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.     

A Bayesian network approach incorporating imputation of missing data enables exploratory analysis of complex causal biological relationships

Bayesian networks can be used to identify possible causal relationships between variables based on their conditional dependencies and independencies, which can be particularly useful in complex biological scenarios with many measured variables. Here we propose two improvements to an existing method for Bayesian network analysis, designed to increase the power to detect potential causal relationships between variables (including potentially a mixture of both discrete and continuous variables). Our first improvement relates to the treatment of missing data. When there is missing data, the standard approach is to remove every individual with any missing data before performing analysis. This can be wasteful and undesirable when there are many individuals with missing data, perhaps with only one or a few variables missing. This motivates the use of imputation. We present a new imputation method that uses a version of nearest neighbour imputation, whereby missing data from one individual is replaced with data from another individual, their nearest neighbour. For each individual with missing data, the subsets of variables to be used to select the nearest neighbour are chosen by sampling without replacement the complete data and estimating a best fit Bayesian network. We show that this approach leads to marked improvements in the recall and precision of directed edges in the final network identified, and we illustrate the approach through application to data from a recent study investigating the causal relationship between methylation and gene expression in early inflammatory arthritis patients. We also describe a second improvement in the form of a pseudo-Bayesian approach for upweighting certain network edges, which can be useful when there is prior evidence concerning their directions.     

c-CSN: Single-cell RNA Sequencing Data Analysis by Conditional Cell-specific Network

The rapid advancement of single-cell technologies has shed new light on the complex mechanisms of cellular heterogeneity. However, compared to bulk RNA sequencing(RNA-seq),single-cell RNA-seq(sc RNA-seq) suffers from higher noise and lower coverage, which brings new computational difficulties. Based on statistical independence, cell-specific network(CSN) is able to quantify the overall associations between genes for each cell, yet suffering from a problem of overestimation related to indirect effects. To overcome this problem, we propose the c-CSN method, which can construct the conditional cell-specific network(CCSN) for each cell. c-CSN method can measure the direct associations between genes by eliminating the indirect associations.c-CSN can be used for cell clustering and dimension reduction on a network basis of single cells.Intuitively, each CCSN can be viewed as the transformation from less ‘‘reliable" gene expression to more ‘‘reliable" gene–gene associations in a cell. Based on CCSN, we further design network flow entropy(NFE) to estimate the differentiation potency of a single cell. A number of sc RNA-seq datasets were used to demonstrate the advantages of our approach. 1) One direct association network is generated for one cell. 2) Most existing sc RNA-seq methods designed for gene expression matrices are also applicable to c-CSN-transformed degree matrices. 3) CCSN-based NFE helps resolving the direction of differentiation trajectories by quantifying the potency of each cell. c-CSN is publicly available at https://github.com/Lin Li-0909/c-CSN.     

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.     

A copula method for modeling directional dependence of genes

Background  

Genes interact with each other as basic building blocks of life, forming a complicated network. The relationship between groups of genes with different functions can be represented as gene networks. With the deposition of huge microarray data sets in public domains, study on gene networking is now possible. In recent years, there has been an increasing interest in the reconstruction of gene networks from gene expression data. Recent work includes linear models, Boolean network models, and Bayesian networks. Among them, Bayesian networks seem to be the most effective in constructing gene networks. A major problem with the Bayesian network approach is the excessive computational time. This problem is due to the interactive feature of the method that requires large search space. Since fitting a model by using the copulas does not require iterations, elicitation of the priors, and complicated calculations of posterior distributions, the need for reference to extensive search spaces can be eliminated leading to manageable computational affords. Bayesian network approach produces a discretely expression of conditional probabilities. Discreteness of the characteristics is not required in the copula approach which involves use of uniform representation of the continuous random variables. Our method is able to overcome the limitation of Bayesian network method for gene-gene interaction, i.e. information loss due to binary transformation.     

CAERUS: predicting CAncER oUtcomeS using relationship between protein structural information, protein networks, gene expression data, and mutation data

Carcinogenesis is a complex process with multiple genetic and environmental factors contributing to the development of one or more tumors. Understanding the underlying mechanism of this process and identifying related markers to assess the outcome of this process would lead to more directed treatment and thus significantly reduce the mortality rate of cancers. Recently, molecular diagnostics and prognostics based on the identification of patterns within gene expression profiles in the context of protein interaction networks were reported. However, the predictive performances of these approaches were limited. In this study we propose a novel integrated approach, named CAERUS, for the identification of gene signatures to predict cancer outcomes based on the domain interaction network in human proteome. We first developed a model to score each protein by quantifying the domain connections to its interacting partners and the somatic mutations present in the domain. We then defined proteins as gene signatures if their scores were above a preset threshold. Next, for each gene signature, we quantified the correlation of the expression levels between this gene signature and its neighboring proteins. The results of the quantification in each patient were then used to predict cancer outcome by a modified naïve Bayes classifier. In this study we achieved a favorable accuracy of 88.3%, sensitivity of 87.2%, and specificity of 88.9% on a set of well-documented gene expression profiles of 253 consecutive breast cancer patients with different outcomes. We also compiled a list of cancer-associated gene signatures and domains, which provided testable hypotheses for further experimental investigation. Our approach proved successful on different independent breast cancer data sets as well as an ovarian cancer data set. This study constitutes the first predictive method to classify cancer outcomes based on the relationship between the domain organization and protein network.     

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.     

Gene Regulatory Network Reconstruction Using Conditional Mutual Information

The inference of gene regulatory network from expression data is an important area of research that provides insight to the inner workings of a biological system. The relevance-network-based approaches provide a simple and easily-scalable solution to the understanding of interaction between genes. Up until now, most works based on relevance network focus on the discovery of direct regulation using correlation coefficient or mutual information. However, some of the more complicated interactions such as interactive regulation and coregulation are not easily detected. In this work, we propose a relevance network model for gene regulatory network inference which employs both mutual information and conditional mutual information to determine the interactions between genes. For this purpose, we propose a conditional mutual information estimator based on adaptive partitioning which allows us to condition on both discrete and continuous random variables. We provide experimental results that demonstrate that the proposed regulatory network inference algorithm can provide better performance when the target network contains coregulated and interactively regulated genes.     

Network-Free Inference of Knockout Effects in Yeast

Perturbation experiments, in which a certain gene is knocked out and the expression levels of other genes are observed, constitute a fundamental step in uncovering the intricate wiring diagrams in the living cell and elucidating the causal roles of genes in signaling and regulation. Here we present a novel framework for analyzing large cohorts of gene knockout experiments and their genome-wide effects on expression levels. We devise clustering-like algorithms that identify groups of genes that behave similarly with respect to the knockout data, and utilize them to predict knockout effects and to annotate physical interactions between proteins as inhibiting or activating. Differing from previous approaches, our prediction approach does not depend on physical network information; the latter is used only for the annotation task. Consequently, it is both more efficient and of wider applicability than previous methods. We evaluate our approach using a large scale collection of gene knockout experiments in yeast, comparing it to the state-of-the-art SPINE algorithm. In cross validation tests, our algorithm exhibits superior prediction accuracy, while at the same time increasing the coverage by over 25-fold. Significant coverage gains are obtained also in the annotation of the physical network.     

Conditional mutual inclusive information enables accurate quantification of associations in gene regulatory networks

Mutual information (MI), a quantity describing the nonlinear dependence between two random variables, has been widely used to construct gene regulatory networks (GRNs). Despite its good performance, MI cannot separate the direct regulations from indirect ones among genes. Although the conditional mutual information (CMI) is able to identify the direct regulations, it generally underestimates the regulation strength, i.e. it may result in false negatives when inferring gene regulations. In this work, to overcome the problems, we propose a novel concept, namely conditional mutual inclusive information (CMI2), to describe the regulations between genes. Furthermore, with CMI2, we develop a new approach, namely CMI2NI (CMI2-based network inference), for reverse-engineering GRNs. In CMI2NI, CMI2 is used to quantify the mutual information between two genes given a third one through calculating the Kullback–Leibler divergence between the postulated distributions of including and excluding the edge between the two genes. The benchmark results on the GRNs from DREAM challenge as well as the SOS DNA repair network in Escherichia coli demonstrate the superior performance of CMI2NI. Specifically, even for gene expression data with small sample size, CMI2NI can not only infer the correct topology of the regulation networks but also accurately quantify the regulation strength between genes. As a case study, CMI2NI was also used to reconstruct cancer-specific GRNs using gene expression data from The Cancer Genome Atlas (TCGA). CMI2NI is freely accessible at http://www.comp-sysbio.org/cmi2ni.     

Efficient gene-specific expression of cre recombinase in the mouse embryo by targeted insertion of a novel IRES-Cre cassette into endogenous loci.

Site specific recombinases have provided the experimental strategy necessary to modulate the expression of gene products in the mouse embryo. In this study we have exploited Cre recombinase to develop a widely applicable cell marking system which functions efficiently even at early post-implantation embryonic stages. Importantly, the techniques and reagents derived in this study are generally applicable to any recombinase driven approach, including strategies to temporally and spatially modulate endogenous or ectopic gene expression in the embryo. The cell marking scheme has two essential components which were derived as separate mouse lines. The first line carries a universal conditional lacZ reporter (UCR) locus which was prepared by using gene targeting in a novel approach to modify a ubiquitously expressed retroviral lacZ promoter trap insertion. The UCR locus is silent until it undergoes a Cre mediated DNA rearrangement to restore lacZ expression. To generate the Cre expressing allele, we outline a flexible strategy which requires the introduction of a novel IRES-Cre cassette into exon sequence of an endogenous locus by gene targeting. We successfully demonstrate this approach by generating a Cre expressing allele of the EphA2 gene, an Eph receptor protein tyrosine kinase expressed early in development. Analysis of double heterozygote embryos clearly demonstrates that Cre recombinase is expressed in vivo from the EphA2 IRES-Cre allele, and that the conditional reporter locus is efficiently restored in EphA2-expressing cells as early as 7.5 dpc. This cell marking experiment establishes the feasibility of expressing Cre recombinase from a single copy allele in the embryo and demonstrates the utility of the conditional reporter mouse which can be used in the analysis of any Cre expressing allele.     

Reconstructing gene regulatory networks: from random to scale-free connectivity

The manipulation of organisms using combinations of gene knockout, RNAi and drug interaction experiments can be used to reveal regulatory interactions between genes. Several algorithms have been proposed that try to reconstruct the underlying regulatory networks from gene expression data sets arising from such experiments. Often these approaches assume that each gene has approximately the same number of interactions within the network, and the methods rely on prior knowledge, or the investigator's best guess, of the average network connectivity. Recent evidence points to scale-free properties in biological networks, however, where network connectivity follows a power-law distribution. For scale-free networks, the average number of regulatory interactions per gene does not satisfactorily characterise the network. With this in mind, a new reverse engineering approach is introduced that does not require prior knowledge of network connectivity and its performance is compared with other published algorithms using simulated gene expression data with biologically relevant network structures. Because this new approach does not make any assumptions about the distribution of network connections, it is suitable for application to scale-free networks.     

Estimating genomic coexpression networks using first-order conditional independence

We describe a computationally efficient statistical framework for estimating networks of coexpressed genes. This framework exploits first-order conditional independence relationships among gene-expression measurements to estimate patterns of association. We use this approach to estimate a coexpression network from microarray gene-expression measurements from Saccharomyces cerevisiae. We demonstrate the biological utility of this approach by showing that a large number of metabolic pathways are coherently represented in the estimated network. We describe a complementary unsupervised graph search algorithm for discovering locally distinct subgraphs of a large weighted graph. We apply this algorithm to our coexpression network model and show that subgraphs found using this approach correspond to particular biological processes or contain representatives of distinct gene families.     

Genomics and genome-wide association studies: an integrative approach to expression QTL mapping

Expression QTL mapping by integrating genome-wide gene expression and genotype data is a promising approach to identifying functional genetic variation, but is hampered by the large number of multiple comparisons inherent in such studies. A novel approach to addressing multiple testing problems in genome-wide family-based association studies is screening candidate markers using heritability or conditional power. We apply these methods in settings in which microarray gene expression data are used as phenotypes, screening for SNPs near the expressed genes. We perform association analyses for phenotypes using a univariate approach. We also perform simulations on trios with large numbers of causal SNPs to determine the optimal number of markers to use in a screen. We demonstrate that our family-based screening approach performs well in the analysis of integrative genomic datasets and that screening using either heritability or conditional power produces similar, though not identical, results.