Detection of regulator genes and eQTLs in gene networks

Genetic differences between individuals associated to quantitative phenotypic traits, including disease states, are usually found in non-coding genomic regions. These genetic variants are often also associated to differences in expression levels of nearby genes (they are "expression quantitative trait loci" or eQTLs for short) and presumably play a gene regulatory role, affecting the status of molecular networks of interacting genes, proteins and metabolites. Computational systems biology approaches to reconstruct causal gene networks from large-scale omics data have therefore become essential to understand the structure of networks controlled by eQTLs together with other regulatory genes, and to generate detailed hypotheses about the molecular mechanisms that lead from genotype to phenotype. Here we review the main analytical methods and softwares to identify eQTLs and their associated genes, to reconstruct co-expression networks and modules, to reconstruct causal Bayesian gene and module networks, and to validate predicted networks in silico.Comment: minor revision with typos corrected; review article; 24 pages, 2 figure

A sparse Bayesian learning method for structural equation model-based gene regulatory network inference

Gene regulatory networks (GRNs) are underlying networks identified by interactive relationships between genes. Reconstructing GRNs from massive genetic data is important for understanding gene functions and biological mechanism, and can provide effective service for medical treatment and genetic research. A series of artificial intelligence based methods have been proposed to infer GRNs from both gene expression data and genetic perturbations. The accuracy of such algorithms can be better than those models that just consider gene expression data. A structural equation model (SEM), which provides a systematic framework integrating both types of gene data conveniently, is a commonly used model for GRN inference. Considering the sparsity of GRNs, in this paper, we develop a novel sparse Bayesian inference algorithm based on Normal-Equation-Gamma (NEG) type hierarchical prior (BaNEG) to infer GRNs modeled with SEMs more accurately. First, we reparameterize an SEM as a linear type model by integrating the endogenous and exogenous variables; Then, a Bayesian adaptive lasso with a three-level NEG prior is applied to deduce the corresponding posterior mode and estimate the parameters. Simulations on synthetic data are run to compare the performance of BaNEG to some state-of-the-art algorithms, the results demonstrate that the proposed algorithm visibly outperforms the others. What’s more, BaNEG is applied to infer underlying GRNs from a real data set composed of 47 yeast genes from Saccharomyces cerevisiae to discover potential relationships between genes

A sparse Bayesian learning method for structural equation model-based gene regulatory network inference

Gene regulatory networks (GRNs) are underlying networks identified by interactive relationships between genes. Reconstructing GRNs from massive genetic data is important for understanding gene functions and biological mechanism, and can provide effective service for medical treatment and genetic research. A series of artificial intelligence based methods have been proposed to infer GRNs from both gene expression data and genetic perturbations. The accuracy of such algorithms can be better than those models that just consider gene expression data. A structural equation model (SEM), which provides a systematic framework integrating both types of gene data conveniently, is a commonly used model for GRN inference. Considering the sparsity of GRNs, in this paper, we develop a novel sparse Bayesian inference algorithm based on Normal-Equation-Gamma (NEG) type hierarchical prior (BaNEG) to infer GRNs modeled with SEMs more accurately. First, we reparameterize an SEM as a linear type model by integrating the endogenous and exogenous variables; Then, a Bayesian adaptive lasso with a three-level NEG prior is applied to deduce the corresponding posterior mode and estimate the parameters. Simulations on synthetic data are run to compare the performance of BaNEG to some state-of-the-art algorithms, the results demonstrate that the proposed algorithm visibly outperforms the others. What’s more, BaNEG is applied to infer underlying GRNs from a real data set composed of 47 yeast genes from Saccharomyces cerevisiae to discover potential relationships between genes

Phenotypic landscape inference reveals multiple evolutionary paths to C4_4 photosynthesis

C$_4$ photosynthesis has independently evolved from the ancestral C$_3$ pathway in at least 60 plant lineages, but, as with other complex traits, how it evolved is unclear. Here we show that the polyphyletic appearance of C$_4$ photosynthesis is associated with diverse and flexible evolutionary paths that group into four major trajectories. We conducted a meta-analysis of 18 lineages containing species that use C$_3$, C$_4$, or intermediate C$_3$-C$_4$ forms of photosynthesis to parameterise a 16-dimensional phenotypic landscape. We then developed and experimentally verified a novel Bayesian approach based on a hidden Markov model that predicts how the C$_4$ phenotype evolved. The alternative evolutionary histories underlying the appearance of C$_4$ photosynthesis were determined by ancestral lineage and initial phenotypic alterations unrelated to photosynthesis. We conclude that the order of C$_4$ trait acquisition is flexible and driven by non-photosynthetic drivers. This flexibility will have facilitated the convergent evolution of this complex trait

Joint estimation of multiple related biological networks

Graphical models are widely used to make inferences concerning interplay in multivariate systems. In many applications, data are collected from multiple related but nonidentical units whose underlying networks may differ but are likely to share features. Here we present a hierarchical Bayesian formulation for joint estimation of multiple networks in this nonidentically distributed setting. The approach is general: given a suitable class of graphical models, it uses an exchangeability assumption on networks to provide a corresponding joint formulation. Motivated by emerging experimental designs in molecular biology, we focus on time-course data with interventions, using dynamic Bayesian networks as the graphical models. We introduce a computationally efficient, deterministic algorithm for exact joint inference in this setting. We provide an upper bound on the gains that joint estimation offers relative to separate estimation for each network and empirical results that support and extend the theory, including an extensive simulation study and an application to proteomic data from human cancer cell lines. Finally, we describe approximations that are still more computationally efficient than the exact algorithm and that also demonstrate good empirical performance.Comment: Published in at http://dx.doi.org/10.1214/14-AOAS761 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

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

The Inferred Cardiogenic Gene Regulatory Network in the Mammalian Heart

Cardiac development is a complex, multiscale process encompassing cell fate adoption, differentiation and morphogenesis. To elucidate pathways underlying this process, a recently developed algorithm to reverse engineer gene regulatory networks was applied to time-course microarray data obtained from the developing mouse heart. Approximately 200 genes of interest were input into the algorithm to generate putative network topologies that are capable of explaining the experimental data via model simulation. To cull specious network interactions, thousands of putative networks are merged and filtered to generate scale-free, hierarchical networks that are statistically significant and biologically relevant. The networks are validated with known gene interactions and used to predict regulatory pathways important for the developing mammalian heart. Area under the precision-recall curve and receiver operator characteristic curve are 9% and 58%, respectively. Of the top 10 ranked predicted interactions, 4 have already been validated. The algorithm is further tested using a network enriched with known interactions and another depleted of them. The inferred networks contained more interactions for the enriched network versus the depleted network. In all test cases, maximum performance of the algorithm was achieved when the purely data-driven method of network inference was combined with a data-independent, functional-based association method. Lastly, the network generated from the list of approximately 200 genes of interest was expanded using gene-profile uniqueness metrics to include approximately 900 additional known mouse genes and to form the most likely cardiogenic gene regulatory network. The resultant network supports known regulatory interactions and contains several novel cardiogenic regulatory interactions. The method outlined herein provides an informative approach to network inference and leads to clear testable hypotheses related to gene regulation