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. RESULTS: Both the computation time and accuracy of the network structures estimated by the proposed method are compared with those of the original BN methods on simulated and real yeast cell cycle microarray gene expression data sets. Our results reveal that the proposed chi-square testing (CST)-based BN method significantly improves the computation time, while its ability to identify all the true network mechanisms was effectively the same as that of full-search BN methods. The proposed BN algorithm is approximately 70.8 and 7.6 times faster than the original BN algorithm when the error sizes of the Best-Fit Extension problem are 0 and 1, respectively. Further, the false positive error rate of the proposed CST-based BN algorithm tends to be less than that of the original BN. CONCLUSION: The CST-based BN method dramatically improves the computation time of the original BN algorithm. Therefore, it can efficiently infer large-scale gene regulatory network mechanisms

Comparison of Probabilistic Boolean Network and Dynamic Bayesian Network Approaches for Inferring Gene Regulatory Networks

Background: The regulation of gene expression is achieved through gene regulatory networks (GRNs) in which collections of genes interact with one another and other substances in a cell. In order to understand the underlying function of organisms, it is necessary to study the behavior of genes in a gene regulatory network context. Several computational approaches are available for modeling gene regulatory networks with different datasets. In order to optimize modeling of GRN, these approaches must be compared and evaluated in terms of accuracy and efficiency. Results: In this paper, two important computational approaches for modeling gene regulatory networks, probabilistic Boolean network methods and dynamic Bayesian network methods, are compared using a biological time-series dataset from the Drosophila Interaction Database to construct a Drosophila gene network. A subset of time points and gene samples from the whole dataset is used to evaluate the performance of these two approaches. Conclusions: The comparison indicates that both approaches had good performance in modeling the gene regulatory networks. The accuracy in terms of recall and precision can be improved if a smaller subset of genes is selected for inferring GRNs. The accuracy of both approaches is dependent upon the number of selected genes and time points of gene samples. In all tested cases, DBN identified more gene interactions and gave better recall than PBN

Constructing Biological Pathways by a Two-Step Counting Approach

Networks are widely used in biology to represent the relationships between genes and gene functions. In Boolean biological models, it is mainly assumed that there are two states to represent a gene: on-state and off-state. It is typically assumed that the relationship between two genes can be characterized by two kinds of pairwise relationships: similarity and prerequisite. Many approaches have been proposed in the literature to reconstruct biological relationships. In this article, we propose a two-step method to reconstruct the biological pathway when the binary array data have measurement error. For a pair of genes in a sample, the first step of this approach is to assign counting numbers for every relationship and select the relationship with counting number greater than a threshold. The second step is to calculate the asymptotic p-values for hypotheses of possible relationships and select relationships with a large p-value. This new method has the advantages of easy calculation for the counting numbers and simple closed forms for the p-value. The simulation study and real data example show that the two-step counting method can accurately reconstruct the biological pathway and outperform the existing methods. Compared with the other existing methods, this two-step method can provide a more accurate and efficient alternative approach for reconstructing the biological network

Inferring Gene Regulatory Networks from Time Series Microarray Data

The innovations and improvements in high-throughput genomic technologies, such as DNA microarray, make it possible for biologists to simultaneously measure dependencies and regulations among genes on a genome-wide scale and provide us genetic information. An important objective of the functional genomics is to understand the controlling mechanism of the expression of these genes and encode the knowledge into gene regulatory network (GRN). To achieve this, computational and statistical algorithms are especially needed. Inference of GRN is a very challenging task for computational biologists because the degree of freedom of the parameters is redundant. Various computational approaches have been proposed for modeling gene regulatory networks, such as Boolean network, differential equations and Bayesian network. There is no so called golden method which can generally give us the best performance for any data set. The research goal is to improve inference accuracy and reduce computational complexity. One of the problems in reconstructing GRN is how to deal with the high dimensionality and short time course gene expression data. In this work, some existing inference algorithms are compared and the limitations lie in that they either suffer from low inference accuracy or computational complexity. To overcome such difficulties, a new approach based on state space model and Expectation-Maximization (EM) algorithms is proposed to model the dynamic system of gene regulation and infer gene regulatory networks. In our model, GRN is represented by a state space model that incorporates noises and has the ability to capture more various biological aspects, such as hidden or missing variables. An EM algorithm is used to estimate the parameters based on the given state space functions and the gene interaction matrix is derived by decomposing the observation matrix using singular value decomposition, and then it is used to infer GRN. The new model is validated using synthetic data sets before applying it to real biological data sets. The results reveal that the developed model can infer the gene regulatory networks from large scale gene expression data and significantly reduce the computational time complexity without losing much inference accuracy compared to dynamic Bayesian network

Reconstructing Generalized Logical Networks of Transcriptional Regulation in Mouse Brain from Temporal Gene Expression Data

Gene expression time course data can be used not only to detect differentially expressed genes but also to find temporal associations among genes. The prsoblem of reconstructing generalized logical networks to account for temporal dependencies among genes and environmental stimuli from transcriptomic data is addressed. A network reconstruction algorithm was developed that uses statistical significance as a criterion for network selection to avoid false-positive interactions arising from pure chance. The multinomial hypothesis testing-based network reconstruction allows for explicit specification of the false-positive rate, unique from all extant network inference algorithms. The method is superior to dynamic Bayesian network modeling in a simulation study. Temporal gene expression data from the brains of alcohol-treated mice in an analysis of the molecular response to alcohol are used for modeling. Genes from major neuronal pathways are identified as putative components of the alcohol response mechanism. Nine of these genes have associations with alcohol reported in literature. Several other potentially relevant genes, compatible with independent results from literature mining, may play a role in the response to alcohol. Additional, previously unknown gene interactions were discovered that, subject to biological verification, may offer new clues in the search for the elusive molecular mechanisms of alcoholism

Reconstructing Generalized Logical Networks of Transcriptional Regulation in Mouse Brain from Temporal Gene Expression Data

Gene expression time course data can be used not only to detect differentially expressed genes but also to find temporal associations among genes. The problem of reconstructing generalized logical networks to account for temporal dependencies among genes and environmental stimuli from transcriptomic data is addressed. A network reconstruction algorithm was developed that uses statistical significance as a criterion for network selection to avoid false-positive interactions arising from pure chance. The multinomial hypothesis testing-based network reconstruction allows for explicit specification of the false-positive rate, unique from all extant network inference algorithms. The method is superior to dynamic Bayesian network modeling in a simulation study. Temporal gene expression data from the brains of alcohol-treated mice in an analysis of the molecular response to alcohol are used for modeling. Genes from major neuronal pathways are identified as putative components of the alcohol response mechanism. Nine of these genes have associations with alcohol reported in literature. Several other potentially relevant genes, compatible with independent results from literature mining, may play a role in the response to alcohol. Additional, previously unknown gene interactions were discovered that, subject to biological verification, may offer new clues in the search for the elusive molecular mechanisms of alcoholism

LegumeGRN: a gene regulatory network prediction server for functional and comparative studies

Building accurate gene regulatory networks (GRNs) from high-throughput gene expression data is a long-standing challenge. However, with the emergence of new algorithms combined with the increase of transcriptomic data availability, it is now reachable. To help biologists to investigate gene regulatory relationships, we developed a web-based computational service to build, analyze and visualize GRNs that govern various biological processes. The web server is preloaded with all available Affymetrix GeneChip-based transcriptomic and annotation data from the three model legume species, i.e., Medicago truncatula, Lotus japonicus and Glycine max. Users can also upload their own transcriptomic and transcription factor datasets from any other species/organisms to analyze their in-house experiments. Users are able to select which experiments, genes and algorithms they will consider to perform their GRN analysis. To achieve this flexibility and improve prediction performance, we have implemented multiple mainstream GRN prediction algorithms including co-expression, Graphical Gaussian Models (GGMs), Context Likelihood of Relatedness (CLR), and parallelized versions of TIGRESS and GENIE3. Besides these existing algorithms, we also proposed a parallel Bayesian network learning algorithm, which can infer causal relationships (i.e., directionality of interaction) and scale up to several thousands of genes. Moreover, this web server also provides tools to allow integrative and comparative analysis between predicted GRNs obtained from different algorithms or experiments, as well as comparisons between legume species. The web site is available at http://legumegrn.noble.org.Oklahoma Center for The Advancement of Science and Technology: (OCAST Grant No. PSB11-031)

LegumeGRN: A Gene Regulatory Network Prediction Server for Functional and Comparative Studies

Building accurate gene regulatory networks (GRNs) from high-throughput gene expression data is a long-standing challenge. However, with the emergence of new algorithms combined with the increase of transcriptomic data availability, it is now reachable. To help biologists to investigate gene regulatory relationships, we developed a web-based computational service to build, analyze and visualize GRNs that govern various biological processes. The web server is preloaded with all available Affymetrix GeneChip-based transcriptomic and annotation data from the three model legume species, i.e., Medicago truncatula, Lotus japonicus and Glycine max. Users can also upload their own transcriptomic and transcription factor datasets from any other species/organisms to analyze their in-house experiments. Users are able to select which experiments, genes and algorithms they will consider to perform their GRN analysis. To achieve this flexibility and improve prediction performance, we have implemented multiple mainstream GRN prediction algorithms including co-expression, Graphical Gaussian Models (GGMs), Context Likelihood of Relatedness (CLR), and parallelized versions of TIGRESS and GENIE3. Besides these existing algorithms, we also proposed a parallel Bayesian network learning algorithm, which can infer causal relationships (i.e., directionality of interaction) and scale up to several thousands of genes. Moreover, this web server also provides tools to allow integrative and comparative analysis between predicted GRNs obtained from different algorithms or experiments, as well as comparisons between legume species. The web site is available at http://legumegrn.noble.org

Analysis and Practical Guideline of Constraint-Based Boolean Method in Genetic Network Inference

Boolean-based method, despite of its simplicity, would be a more attractive approach for inferring a network from high-throughput expression data if its effectiveness has not been limited by high false positive prediction. In this study, we explored factors that could simply be adjusted to improve the accuracy of inferring networks. Our work focused on the analysis of the effects of discretisation methods, biological constraints, and stringency of Boolean function assignment on the performance of Boolean network, including accuracy, precision, specificity and sensitivity, using three sets of microarray time-series data. The study showed that biological constraints have pivotal influence on the network performance over the other factors. It can reduce the variation in network performance resulting from the arbitrary selection of discretisation methods and stringency settings. We also presented the master Boolean network as an approach to establish the unique solution for Boolean analysis. The information acquired from the analysis was summarised and deployed as a general guideline for an efficient use of Boolean-based method in the network inference. In the end, we provided an example of the use of such a guideline in the study of Arabidopsis circadian clock genetic network from which much interesting biological information can be inferred