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.     

Reverse engineering of regulatory networks: simulation studies on a genetic algorithm approach for ranking hypotheses

Reverse engineering algorithms (REAs) aim at using gene expression data to reconstruct interactions in regulatory genetic networks. This may help to understand the basis of gene regulation, the core task of functional genomics. Collecting data for a number of environmental conditions is necessary to reengineer even the smallest regulatory networks with reasonable confidence. We systematically tested the requirements for the experimental design necessary for ranking alternative hypotheses about the structure of a given regulatory network. A genetic algorithm (GA) was used to explore the parameter space of a multistage discrete genetic network model with fixed connectivity and number of states per node. Our results show that it is not necessary to determine all parameters of the genetic network in order to rank hypotheses. The ranking process is easier the more experimental environmental conditions are used for the data set. During the ranking, the number of fixed parameters increases with the number of environmental conditions, while some errors in the hypothetical network structure may pass undetected, due to a maintained dynamical behaviour.     

Reverse engineering and analysis of genome-wide gene regulatory networks from gene expression profiles using high-performance computing

Regulation of gene expression is a carefully regulated phenomenon in the cell. “Reverse-engineering” algorithms try to reconstruct the regulatory interactions among genes from genome-scale measurements of gene expression profiles (microarrays). Mammalian cells express tens of thousands of genes; hence, hundreds of gene expression profiles are necessary in order to have acceptable statistical evidence of interactions between genes. As the number of profiles to be analyzed increases, so do computational costs and memory requirements. In this work, we designed and developed a parallel computing algorithm to reverse-engineer genome-scale gene regulatory networks from thousands of gene expression profiles. The algorithm is based on computing pairwise Mutual Information between each gene-pair. We successfully tested it to reverse engineer the Mus Musculus (mouse) gene regulatory network in liver from gene expression profiles collected from a public repository. A parallel hierarchical clustering algorithm was implemented to discover “communities” within the gene network. Network communities are enriched for genes involved in the same biological functions. The inferred network was used to identify two mitochondrial proteins.     

Gene expression network reconstruction by convex feature selection when incorporating genetic perturbations

Cellular gene expression measurements contain regulatory information that can be used to discover novel network relationships. Here, we present a new algorithm for network reconstruction powered by the adaptive lasso, a theoretically and empirically well-behaved method for selecting the regulatory features of a network. Any algorithms designed for network discovery that make use of directed probabilistic graphs require perturbations, produced by either experiments or naturally occurring genetic variation, to successfully infer unique regulatory relationships from gene expression data. Our approach makes use of appropriately selected cis-expression Quantitative Trait Loci (cis-eQTL), which provide a sufficient set of independent perturbations for maximum network resolution. We compare the performance of our network reconstruction algorithm to four other approaches: the PC-algorithm, QTLnet, the QDG algorithm, and the NEO algorithm, all of which have been used to reconstruct directed networks among phenotypes leveraging QTL. We show that the adaptive lasso can outperform these algorithms for networks of ten genes and ten cis-eQTL, and is competitive with the QDG algorithm for networks with thirty genes and thirty cis-eQTL, with rich topologies and hundreds of samples. Using this novel approach, we identify unique sets of directed relationships in Saccharomyces cerevisiae when analyzing genome-wide gene expression data for an intercross between a wild strain and a lab strain. We recover novel putative network relationships between a tyrosine biosynthesis gene (TYR1), and genes involved in endocytosis (RCY1), the spindle checkpoint (BUB2), sulfonate catabolism (JLP1), and cell-cell communication (PRM7). Our algorithm provides a synthesis of feature selection methods and graphical model theory that has the potential to reveal new directed regulatory relationships from the analysis of population level genetic and gene expression data.     

Inference of biological pathway from gene expression profiles by time delay boolean networks

One great challenge of genomic research is to efficiently and accurately identify complex gene regulatory networks. The development of high-throughput technologies provides numerous experimental data such as DNA sequences, protein sequence, and RNA expression profiles makes it possible to study interactions and regulations among genes or other substance in an organism. However, it is crucial to make inference of genetic regulatory networks from gene expression profiles and protein interaction data for systems biology. This study will develop a new approach to reconstruct time delay Boolean networks as a tool for exploring biological pathways. In the inference strategy, we will compare all pairs of input genes in those basic relationships by their corresponding [Formula: see text]-scores for every output gene. Then, we will combine those consistent relationships to reveal the most probable relationship and reconstruct the genetic network. Specifically, we will prove that [Formula: see text] state transition pairs are sufficient and necessary to reconstruct the time delay Boolean network of [Formula: see text] nodes with high accuracy if the number of input genes to each gene is bounded. We also have implemented this method on simulated and empirical yeast gene expression data sets. The test results show that this proposed method is extensible for realistic networks.     

SEBINI: Software Environment for BIological Network Inference

The Software Environment for BIological Network Inference (SEBINI) has been created to provide an interactive environment for the deployment and evaluation of algorithms used to reconstruct the structure of biological regulatory and interaction networks. SEBINI can be used to compare and train network inference methods on artificial networks and simulated gene expression perturbation data. It also allows the analysis within the same framework of experimental high-throughput expression data using the suite of (trained) inference methods; hence SEBINI should be useful to software developers wishing to evaluate, compare, refine or combine inference techniques, and to bioinformaticians analyzing experimental data. SEBINI provides a platform that aids in more accurate reconstruction of biological networks, with less effort, in less time. AVAILABILITY: A demonstration website is located at https://www.emsl.pnl.gov/NIT/NIT.html. The Java source code and PostgreSQL database schema are available freely for non-commercial use.     

Harnessing Diversity towards the Reconstructing of Large Scale Gene Regulatory Networks

Elucidating gene regulatory network (GRN) from large scale experimental data remains a central challenge in systems biology. Recently, numerous techniques, particularly consensus driven approaches combining different algorithms, have become a potentially promising strategy to infer accurate GRNs. Here, we develop a novel consensus inference algorithm, TopkNet that can integrate multiple algorithms to infer GRNs. Comprehensive performance benchmarking on a cloud computing framework demonstrated that (i) a simple strategy to combine many algorithms does not always lead to performance improvement compared to the cost of consensus and (ii) TopkNet integrating only high-performance algorithms provide significant performance improvement compared to the best individual algorithms and community prediction. These results suggest that a priori determination of high-performance algorithms is a key to reconstruct an unknown regulatory network. Similarity among gene-expression datasets can be useful to determine potential optimal algorithms for reconstruction of unknown regulatory networks, i.e., if expression-data associated with known regulatory network is similar to that with unknown regulatory network, optimal algorithms determined for the known regulatory network can be repurposed to infer the unknown regulatory network. Based on this observation, we developed a quantitative measure of similarity among gene-expression datasets and demonstrated that, if similarity between the two expression datasets is high, TopkNet integrating algorithms that are optimal for known dataset perform well on the unknown dataset. The consensus framework, TopkNet, together with the similarity measure proposed in this study provides a powerful strategy towards harnessing the wisdom of the crowds in reconstruction of unknown regulatory networks.     

An integer optimization algorithm for robust identification of non-linear gene regulatory networks

ABSTRACT: BACKGROUND: Reverse engineering gene networks and identifying regulatory interactions are integral to understanding cellular decision making processes. Advancement in high throughput experimental techniques has initiated innovative data driven analysis of gene regulatory networks. However, inherent noise associated with biological systems requires numerous experimental replicates for reliable conclusions. Furthermore, evidence of robust algorithms directly exploiting basic biological traits are few. Such algorithms are expected to be efficient in their performance and robust in their prediction. RESULTS: We have developed a network identification algorithm to accurately infer both the topology and strength of regulatory interactions from time series gene expression data in the presence of significant experimental noise and non-linear behavior. In this novel formulism, we have addressed data variability in biological systems by integrating network identification with the bootstrap resampling technique, hence predicting robust interactions from limited experimental replicates subjected to noise. Furthermore, we have incorporated non-linearity in gene dynamics using the S-system formulation. The basic network identification formulation exploits the trait of sparsity of biological interactions. Towards that, the identification algorithm is formulated as an integer-programming problem by introducing binary variables for each network component. The objective function is targeted to minimize the network connections subjected to the constraint of maximal agreement between the experimental and predicted gene dynamics. The developed algorithm is validated using both in-silico and experimental data-sets. These studies show that the algorithm can accurately predict the topology and connection strength of the in silico networks, as quantified by high precision and recall, and small discrepancy between the actual and predicted kinetic parameters. Furthermore, in both the in silico and experimental case studies, the predicted gene expression profiles are in very close agreement with the dynamics of the input data. CONCLUSIONS: Our integer programming algorithm effectively utilizes bootstrapping to identify robust gene regulatory networks from noisy, non-linear time-series gene expression data. With significant noise and non-linearities being inherent to biological systems, the present formulism, with the incorporation of network sparsity, is extremely relevant to gene regulatory networks, and while the formulation has been validated against in silico and E. Coli data, it can be applied to any biological system.     

Reverse-engineering of gene networks for regulating early blood development from single-cell measurements

Background

Recent advances in omics technologies have raised great opportunities to study large-scale regulatory networks inside the cell. In addition, single-cell experiments have measured the gene and protein activities in a large number of cells under the same experimental conditions. However, a significant challenge in computational biology and bioinformatics is how to derive quantitative information from the single-cell observations and how to develop sophisticated mathematical models to describe the dynamic properties of regulatory networks using the derived quantitative information.

Methods

This work designs an integrated approach to reverse-engineer gene networks for regulating early blood development based on singel-cell experimental observations. The wanderlust algorithm is initially used to develop the pseudo-trajectory for the activities of a number of genes. Since the gene expression data in the developed pseudo-trajectory show large fluctuations, we then use Gaussian process regression methods to smooth the gene express data in order to obtain pseudo-trajectories with much less fluctuations. The proposed integrated framework consists of both bioinformatics algorithms to reconstruct the regulatory network and mathematical models using differential equations to describe the dynamics of gene expression.

Results

The developed approach is applied to study the network regulating early blood cell development. A graphic model is constructed for a regulatory network with forty genes and a dynamic model using differential equations is developed for a network of nine genes. Numerical results suggests that the proposed model is able to match experimental data very well. We also examine the networks with more regulatory relations and numerical results show that more regulations may exist. We test the possibility of auto-regulation but numerical simulations do not support the positive auto-regulation. In addition, robustness is used as an importantly additional criterion to select candidate networks.

Conclusion

The research results in this work shows that the developed approach is an efficient and effective method to reverse-engineer gene networks using single-cell experimental observations.

     

Gene Regulatory Network Inferences Using a Maximum-Relevance and Maximum-Significance Strategy

Recovering gene regulatory networks from expression data is a challenging problem in systems biology that provides valuable information on the regulatory mechanisms of cells. A number of algorithms based on computational models are currently used to recover network topology. However, most of these algorithms have limitations. For example, many models tend to be complicated because of the “large p, small n” problem. In this paper, we propose a novel regulatory network inference method called the maximum-relevance and maximum-significance network (MRMSn) method, which converts the problem of recovering networks into a problem of how to select the regulator genes for each gene. To solve the latter problem, we present an algorithm that is based on information theory and selects the regulator genes for a specific gene by maximizing the relevance and significance. A first-order incremental search algorithm is used to search for regulator genes. Eventually, a strict constraint is adopted to adjust all of the regulatory relationships according to the obtained regulator genes and thus obtain the complete network structure. We performed our method on five different datasets and compared our method to five state-of-the-art methods for network inference based on information theory. The results confirm the effectiveness of our method.     

High-confidence discovery of genetic network regulators in expression quantitative trait loci data

Expression QTL (eQTL) studies involve the collection of microarray gene expression data and genetic marker data from segregating individuals in a population to search for genetic determinants of differential gene expression. Previous studies have found large numbers of trans-regulated genes (regulated by unlinked genetic loci) that link to a single locus or eQTL "hotspot," and it would be desirable to find the mechanism of coregulation for these gene groups. However, many difficulties exist with current network reconstruction algorithms such as low power and high computational cost. A common observation for biological networks is that they have a scale-free or power-law architecture. In such an architecture, highly influential nodes exist that have many connections to other nodes. If we assume that this type of architecture applies to genetic networks, then we can simplify the problem of genetic network reconstruction by focusing on discovery of the key regulatory genes at the top of the network. We introduce the concept of "shielding" in which a specific gene expression variable (the shielder) renders a set of other gene expression variables (the shielded genes) independent of the eQTL. We iteratively build networks from the eQTL to the shielder down using tests of conditional independence. We have proposed a novel test for controlling the shielder false-positive rate at a predetermined level by requiring a threshold number of shielded genes per shielder. Using simulation, we have demonstrated that we can control the shielder false-positive rate as well as obtain high shielder and edge specificity. In addition, we have shown our method to be robust to violation of the latent variable assumption, an important feature in the practical application of our method. We have applied our method to a yeast expression QTL data set in which microarray and marker data were collected from the progeny of a backcross of two species of Saccharomyces cerevisiae (Brem et al. 2002). Seven genetic networks have been discovered, and bioinformatic analysis of the discovered regulators and corresponding regulated genes has generated plausible hypotheses for mechanisms of regulation that can be tested in future experiments.     

An analysis of the class of gene regulatory functions implied by a biochemical model

Understanding the integrated behavior of genetic regulatory networks, in which genes regulate one another's activities via RNA and protein products, is emerging as a dominant problem in systems biology. One widely studied class of models of such networks includes genes whose expression values assume Boolean values (i.e., on or off). Design decisions in the development of Boolean network models of gene regulatory systems include the topology of the network (including the distribution of input- and output-connectivity) and the class of Boolean functions used by each gene (e.g., canalizing functions, post functions, etc.). For example, evidence from simulations suggests that biologically realistic dynamics can be produced by scale-free network topologies with canalizing Boolean functions. This work seeks further insights into the design of Boolean network models through the construction and analysis of a class of models that include more concrete biochemical mechanisms than the usual abstract model, including genes and gene products, dimerization, cis-binding sites, promoters and repressors. In this model, it is assumed that the system consists of N genes, with each gene producing one protein product. Proteins may form complexes such as dimers, trimers, etc. The model also includes cis-binding sites to which proteins may bind to form activators or repressors. Binding affinities are based on structural complementarity between proteins and binding sites, with molecular binding sites modeled by bit-strings. Biochemically plausible gene expression rules are used to derive a Boolean regulatory function for each gene in the system. The result is a network model in which both topological features and Boolean functions arise as emergent properties of the interactions of components at the biochemical level. A highly biased set of Boolean functions is observed in simulations of networks of various sizes, suggesting a new characterization of the subset of Boolean functions that are likely to appear in gene regulatory networks.     

Reverse Engineering Boolean Networks: From Bernoulli Mixture Models to Rule Based Systems

A Boolean network is a graphical model for representing and analyzing the behavior of gene regulatory networks (GRN). In this context, the accurate and efficient reconstruction of a Boolean network is essential for understanding the gene regulation mechanism and the complex relations that exist therein. In this paper we introduce an elegant and efficient algorithm for the reverse engineering of Boolean networks from a time series of multivariate binary data corresponding to gene expression data. We call our method ReBMM, i.e., reverse engineering based on Bernoulli mixture models. The time complexity of most of the existing reverse engineering techniques is quite high and depends upon the indegree of a node in the network. Due to the high complexity of these methods, they can only be applied to sparsely connected networks of small sizes. ReBMM has a time complexity factor, which is independent of the indegree of a node and is quadratic in the number of nodes in the network, a big improvement over other techniques and yet there is little or no compromise in accuracy. We have tested ReBMM on a number of artificial datasets along with simulated data derived from a plant signaling network. We also used this method to reconstruct a network from real experimental observations of microarray data of the yeast cell cycle. Our method provides a natural framework for generating rules from a probabilistic model. It is simple, intuitive and illustrates excellent empirical results.