Hub-centered gene network reconstruction using automatic relevance determination

Network inference deals with the reconstruction of biological networks from experimental data. A variety of different reverse engineering techniques are available; they differ in the underlying assumptions and mathematical models used. One common problem for all approaches stems from the complexity of the task, due to the combinatorial explosion of different network topologies for increasing network size. To handle this problem, constraints are frequently used, for example on the node degree, number of edges, or constraints on regulation functions between network components. We propose to exploit topological considerations in the inference of gene regulatory networks. Such systems are often controlled by a small number of hub genes, while most other genes have only limited influence on the network's dynamic. We model gene regulation using a Bayesian network with discrete, Boolean nodes. A hierarchical prior is employed to identify hub genes. The first layer of the prior is used to regularize weights on edges emanating from one specific node. A second prior on hyperparameters controls the magnitude of the former regularization for different nodes. The net effect is that central nodes tend to form in reconstructed networks. Network reconstruction is then performed by maximization of or sampling from the posterior distribution. We evaluate our approach on simulated and real experimental data, indicating that we can reconstruct main regulatory interactions from the data. We furthermore compare our approach to other state-of-the art methods, showing superior performance in identifying hubs. Using a large publicly available dataset of over 800 cell cycle regulated genes, we are able to identify several main hub genes. Our method may thus provide a valuable tool to identify interesting candidate genes for further study. Furthermore, the approach presented may stimulate further developments in regularization methods for network reconstruction from data.     

Molecular evolution and network-level analysis of the N-glycosylation metabolic pathway across primates

N-glycosylation is one of the most important forms of protein modification, serving key biological functions in multicellular organisms. N-glycans at the cell surface mediate the interaction between cells and the surrounding matrix and may act as pathogen receptors, making the genes responsible for their synthesis good candidates to show signatures of adaptation to different pathogen environments. Here, we study the forces that shaped the evolution of the genes involved in the synthesis of the N-glycans during the divergence of primates within the framework of their functional network. We have found that, despite their function of producing glycan repertoires capable of evading rapidly evolving pathogens, genes involved in the synthesis of the glycans are highly conserved, and no signals of positive selection have been detected within the time of divergence of primates. This suggests strong functional constraints as the main force driving their evolution. We studied the strength of the purifying selection acting on the genes in relation to the network structure considering the position of each gene along the pathway, its connectivity, and the rates of evolution in neighboring genes. We found a strong and highly significant negative correlation between the strength of purifying selection and the connectivity of each gene, indicating that genes encoding for highly connected enzymes evolve slower and thus are subject to stronger selective constraints. This result confirms that network topology does shape the evolution of the genes and that the connectivity within metabolic pathways and networks plays a major role in constraining evolutionary rates.     

Two-phase resolution of polyploidy in the Arabidopsis metabolic network gives rise to relative and absolute dosage constraints

The abundance of detected ancient polyploids in extant genomes raises questions regarding evolution after whole-genome duplication (WGD). For instance, what rules govern the preservation or loss of the duplicated genes created by WGD? We explore this question by contrasting two possible preservation forces: selection on relative and absolute gene dosages. Constraints on the relative dosages of central network genes represent an important force for maintaining duplicates (the dosage balance hypothesis). However, preservation may also result from selection on the absolute abundance of certain gene products. The metabolic network of the model plant Arabidopsis thaliana is a powerful system for comparing these hypotheses. We analyzed the surviving WGD-produced duplicate genes in this network, finding evidence that the surviving duplicates from the most recent WGD (WGD-α) are clustered in the network, as predicted by the dosage balance hypothesis. A flux balance analysis suggests an association between the survival of duplicates from a more ancient WGD (WGD-β) and reactions with high metabolic flux. We argue for an interplay of relative and absolute dosage constraints, such that the relative constraints imposed by the recent WGD are still being resolved by evolution, while they have been essentially fully resolved for the ancient event.     

Control design for sustained oscillation in a two-gene regulatory network

Control strategies for gene regulatory networks have begun to be explored, both experimentally and theoretically, with implications for control of disease as well as for synthetic biology. Recent work has focussed on controls designed to achieve desired stationary states. Another useful objective, however, is the initiation of sustained oscillations in systems where oscillations are normally damped, or even not present. Alternatively, it may be desired to suppress (by damping) oscillations that naturally occur in an uncontrolled network. Here we address these questions in the context of piecewise-affine models of gene regulatory networks with affine controls that match the qualitative nature of the model. In the case of two genes with a single relevant protein concentration threshold per gene, we find that control of production terms (constant control) is effective in generating or suppressing sustained oscillations, while control of decay terms (linear control) is not effective. We derive an easily calculated condition to determine an effective constant control. As an example, we apply our analysis to a model of the carbon response network in Escherichia coli, reduced to the two genes that are essential in understanding its behavior.     

Hippocampal gene expression analysis highlights Ly6a/Sca-1 as candidate gene for previously mapped novelty induced behaviors in mice

In this study, we show that the covariance between behavior and gene expression in the brain can help further unravel the determinants of neurobehavioral traits. Previously, a QTL for novelty induced motor activity levels was identified on murine chromosome 15 using consomic strains. With the goal of narrowing down the linked region and possibly identifying the gene underlying the quantitative trait, gene expression data from this F(2)-population was collected and used for expression QTL analysis. While genetic variation in these mice was limited to chromosome 15, eQTL analysis of gene expression showed strong cis-effects as well as trans-effects elsewhere in the genome. Using weighted gene co-expression network analysis, we were able to identify modules of co-expressed genes related to novelty induced motor activity levels. In eQTL analyses, the expression of Ly6a (a.k.a. Sca-1) was found to be cis-regulated by chromosome 15. Ly6a also surfaced in a group of genes resulting from the network analysis that was correlated with behavior. Behavioral analysis of Ly6a knock-out mice revealed reduced novelty induced motor activity levels when compared to wild type controls, confirming functional importance of Ly6a in this behavior, possibly through regulating other genes in a pathway. This study shows that gene expression profiling can be used to narrow down a previously identified behavioral QTL in mice, providing support for Ly6a as a candidate gene for functional involvement in novelty responsiveness.     

DEVELOPMENTAL DECOUPLING OF ALTERNATIVE PHENOTYPES: INSIGHTS FROM THE TRANSCRIPTOMES OF HORN‐POLYPHENIC BEETLES

Developmental mechanisms play an important role in determining the costs, limits, and evolutionary consequences of phenotypic plasticity. One issue central to these claims is the hypothesis of developmental decoupling, where alternate morphs result from evolutionarily independent developmental pathways. We address this assumption through a microarray study that tests whether differences in gene expression between alternate morphs are as divergent as those between sexes, a classic example of developmental decoupling. We then examine whether genes with morph‐biased expression are less conserved than genes with shared expression between morphs, as predicted if developmental decoupling relaxes pleiotropic constraints on divergence. We focus on the developing horns and brains of two species of horned beetles with impressive sexual‐ and morph‐dimorphism in the expression of horns and fighting behavior. We find that patterns of gene expression were as divergent between morphs as they were between sexes. However, overall patterns of gene expression were also highly correlated across morphs and sexes. Morph‐biased genes were more evolutionarily divergent, suggesting a role of relaxed pleiotropic constraints or relaxed selection. Together these results suggest that alternate morphs are to some extent developmentally decoupled, and that this decoupling has significant evolutionary consequences. However, alternative morphs may not be as developmentally decoupled as sometimes assumed and such hypotheses of development should be revisited and refined.     

METABOLIC FLUX IS A DETERMINANT OF THE EVOLUTIONARY RATES OF ENZYME‐ENCODING GENES

Relationships between evolutionary rates and gene properties on a genomic, functional, pathway, or system level are being explored to unravel the principles of the evolutionary process. In particular, functional network properties have been analyzed to recognize the constraints they may impose on the evolutionary fate of genes. Here we took as a case study the core metabolic network in human erythrocytes and we analyzed the relationship between the evolutionary rates of its genes and the metabolic flux distribution throughout it. We found that metabolic flux correlates with the ratio of nonsynonymous to synonymous substitution rates. Genes encoding enzymes that carry high fluxes have been more constrained in their evolution, while purifying selection is more relaxed in genes encoding enzymes carrying low metabolic fluxes. These results demonstrate the importance of considering the dynamical functioning of gene networks when assessing the action of selection on system‐level properties.     

Gene perturbation and intervention in probabilistic Boolean networks

MOTIVATION: A major objective of gene regulatory network modeling, in addition to gaining a deeper understanding of genetic regulation and control, is the development of computational tools for the identification and discovery of potential targets for therapeutic intervention in diseases such as cancer. We consider the general question of the potential effect of individual genes on the global dynamical network behavior, both from the view of random gene perturbation as well as intervention in order to elicit desired network behavior. RESULTS: Using a recently introduced class of models, called Probabilistic Boolean Networks (PBNs), this paper develops a model for random gene perturbations and derives an explicit formula for the transition probabilities in the new PBN model. This result provides a building block for performing simulations and deriving other results concerning network dynamics. An example is provided to show how the gene perturbation model can be used to compute long-term influences of genes on other genes. Following this, the problem of intervention is addressed via the development of several computational tools based on first-passage times in Markov chains. The consequence is a methodology for finding the best gene with which to intervene in order to most likely achieve desirable network behavior. The ideas are illustrated with several examples in which the goal is to induce the network to transition into a desired state, or set of states. The corresponding issue of avoiding undesirable states is also addressed. Finally, the paper turns to the important problem of assessing the effect of gene perturbations on long-run network behavior. A bound on the steady-state probabilities is derived in terms of the perturbation probability. The result demonstrates that states of the network that are more 'easily reachable' from other states are more stable in the presence of gene perturbations. Consequently, these are hypothesized to correspond to cellular functional states. AVAILABILITY: A library of functions written in MATLAB for simulating PBNs, constructing state-transition matrices, computing steady-state distributions, computing influences, modeling random gene perturbations, and finding optimal intervention targets, as described in this paper, is available on request from is@ieee.org.     

Steady-state expression of self-regulated genes

MOTIVATION: Regulatory gene networks contain generic modules such as feedback loops that are essential for the regulation of many biological functions. The study of the stochastic mechanisms of gene regulation is instrumental for the understanding of how cells maintain their expression at levels commensurate with their biological role, as well as to engineer gene expression switches of appropriate behavior. The lack of precise knowledge on the steady-state distribution of gene expression requires the use of Gillespie algorithms and Monte-Carlo approximations. Methodology: In this study, we provide new exact formulas and efficient numerical algorithms for computing/modeling the steady-state of a class of self-regulated genes, and we use it to model/compute the stochastic expression of a gene of interest in an engineered network introduced in mammalian cells. The behavior of the genetic network is then analyzed experimentally in living cells. RESULTS: Stochastic models often reveal counter-intuitive experimental behaviors, and we find that this genetic architecture displays a unimodal behavior in mammalian cells, which was unexpected given its known bimodal response in unicellular organisms. We provide a molecular rationale for this behavior, and we implement it in the mathematical picture to explain the experimental results obtained from this network.     

Conservation of expression and sequence of metabolic genes is reflected by activity across metabolic states

Variation in gene expression levels on a genomic scale has been detected among different strains, among closely related species, and within populations of genetically identical cells. What are the driving forces that lead to expression divergence in some genes and conserved expression in others? Here we employ flux balance analysis to address this question for metabolic genes. We consider the genome-scale metabolic model of Saccharomyces cerevisiae, and its entire space of optimal and near-optimal flux distributions. We show that this space reveals underlying evolutionary constraints on expression regulation, as well as on the conservation of the underlying gene sequences. Genes that have a high range of optimal flux levels tend to display divergent expression levels among different yeast strains and species. This suggests that gene regulation has diverged in those parts of the metabolic network that are less constrained. In addition, we show that genes that are active in a large fraction of the space of optimal solutions tend to have conserved sequences. This supports the possibility that there is less selective pressure to maintain genes that are relevant for only a small number of metabolic states.     

Network Features of the Mammalian Circadian Clock

The mammalian circadian clock is a cell-autonomous system that drives oscillations in behavior and physiology in anticipation of daily environmental change. To assess the robustness of a human molecular clock, we systematically depleted known clock components and observed that circadian oscillations are maintained over a wide range of disruptions. We developed a novel strategy termed Gene Dosage Network Analysis (GDNA) in which small interfering RNA (siRNA)-induced dose-dependent changes in gene expression were used to build gene association networks consistent with known biochemical constraints. The use of multiple doses powered the analysis to uncover several novel network features of the circadian clock, including proportional responses and signal propagation through interacting genetic modules. We also observed several examples where a gene is up-regulated following knockdown of its paralog, suggesting the clock network utilizes active compensatory mechanisms rather than simple redundancy to confer robustness and maintain function. We propose that these network features act in concert as a genetic buffering system to maintain clock function in the face of genetic and environmental perturbation.     

Coordinated gene networks regulating Arabidopsis plant metabolism in response to various stresses and nutritional cues

The expression pattern of any pair of genes may be negatively correlated, positively correlated, or not correlated at all in response to different stresses and even different progression stages of the stress. This makes it difficult to identify such relationships by classical statistical tools such as the Pearson correlation coefficient. Hence, dedicated bioinformatics approaches that are able to identify groups of cues in which there is a positive or negative expression correlation between pairs or groups of genes are called for. We herein introduce and discuss a bioinformatics approach, termed Gene Coordination, that is devoted to the identification of specific or multiple cues in which there is a positive or negative coordination between pairs of genes and can further incorporate additional coordinated genes to form large coordinated gene networks. We demonstrate the utility of this approach by providing a case study in which we were able to discover distinct expression behavior of the energy-associated gene network in response to distinct biotic and abiotic stresses. This bioinformatics approach is suitable to a broad range of studies that compare treatments versus controls, such as effects of various cues, or expression changes between a mutant and the control wild-type genotype.     

Gene and epigene networks: Two levels in organizing the hereditary system

Intracellular governing gene networks consisting of genes and regulatory bonds among them are considered as the first level in organizing the hereditary system. We give examples of both prokaryotic gene network that controls the development of the λ-phage and eukaryotic gene network that controls the early Drosophila ontogenesis. Using the method of generalized threshold models kinetic curves are shown for some gene products of these networks. Gene networks that govern ontogenetic processes can be envisioned as epigene networks, the networks of the subsequent level in organizing the hereditary systems. Based on the mathematical model our computer experiments show that even the simplest hypothetical two-epigene network is capable of ensuring divergent determination, conservation of determinate states and reproduction of the initial “zygotic” functional state. In addition, the experimental results are given on construction an artificial epigene.     

The formulation of the control of an expression pattern in a gene network by propositional calculus

In this study we model a gene network as a continuous-time switching network. In this model, each gene has a binary state which indicates if the gene expresses or not. We propose a method to control a sequence of expression patterns in the gene network model by adding another continuous-time switching network. By using propositional calculus, we will show that the control problem can be formulated as a mixed-integer linear programming problem with linear constraints.     

Prediction of nitrogen metabolism-related genes in Anabaena by kernel-based network analysis

Prediction of molecular interaction networks from large-scale datasets in genomics and other omics experiments is an important task in terms of both developing bioinformatics methods and solving biological problems. We have applied a kernel-based network inference method for extracting functionally related genes to the response of nitrogen deprivation in cyanobacteria Anabaena sp. PCC 7120 integrating three heterogeneous datasets: microarray data, phylogenetic profiles, and gene orders on the chromosome. We obtained 1348 predicted genes that are somehow related to known genes in the Kyoto Encyclopedia of Genes and Genomes (KEGG) pathways. While this dataset contained previously known genes related to the nitrogen deprivation condition, it also contained additional genes. Thus, we attempted to select any relevant genes using the constraints of Pfam domains and NtcA-binding sites. We found candidates of nitrogen metabolism-related genes, which are depicted as extensions of existing KEGG pathways. The prediction of functional relationships between proteins rather than functions of individual proteins will thus assist the discovery from the large-scale datasets.     

Gene expression in the social behavior network of the wire‐tailed manakin (Pipra filicauda) brain

The vertebrate basal forebrain and midbrain contain a set of interconnected nuclei that control social behavior. Conserved anatomical structures and functions of these nuclei have now been documented among fish, amphibians, reptiles, birds and mammals, and these brain regions have come to be known as the vertebrate social behavior network (SBN). While it is known that nuclei (nodes) of the SBN are rich in steroid and neuropeptide activity linked to behavior, simultaneous variation in the expression of neuroendocrine genes among several SBN nuclei has not yet been described in detail. In this study, we use RNA‐seq to profile gene expression across seven brain regions representing five nodes of the vertebrate SBN in a passerine bird, the wire‐tailed manakin Pipra filicauda. Using weighted gene co‐expression network analysis, we reconstructed sets of coregulated genes, showing striking patterns of variation in neuroendocrine gene expression across the SBN. We describe regional variation in gene networks comprising a broad set of hormone receptors, neuropeptides, steroidogenic enzymes, catecholamines and other neuroendocrine signaling molecules. Our findings show heterogeneous patterns of brain gene expression across nodes of the avian SBN and provide a foundation for future analyses of how the regulation of gene networks may mediate social behavior. These results highlight the importance of region‐specific sampling in studies of the mechanisms of behavior.     

Regression approaches for microarray data analysis.

A variety of new procedures have been devised to handle the two-sample comparison (e.g., tumor versus normal tissue) of gene expression values as measured with microarrays. Such new methods are required in part because of some defining characteristics of microarray-based studies: (i) the very large number of genes contributing expression measures which far exceeds the number of samples (observations) available and (ii) the fact that by virtue of pathway/network relationships, the gene expression measures tend to be highly correlated. These concerns are exacerbated in the regression setting, where the objective is to relate gene expression, simultaneously for multiple genes, to some external outcome or phenotype. Correspondingly, several methods have been recently proposed for addressing these issues. We briefly critique some of these methods prior to a detailed evaluation of gene harvesting. This reveals that gene harvesting, without additional constraints, can yield artifactual solutions. Results obtained employing such constraints motivate the use of regularized regression procedures such as the lasso, least angle regression, and support vector machines. Model selection and solution multiplicity issues are also discussed. The methods are evaluated using a microarray-based study of cardiomyopathy in transgenic mice.