for constructing gene networks accurately in many cases. Our method adds biological knowledge to the estimation method of gene networks under a Bayesian statistical framework, and also controls the trade-off between microarray information and biological knowledge automatically. We conduct Monte Carlo simulations to show the effectiveness of the proposed method. We analyze Saccharomyces cerevisiae gene expression data as an application.     

Use of gene networks for identifying and validating drug targets

We propose a new method for identifying and validating drug targets by using gene networks, which are estimated from cDNA microarray gene expression profile data. We created novel gene disruption and drug response microarray gene expression profile data libraries for the purpose of drug target elucidation. We use two types of microarray gene expression profile data for estimating gene networks and then identifying drug targets. The estimated gene networks play an essential role in understanding drug response data and this information is unattainable from clustering methods, which are the standard for gene expression analysis. In the construction of gene networks, we use the Bayesian network model. We use an actual example from analysis of the Saccharomyces cerevisiae gene expression profile data to express a concrete strategy for the application of gene network information to drug discovery.     

Identification of retinoblastoma related genes with shortest path in a protein-protein interaction network

This paper presents a new method for identifying retinoblastoma related genes by integrating gene expression profile and shortest path in a functional linkage graph. With the existing protein-protein interaction data from STRING, a weighted functional linkage graph is constructed. 119 consistently differentially expressed genes between retinoblastoma and normal retina were obtained from the overlap of two gene expression studies of retinoblastoma. Then the shortest paths between each pair of these 119 genes were determined with Dijkstra's algorithm. Finally, all the genes present on the shortest paths were extracted and ranked according to their betweenness and the 119 shortest genes with a betweenness greater than 100 and with a p-value less than 0.05 were selected for further analysis. We also identified 53 retinoblastoma related miRNAs from published miRNA array data and most of the 238 (119 consistently differentially expressed genes and 119 shortest path genes) retinoblastoma genes were shown to be target genes of these 53 miRNAs. Interestingly, the genes we identified from both the gene expression profiles and the functional protein association network included more cancer genes than did the genes identified from the gene expression profiles alone. In addition, these genes also had greater functional similarity to the reported cancer genes than did the genes identified from the gene expression profiles alone. This study shows promising results and proves the efficiency of the proposed methods.     

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     

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.     

A Bayesian network classification methodology for gene expression data.

We present new techniques for the application of a Bayesian network learning framework to the problem of classifying gene expression data. The focus on classification permits us to develop techniques that address in several ways the complexities of learning Bayesian nets. Our classification model reduces the Bayesian network learning problem to the problem of learning multiple subnetworks, each consisting of a class label node and its set of parent genes. We argue that this classification model is more appropriate for the gene expression domain than are other structurally similar Bayesian network classification models, such as Naive Bayes and Tree Augmented Naive Bayes (TAN), because our model is consistent with prior domain experience suggesting that a relatively small number of genes, taken in different combinations, is required to predict most clinical classes of interest. Within this framework, we consider two different approaches to identifying parent sets which are supported by the gene expression observations and any other currently available evidence. One approach employs a simple greedy algorithm to search the universe of all genes; the second approach develops and applies a gene selection algorithm whose results are incorporated as a prior to enable an exhaustive search for parent sets over a restricted universe of genes. Two other significant contributions are the construction of classifiers from multiple, competing Bayesian network hypotheses and algorithmic methods for normalizing and binning gene expression data in the absence of prior expert knowledge. Our classifiers are developed under a cross validation regimen and then validated on corresponding out-of-sample test sets. The classifiers attain a classification rate in excess of 90% on out-of-sample test sets for two publicly available datasets. We present an extensive compilation of results reported in the literature for other classification methods run against these same two datasets. Our results are comparable to, or better than, any we have found reported for these two sets, when a train-test protocol as stringent as ours is followed.     

Learning genetic regulatory network connectivity from time series data

Recent experimental advances facilitate the collection of time series data that indicate which genes in a cell are expressed. This information can be used to understand the genetic regulatory network that generates the data. Typically, Bayesian analysis approaches are applied which neglect the time series nature of the experimental data, have difficulty in determining the direction of causality, and do not perform well on networks with tight feedback. To address these problems, this paper presents a method to learn genetic network connectivity which exploits the time series nature of experimental data to achieve better causal predictions. This method first breaks up the data into bins. Next, it determines an initial set of potential influence vectors for each gene based upon the probability of the gene's expression increasing in the next time step. These vectors are then combined to form new vectors with better scores. Finally, these influence vectors are competed against each other to determine the final influence vector for each gene. The result is a directed graph representation of the genetic network's repression and activation connections. Results are reported for several synthetic networks with tight feedback showing significant improvements in recall and runtime over Yu's dynamic Bayesian approach. Promising preliminary results are also reported for an analysis of experimental data for genes involved in the yeast cell cycle.     

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.     

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.     

Bayesian Network Expansion Identifies New ROS and Biofilm Regulators

Signaling and regulatory pathways that guide gene expression have only been partially defined for most organisms. However, given the increasing number of microarray measurements, it may be possible to reconstruct such pathways and uncover missing connections directly from experimental data. Using a compendium of microarray gene expression data obtained from Escherichia coli, we constructed a series of Bayesian network models for the reactive oxygen species (ROS) pathway as defined by EcoCyc. A consensus Bayesian network model was generated using those networks sharing the top recovered score. This microarray-based network only partially agreed with the known ROS pathway curated from the literature and databases. A top network was then expanded to predict genes that could enhance the Bayesian network model using an algorithm we termed ‘BN+1’. This expansion procedure predicted many stress-related genes (e.g., dusB and uspE), and their possible interactions with other ROS pathway genes. A term enrichment method discovered that biofilm-associated microarray data usually contained high expression levels of both uspE and gadX. The predicted involvement of gene uspE in the ROS pathway and interactions between uspE and gadX were confirmed experimentally using E. coli reporter strains. Genes gadX and uspE showed a feedback relationship in regulating each other''s expression. Both genes were verified to regulate biofilm formation through gene knockout experiments. These data suggest that the BN+1 expansion method can faithfully uncover hidden or unknown genes for a selected pathway with significant biological roles. The presently reported BN+1 expansion method is a generalized approach applicable to the characterization and expansion of other biological pathways and living systems.