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.     

The selective values of alleles in a molecular network model are context dependent

Classical quantitative genetics has applied linear modeling to the problem of mapping genotypic to phenotypic variation. Much of this theory was developed prior to the availability of molecular biology. The current understanding of the mechanisms of gene expression indicates the importance of nonlinear effects resulting from gene interactions. We provide a bridge between genetics and gene network theories by relating key concepts from quantitative genetics to the parameters, variables, and performance functions of genetic networks. We illustrate this methodology by simulating the genetic switch controlling galactose metabolism in yeast and its response to selection for a population of individuals. Results indicate that genes have heterogeneous contributions to phenotypes and that additive and nonadditive effects are context dependent. Early cycles of selection suggest strong additive effects attributed to some genes. Later cycles suggest the presence of strong context-dependent nonadditive effects that are conditional on the outcomes of earlier selection cycles. A single favorable allele cannot be consistently identified for most loci. These results highlight the complications that can arise with the presence of nonlinear effects associated with genes acting in networks when selection is conducted on a population of individuals segregating for the genes contributing to the network.     

Models from experiments: combinatorial drug perturbations of cancer cells

We present a novel method for deriving network models from molecular profiles of perturbed cellular systems. The network models aim to predict quantitative outcomes of combinatorial perturbations, such as drug pair treatments or multiple genetic alterations. Mathematically, we represent the system by a set of nodes, representing molecular concentrations or cellular processes, a perturbation vector and an interaction matrix. After perturbation, the system evolves in time according to differential equations with built‐in nonlinearity, similar to Hopfield networks, capable of representing epistasis and saturation effects. For a particular set of experiments, we derive the interaction matrix by minimizing a composite error function, aiming at accuracy of prediction and simplicity of network structure. To evaluate the predictive potential of the method, we performed 21 drug pair treatment experiments in a human breast cancer cell line (MCF7) with observation of phospho‐proteins and cell cycle markers. The best derived network model rediscovered known interactions and contained interesting predictions. Possible applications include the discovery of regulatory interactions, the design of targeted combination therapies and the engineering of molecular biological networks.     

Expression QTL modules as functional components underlying higher-order phenotypes

Systems genetics studies often involve the mapping of numerous regulatory relations between genetic loci and expression traits. These regulatory relations form a bipartite network consisting of genetic loci and expression phenotypes. Modular network organizations may arise from the pleiotropic and polygenic regulation of gene expression. Here we analyzed the expression QTL (eQTL) networks derived from expression genetic data of yeast and mouse liver and found 65 and 98 modules respectively. Computer simulation result showed that such modules rarely occurred in randomized networks with the same number of nodes and edges and same degree distribution. We also found significant within-module functional coherence. The analysis of genetic overlaps and the evidences from biomedical literature have linked some eQTL modules to physiological phenotypes. Functional coherence within the eQTL modules and genetic overlaps between the modules and physiological phenotypes suggests that eQTL modules may act as functional units underlying the higher-order phenotypes.     

Perturbation Biology: Inferring Signaling Networks in Cellular Systems

We present a powerful experimental-computational technology for inferring network models that predict the response of cells to perturbations, and that may be useful in the design of combinatorial therapy against cancer. The experiments are systematic series of perturbations of cancer cell lines by targeted drugs, singly or in combination. The response to perturbation is quantified in terms of relative changes in the measured levels of proteins, phospho-proteins and cellular phenotypes such as viability. Computational network models are derived de novo, i.e., without prior knowledge of signaling pathways, and are based on simple non-linear differential equations. The prohibitively large solution space of all possible network models is explored efficiently using a probabilistic algorithm, Belief Propagation (BP), which is three orders of magnitude faster than standard Monte Carlo methods. Explicit executable models are derived for a set of perturbation experiments in SKMEL-133 melanoma cell lines, which are resistant to the therapeutically important inhibitor of RAF kinase. The resulting network models reproduce and extend known pathway biology. They empower potential discoveries of new molecular interactions and predict efficacious novel drug perturbations, such as the inhibition of PLK1, which is verified experimentally. This technology is suitable for application to larger systems in diverse areas of molecular biology.     

A Bayesian framework for inference of the genotype-phenotype map for segregating populations

Complex genetic interactions lie at the foundation of many diseases. Understanding the nature of these interactions is critical to developing rational intervention strategies. In mammalian systems hypothesis testing in vivo is expensive, time consuming, and often restricted to a few physiological endpoints. Thus, computational methods that generate causal hypotheses can help to prioritize targets for experimental intervention. We propose a Bayesian statistical method to infer networks of causal relationships among genotypes and phenotypes using expression quantitative trait loci (eQTL) data from genetically randomized populations. Causal relationships between network variables are described with hierarchical regression models. Prior distributions on the network structure enforce graph sparsity and have the potential to encode prior biological knowledge about the network. An efficient Monte Carlo method is used to search across the model space and sample highly probable networks. The result is an ensemble of networks that provide a measure of confidence in the estimated network topology. These networks can be used to make predictions of system-wide response to perturbations. We applied our method to kidney gene expression data from an MRL/MpJ × SM/J intercross population and predicted a previously uncharacterized feedback loop in the local renin-angiotensin system.     

From proteomics toward systems biology: integration of different types of proteomics data into network models

Living organisms are comprised of various systems at different levels, i.e., organs, tissues, and cells. Each system carries out its diverse functions in response to environmental and genetic perturbations, by utilizing biological networks, in which nodal components, such as, DNA, mRNAs, proteins, and metabolites, closely interact with each other. Systems biology investigates such systems by producing comprehensive global data that represent different levels of biological information, i.e., at the DNA, mRNA, protein, or metabolite levels, and by integrating this data into network models that generate coherent hypotheses for given biological situations. This review presents a systems biology framework, called the 'Integrative Proteomics Data Analysis Pipeline' (IPDAP), which generates mechanistic hypotheses from network models reconstructed by integrating diverse types of proteomic data generated by mass spectrometry-based proteomic analyses. The devised framework includes a serial set of computational and network analysis tools. Here, we demonstrate its functionalities by applying these tools to several conceptual examples.     

Functional gene expression profiling in yeast implicates translational dysfunction in mutant huntingtin toxicity

Huntington disease (HD) is a neurodegenerative disorder caused by the expansion of a polyglutamine tract in the huntingtin (htt) protein. To uncover candidate therapeutic targets and networks involved in pathogenesis, we integrated gene expression profiling and functional genetic screening to identify genes critical for mutant htt toxicity in yeast. Using mRNA profiling, we have identified genes differentially expressed in wild-type yeast in response to mutant htt toxicity as well as in three toxicity suppressor strains: bna4Δ, mbf1Δ, and ume1Δ. BNA4 encodes the yeast homolog of kynurenine 3-monooxygenase, a promising drug target for HD. Intriguingly, despite playing diverse cellular roles, these three suppressors share common differentially expressed genes involved in stress response, translation elongation, and mitochondrial transport. We then systematically tested the ability of the differentially expressed genes to suppress mutant htt toxicity when overexpressed and have thereby identified 12 novel suppressors, including genes that play a role in stress response, Golgi to endosome transport, and rRNA processing. Integrating the mRNA profiling data and the genetic screening data, we have generated a robust network that shows enrichment in genes involved in rRNA processing and ribosome biogenesis. Strikingly, these observations implicate dysfunction of translation in the pathology of HD. Recent work has shown that regulation of translation is critical for life span extension in Drosophila and that manipulation of this process is protective in Parkinson disease models. In total, these observations suggest that pharmacological manipulation of translation may have therapeutic value in HD.     

Generalizing genetical genomics: getting added value from environmental perturbation

Genetical genomics is a useful approach for studying the effect of genetic perturbations on biological systems at the molecular level. However, molecular networks depend on the environmental conditions and, thus, a comprehensive understanding of biological systems requires studying them across multiple environments. We propose a generalization of genetical genomics, which combines genetic and sensibly chosen environmental perturbations, to study the plasticity of molecular networks. This strategy forms a crucial step toward understanding why individuals respond differently to drugs, toxins, pathogens, nutrients and other environmental influences. Here we outline a strategy for selecting and allocating individuals to particular treatments, and we discuss the promises and pitfalls of the generalized genetical genomics approach.     

Systems Genetics of Metabolism: The Use of the BXD Murine Reference Panel for Multiscalar Integration of Traits

Metabolic homeostasis is achieved by complex molecular and cellular networks that differ significantly among individuals and are difficult to model with genetically engineered lines of mice optimized to study single gene function. Here, we systematically acquired metabolic phenotypes by using the EUMODIC EMPReSS protocols across a large panel of isogenic but diverse strains of mice (BXD type) to study the genetic control of metabolism. We generated and analyzed 140 classical phenotypes and deposited these in an open-access web service for systems genetics (www.genenetwork.org). Heritability, influence of sex, and genetic modifiers of traits were examined singly and jointly by using quantitative-trait locus (QTL) and expression QTL-mapping methods. Traits and networks were linked to loci encompassing both known variants and novel candidate genes, including alkaline phosphatase (ALPL), here linked to hypophosphatasia. The assembled and curated phenotypes provide key resources and exemplars that can be used to dissect complex metabolic traits and disorders.     

Validation and refinement of gene-regulatory pathways on a network of physical interactions

As genome-scale measurements lead to increasingly complex models of gene regulation, systematic approaches are needed to validate and refine these models. Towards this goal, we describe an automated procedure for prioritizing genetic perturbations in order to discriminate optimally between alternative models of a gene-regulatory network. Using this procedure, we evaluate 38 candidate regulatory networks in yeast and perform four high-priority gene knockout experiments. The refined networks support previously unknown regulatory mechanisms downstream of SOK2 and SWI4.     

Rare de novo variants associated with autism implicate a large functional network of genes involved in formation and function of synapses

Identification of complex molecular networks underlying common human phenotypes is a major challenge of modern genetics. In this study, we develop a method for network-based analysis of genetic associations (NETBAG). We use NETBAG to identify a large biological network of genes affected by rare de novo CNVs in autism. The genes forming the network are primarily related to synapse development, axon targeting, and neuron motility. The identified network is strongly related to genes previously implicated in autism and intellectual disability phenotypes. Our results are also consistent with the hypothesis that significantly stronger functional perturbations are required to trigger the autistic phenotype in females compared to males. Overall, the presented analysis of de novo variants supports the hypothesis that perturbed synaptogenesis is at the heart of autism. More generally, our study provides proof of the principle that networks underlying complex human phenotypes can be identified by a network-based functional analysis of rare genetic variants.     

Nonlinear Dynamics Analysis of a Self-Organizing Recurrent Neural Network: Chaos Waning

Self-organization is thought to play an important role in structuring nervous systems. It frequently arises as a consequence of plasticity mechanisms in neural networks: connectivity determines network dynamics which in turn feed back on network structure through various forms of plasticity. Recently, self-organizing recurrent neural network models (SORNs) have been shown to learn non-trivial structure in their inputs and to reproduce the experimentally observed statistics and fluctuations of synaptic connection strengths in cortex and hippocampus. However, the dynamics in these networks and how they change with network evolution are still poorly understood. Here we investigate the degree of chaos in SORNs by studying how the networks'' self-organization changes their response to small perturbations. We study the effect of perturbations to the excitatory-to-excitatory weight matrix on connection strengths and on unit activities. We find that the network dynamics, characterized by an estimate of the maximum Lyapunov exponent, becomes less chaotic during its self-organization, developing into a regime where only few perturbations become amplified. We also find that due to the mixing of discrete and (quasi-)continuous variables in SORNs, small perturbations to the synaptic weights may become amplified only after a substantial delay, a phenomenon we propose to call deferred chaos.     

Application of network methods for understanding evolutionary dynamics in discrete habitats

In populations occupying discrete habitat patches, gene flow between habitat patches may form an intricate population structure. In such structures, the evolutionary dynamics resulting from interaction of gene‐flow patterns with other evolutionary forces may be exceedingly complex. Several models describing gene flow between discrete habitat patches have been presented in the population‐genetics literature; however, these models have usually addressed relatively simple settings of habitable patches and have stopped short of providing general methodologies for addressing nontrivial gene‐flow patterns. In the last decades, network theory – a branch of discrete mathematics concerned with complex interactions between discrete elements – has been applied to address several problems in population genetics by modelling gene flow between habitat patches using networks. Here, we present the idea and concepts of modelling complex gene flows in discrete habitats using networks. Our goal is to raise awareness to existing network theory applications in molecular ecology studies, as well as to outline the current and potential contribution of network methods to the understanding of evolutionary dynamics in discrete habitats. We review the main branches of network theory that have been, or that we believe potentially could be, applied to population genetics and molecular ecology research. We address applications to theoretical modelling and to empirical population‐genetic studies, and we highlight future directions for extending the integration of network science with molecular ecology.     

Lung eQTLs to Help Reveal the Molecular Underpinnings of Asthma

Genome-wide association studies (GWAS) have identified loci reproducibly associated with pulmonary diseases; however, the molecular mechanism underlying these associations are largely unknown. The objectives of this study were to discover genetic variants affecting gene expression in human lung tissue, to refine susceptibility loci for asthma identified in GWAS studies, and to use the genetics of gene expression and network analyses to find key molecular drivers of asthma. We performed a genome-wide search for expression quantitative trait loci (eQTL) in 1,111 human lung samples. The lung eQTL dataset was then used to inform asthma genetic studies reported in the literature. The top ranked lung eQTLs were integrated with the GWAS on asthma reported by the GABRIEL consortium to generate a Bayesian gene expression network for discovery of novel molecular pathways underpinning asthma. We detected 17,178 cis- and 593 trans- lung eQTLs, which can be used to explore the functional consequences of loci associated with lung diseases and traits. Some strong eQTLs are also asthma susceptibility loci. For example, rs3859192 on chr17q21 is robustly associated with the mRNA levels of GSDMA (P = 3.55×10⁻¹⁵¹). The genetic-gene expression network identified the SOCS3 pathway as one of the key drivers of asthma. The eQTLs and gene networks identified in this study are powerful tools for elucidating the causal mechanisms underlying pulmonary disease. This data resource offers much-needed support to pinpoint the causal genes and characterize the molecular function of gene variants associated with lung diseases.     

Exploring and exploiting disease interactions from multi-relational gene and phenotype networks

The availability of electronic health care records is unlocking the potential for novel studies on understanding and modeling disease co-morbidities based on both phenotypic and genetic data. Moreover, the insurgence of increasingly reliable phenotypic data can aid further studies on investigating the potential genetic links among diseases. The goal is to create a feedback loop where computational tools guide and facilitate research, leading to improved biological knowledge and clinical standards, which in turn should generate better data. We build and analyze disease interaction networks based on data collected from previous genetic association studies and patient medical histories, spanning over 12 years, acquired from a regional hospital. By exploring both individual and combined interactions among these two levels of disease data, we provide novel insight into the interplay between genetics and clinical realities. Our results show a marked difference between the well defined structure of genetic relationships and the chaotic co-morbidity network, but also highlight clear interdependencies. We demonstrate the power of these dependencies by proposing a novel multi-relational link prediction method, showing that disease co-morbidity can enhance our currently limited knowledge of genetic association. Furthermore, our methods for integrated networks of diverse data are widely applicable and can provide novel advances for many problems in systems biology and personalized medicine.