Structural systems identification of genetic regulatory networks

MOTIVATION: Reverse engineering of genetic regulatory networks from experimental data is the first step toward the modeling of genetic networks. Linear state-space models, also known as linear dynamical models, have been applied to model genetic networks from gene expression time series data, but existing works have not taken into account available structural information. Without structural constraints, estimated models may contradict biological knowledge and estimation methods may over-fit. RESULTS: In this report, we extended expectation-maximization (EM) algorithms to incorporate prior network structure and to estimate genetic regulatory networks that can track and predict gene expression profiles. We applied our method to synthetic data and to SOS data and showed that our method significantly outperforms the regular EM without structural constraints. AVAILABILITY: The Matlab code is available upon request and the SOS data can be downloaded from http://www.weizmann.ac.il/mcb/UriAlon/Papers/SOSData/, courtesy of Uri Alon. Zak's data is available from his website, http://www.che.udel.edu/systems/people/zak.     

Learning Gene Networks under SNP Perturbations Using eQTL Datasets

The standard approach for identifying gene networks is based on experimental perturbations of gene regulatory systems such as gene knock-out experiments, followed by a genome-wide profiling of differential gene expressions. However, this approach is significantly limited in that it is not possible to perturb more than one or two genes simultaneously to discover complex gene interactions or to distinguish between direct and indirect downstream regulations of the differentially-expressed genes. As an alternative, genetical genomics study has been proposed to treat naturally-occurring genetic variants as potential perturbants of gene regulatory system and to recover gene networks via analysis of population gene-expression and genotype data. Despite many advantages of genetical genomics data analysis, the computational challenge that the effects of multifactorial genetic perturbations should be decoded simultaneously from data has prevented a widespread application of genetical genomics analysis. In this article, we propose a statistical framework for learning gene networks that overcomes the limitations of experimental perturbation methods and addresses the challenges of genetical genomics analysis. We introduce a new statistical model, called a sparse conditional Gaussian graphical model, and describe an efficient learning algorithm that simultaneously decodes the perturbations of gene regulatory system by a large number of SNPs to identify a gene network along with expression quantitative trait loci (eQTLs) that perturb this network. While our statistical model captures direct genetic perturbations of gene network, by performing inference on the probabilistic graphical model, we obtain detailed characterizations of how the direct SNP perturbation effects propagate through the gene network to perturb other genes indirectly. We demonstrate our statistical method using HapMap-simulated and yeast eQTL datasets. In particular, the yeast gene network identified computationally by our method under SNP perturbations is well supported by the results from experimental perturbation studies related to DNA replication stress response.     

Comprehensive analysis of gene-environmental interactions with temporal gene expression profiles in Pseudomonas aeruginosa

To explore gene-environment interactions, based on temporal gene expression information, we analyzed gene and treatment information intensively and inferred interaction networks accordingly. The main idea is that gene expression reflects the response of genes to environmental factors, assuming that variations of gene expression occur under different conditions. Then we classified experimental conditions into several subgroups based on the similarity of temporal gene expression profiles. This procedure is useful because it allows us to combine diverse gene expression data as they become available, and, especially, allowing us to lay the regulatory relationships on a concrete biological basis. By estimating the activation points, we can visualize the gene behavior, and obtain a consensus gene activation order, and hence describe conditional regulatory relationships. The estimation of activation points and building of synthetic genetic networks may result in important new insights in the ongoing endeavor to understand the complex network of gene regulation.     

Inference of a genetic network by a combined approach of cluster analysis and graphical Gaussian modeling

MOTIVATION: Recent advances in DNA microarray technologies have made it possible to measure the expression levels of thousands of genes simultaneously under different conditions. The data obtained by microarray analyses are called expression profile data. One type of important information underlying the expression profile data is the 'genetic network,' that is, the regulatory network among genes. Graphical Gaussian Modeling (GGM) is a widely utilized method to infer or test relationships among a plural of variables. RESULTS: In this study, we developed a method combining the cluster analysis with GGM for the inference of the genetic network from the expression profile data. The expression profile data of 2467 Saccharomyces cerevisiae genes measured under 79 different conditions (Eisen et al., PROC: Natl Acad. Sci. USA, 95, 14683-14868, 1998) were used for this study. At first, the 2467 genes were classified into 34 clusters by a cluster analysis, as a preprocessing for GGM. Then, the expression levels of the genes in each cluster were averaged for each condition. The averaged expression profile data of 34 clusters were subjected to GGM, and a partial correlation coefficient matrix was obtained as a model of the genetic network of S. cerevisiae. The accuracy of the inferred network was examined by the agreement of our results with the cumulative results of experimental studies.     

Genetic Network Analyzer: qualitative simulation of genetic regulatory networks

MOTIVATION: The study of genetic regulatory networks has received a major impetus from the recent development of experimental techniques allowing the measurement of patterns of gene expression in a massively parallel way. This experimental progress calls for the development of appropriate computer tools for the modeling and simulation of gene regulation processes. RESULTS: We present Genetic Network Analyzer (GNA), a computer tool for the modeling and simulation of genetic regulatory networks. The tool is based on a qualitative simulation method that employs coarse-grained models of regulatory networks. The use of GNA is illustrated by a case study of the network of genes and interactions regulating the initiation of sporulation in Bacillus subtilis. AVAILABILITY: GNA and the model of the sporulation network are available at http://www-helix.inrialpes.fr/gna.     

An intelligent two-stage evolutionary algorithm for dynamic pathway identification from gene expression profiles

From gene expression profiles, it is desirable to rebuild cellular dynamic regulation networks to discover more delicate and substantial functions in molecular biology, biochemistry, bioengineering and pharmaceutics. S-system model is suitable to characterize biochemical network systems and capable to analyze the regulatory system dynamics. However, inference of an S-system model of N-gene genetic networks has 2N(N+1) parameters in a set of non-linear differential equations to be optimized. This paper proposes an intelligent two-stage evolutionary algorithm (iTEA) to efficiently infer the S-system models of genetic networks from time-series data of gene expression. To cope with curse of dimensionality, the proposed algorithm consists of two stages where each uses a divide-and-conquer strategy. The optimization problem is first decomposed into N subproblems having 2(N+1) parameters each. At the first stage, each subproblem is solved using a novel intelligent genetic algorithm (IGA) with intelligent crossover based on orthogonal experimental design (OED). At the second stage, the obtained N solutions to the N subproblems are combined and refined using an OED-based simulated annealing algorithm for handling noisy gene expression profiles. The effectiveness of iTEA is evaluated using simulated expression patterns with and without noise running on a single-processor PC. It is shown that 1) IGA is efficient enough to solve subproblems; 2) IGA is significantly superior to the existing method SPXGA; and 3) iTEA performs well in inferring S-system models for dynamic pathway identification.     

System for Automatically Inferring a Genetic Netwerk from Expression Profiles

A system is constructed to automatically infer a genetic network byapplication of graphical Gaussian modeling to the expression profiledata. Our system is composed of two parts: one part is automaticdetermination of cluster boundaries of profiles in hierarchicalclustering, and another part is inference of a genetic network byapplication of graphical Gaussian modeling to the clustered profiles.Since thousands of or tens of thousands of gene expression profiles aremeasured under only one hundred conditions, the profiles naturally showsome similar patterns. Therefore, a preprocessing for systematicallyclustering the profiles is prerequisite to infer the relationship betweenthe genes. For this purpose, a method for automatic determination ofcluster boundaries is newly developed without any biological knowledgeand any additional analyses. Then, the profiles for each cluster areanalyzed by graphical Gaussian modeling to infer the relationship betweenthe clusters. Thus, our system automatically provides a graph betweenclusters only by input the profile data. The performance of the presentsystem is validated by 2467 profiles from yeast genes. The clusters andthe genetic network obtained by our system are discussed in terms of thegene function and the known regulatory relationship between genes.     

AtGGM2014, an Arabidopsis gene co-expression network for functional studies

Gene co-expression networks provide an important tool for systems biology studies. Using microarray data from the Array Express database, we constructed an Arabidopsis gene co-expression network, termed At GGM2014, based on the graphical Gaussian model, which contains 102,644 co-expression gene pairs among 18,068 genes. The network was grouped into 622 gene co-expression modules. These modules function in diverse house-keeping, cell cycle, development, hormone response, metabolism, and stress response pathways. We developed a tool to facilitate easy visualization of the expression patterns of these modules either in a tissue context or their regulation under different treatment conditions. The results indicate that at least six modules with tissue-specific expression pattern failed to record modular regulation under various stress conditions. This discrepancy could be best explained by the fact that experiments to study plant stress responses focused mainly on leaves and less on roots, and thus failed to recover specific regulation pattern in other tissues. Overall, the modular structures revealed by our network provide extensive information to generate testable hypotheses about diverse plant signaling pathways. At GGM2014 offers a constructive tool for plant systems biology studies.     

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.     

Reverse engineering of regulatory networks: simulation studies on a genetic algorithm approach for ranking hypotheses

Reverse engineering algorithms (REAs) aim at using gene expression data to reconstruct interactions in regulatory genetic networks. This may help to understand the basis of gene regulation, the core task of functional genomics. Collecting data for a number of environmental conditions is necessary to reengineer even the smallest regulatory networks with reasonable confidence. We systematically tested the requirements for the experimental design necessary for ranking alternative hypotheses about the structure of a given regulatory network. A genetic algorithm (GA) was used to explore the parameter space of a multistage discrete genetic network model with fixed connectivity and number of states per node. Our results show that it is not necessary to determine all parameters of the genetic network in order to rank hypotheses. The ranking process is easier the more experimental environmental conditions are used for the data set. During the ranking, the number of fixed parameters increases with the number of environmental conditions, while some errors in the hypothetical network structure may pass undetected, due to a maintained dynamical behaviour.     

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.     

An analysis of the class of gene regulatory functions implied by a biochemical model

Understanding the integrated behavior of genetic regulatory networks, in which genes regulate one another's activities via RNA and protein products, is emerging as a dominant problem in systems biology. One widely studied class of models of such networks includes genes whose expression values assume Boolean values (i.e., on or off). Design decisions in the development of Boolean network models of gene regulatory systems include the topology of the network (including the distribution of input- and output-connectivity) and the class of Boolean functions used by each gene (e.g., canalizing functions, post functions, etc.). For example, evidence from simulations suggests that biologically realistic dynamics can be produced by scale-free network topologies with canalizing Boolean functions. This work seeks further insights into the design of Boolean network models through the construction and analysis of a class of models that include more concrete biochemical mechanisms than the usual abstract model, including genes and gene products, dimerization, cis-binding sites, promoters and repressors. In this model, it is assumed that the system consists of N genes, with each gene producing one protein product. Proteins may form complexes such as dimers, trimers, etc. The model also includes cis-binding sites to which proteins may bind to form activators or repressors. Binding affinities are based on structural complementarity between proteins and binding sites, with molecular binding sites modeled by bit-strings. Biochemically plausible gene expression rules are used to derive a Boolean regulatory function for each gene in the system. The result is a network model in which both topological features and Boolean functions arise as emergent properties of the interactions of components at the biochemical level. A highly biased set of Boolean functions is observed in simulations of networks of various sizes, suggesting a new characterization of the subset of Boolean functions that are likely to appear in gene regulatory networks.