A relative variation-based method to unraveling gene regulatory networks

Gene regulatory network (GRN) reconstruction is essential in understanding the functioning and pathology of a biological system. Extensive models and algorithms have been developed to unravel a GRN. The DREAM project aims to clarify both advantages and disadvantages of these methods from an application viewpoint. An interesting yet surprising observation is that compared with complicated methods like those based on nonlinear differential equations, etc., methods based on a simple statistics, such as the so-called Z-score, usually perform better. A fundamental problem with the Z-score, however, is that direct and indirect regulations can not be easily distinguished. To overcome this drawback, a relative expression level variation (RELV) based GRN inference algorithm is suggested in this paper, which consists of three major steps. Firstly, on the basis of wild type and single gene knockout/knockdown experimental data, the magnitude of RELV of a gene is estimated. Secondly, probability for the existence of a direct regulation from a perturbed gene to a measured gene is estimated, which is further utilized to estimate whether a gene can be regulated by other genes. Finally, the normalized RELVs are modified to make genes with an estimated zero in-degree have smaller RELVs in magnitude than the other genes, which is used afterwards in queuing possibilities of the existence of direct regulations among genes and therefore leads to an estimate on the GRN topology. This method can in principle avoid the so-called cascade errors under certain situations. Computational results with the Size 100 sub-challenges of DREAM3 and DREAM4 show that, compared with the Z-score based method, prediction performances can be substantially improved, especially the AUPR specification. Moreover, it can even outperform the best team of both DREAM3 and DREAM4. Furthermore, the high precision of the obtained most reliable predictions shows that the suggested algorithm may be very helpful in guiding biological experiment designs.     

Inferring Regulatory Networks from Expression Data Using Tree-Based Methods

One of the pressing open problems of computational systems biology is the elucidation of the topology of genetic regulatory networks (GRNs) using high throughput genomic data, in particular microarray gene expression data. The Dialogue for Reverse Engineering Assessments and Methods (DREAM) challenge aims to evaluate the success of GRN inference algorithms on benchmarks of simulated data. In this article, we present GENIE3, a new algorithm for the inference of GRNs that was best performer in the DREAM4 In Silico Multifactorial challenge. GENIE3 decomposes the prediction of a regulatory network between p genes into p different regression problems. In each of the regression problems, the expression pattern of one of the genes (target gene) is predicted from the expression patterns of all the other genes (input genes), using tree-based ensemble methods Random Forests or Extra-Trees. The importance of an input gene in the prediction of the target gene expression pattern is taken as an indication of a putative regulatory link. Putative regulatory links are then aggregated over all genes to provide a ranking of interactions from which the whole network is reconstructed. In addition to performing well on the DREAM4 In Silico Multifactorial challenge simulated data, we show that GENIE3 compares favorably with existing algorithms to decipher the genetic regulatory network of Escherichia coli. It doesn''t make any assumption about the nature of gene regulation, can deal with combinatorial and non-linear interactions, produces directed GRNs, and is fast and scalable. In conclusion, we propose a new algorithm for GRN inference that performs well on both synthetic and real gene expression data. The algorithm, based on feature selection with tree-based ensemble methods, is simple and generic, making it adaptable to other types of genomic data and interactions.     

Ensemble Inference and Inferability of Gene Regulatory Networks

The inference of gene regulatory network (GRN) from gene expression data is an unsolved problem of great importance. This inference has been stated, though not proven, to be underdetermined implying that there could be many equivalent (indistinguishable) solutions. Motivated by this fundamental limitation, we have developed new framework and algorithm, called TRaCE, for the ensemble inference of GRNs. The ensemble corresponds to the inherent uncertainty associated with discriminating direct and indirect gene regulations from steady-state data of gene knock-out (KO) experiments. We applied TRaCE to analyze the inferability of random GRNs and the GRNs of E. coli and yeast from single- and double-gene KO experiments. The results showed that, with the exception of networks with very few edges, GRNs are typically not inferable even when the data are ideal (unbiased and noise-free). Finally, we compared the performance of TRaCE with top performing methods of DREAM4 in silico network inference challenge.     

How Difficult Is Inference of Mammalian Causal Gene Regulatory Networks?

Gene regulatory networks (GRNs) play a central role in systems biology, especially in the study of mammalian organ development. One key question remains largely unanswered: Is it possible to infer mammalian causal GRNs using observable gene co-expression patterns alone? We assembled two mouse GRN datasets (embryonic tooth and heart) and matching microarray gene expression profiles to systematically investigate the difficulties of mammalian causal GRN inference. The GRNs were assembled based on pieces of experimental genetic perturbation evidence from manually reading primary research articles. Each piece of perturbation evidence records the qualitative change of the expression of one gene following knock-down or over-expression of another gene. Our data have thorough annotation of tissue types and embryonic stages, as well as the type of regulation (activation, inhibition and no effect), which uniquely allows us to estimate both sensitivity and specificity of the inference of tissue specific causal GRN edges. Using these unprecedented datasets, we found that gene co-expression does not reliably distinguish true positive from false positive interactions, making inference of GRN in mammalian development very difficult. Nonetheless, if we have expression profiling data from genetic or molecular perturbation experiments, such as gene knock-out or signalling stimulation, it is possible to use the set of differentially expressed genes to recover causal regulatory relationships with good sensitivity and specificity. Our result supports the importance of using perturbation experimental data in causal network reconstruction. Furthermore, we showed that causal gene regulatory relationship can be highly cell type or developmental stage specific, suggesting the importance of employing expression profiles from homogeneous cell populations. This study provides essential datasets and empirical evidence to guide the development of new GRN inference methods for mammalian organ development.     

A New Asynchronous Parallel Algorithm for Inferring Large-Scale Gene Regulatory Networks

The reconstruction of gene regulatory networks (GRNs) from high-throughput experimental data has been considered one of the most important issues in systems biology research. With the development of high-throughput technology and the complexity of biological problems, we need to reconstruct GRNs that contain thousands of genes. However, when many existing algorithms are used to handle these large-scale problems, they will encounter two important issues: low accuracy and high computational cost. To overcome these difficulties, the main goal of this study is to design an effective parallel algorithm to infer large-scale GRNs based on high-performance parallel computing environments. In this study, we proposed a novel asynchronous parallel framework to improve the accuracy and lower the time complexity of large-scale GRN inference by combining splitting technology and ordinary differential equation (ODE)-based optimization. The presented algorithm uses the sparsity and modularity of GRNs to split whole large-scale GRNs into many small-scale modular subnetworks. Through the ODE-based optimization of all subnetworks in parallel and their asynchronous communications, we can easily obtain the parameters of the whole network. To test the performance of the proposed approach, we used well-known benchmark datasets from Dialogue for Reverse Engineering Assessments and Methods challenge (DREAM), experimentally determined GRN of Escherichia coli and one published dataset that contains more than 10 thousand genes to compare the proposed approach with several popular algorithms on the same high-performance computing environments in terms of both accuracy and time complexity. The numerical results demonstrate that our parallel algorithm exhibits obvious superiority in inferring large-scale GRNs.     

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.     

Experimental design for parameter estimation of gene regulatory networks

Systems biology aims for building quantitative models to address unresolved issues in molecular biology. In order to describe the behavior of biological cells adequately, gene regulatory networks (GRNs) are intensively investigated. As the validity of models built for GRNs depends crucially on the kinetic rates, various methods have been developed to estimate these parameters from experimental data. For this purpose, it is favorable to choose the experimental conditions yielding maximal information. However, existing experimental design principles often rely on unfulfilled mathematical assumptions or become computationally demanding with growing model complexity. To solve this problem, we combined advanced methods for parameter and uncertainty estimation with experimental design considerations. As a showcase, we optimized three simulated GRNs in one of the challenges from the Dialogue for Reverse Engineering Assessment and Methods (DREAM). This article presents our approach, which was awarded the best performing procedure at the DREAM6 Estimation of Model Parameters challenge. For fast and reliable parameter estimation, local deterministic optimization of the likelihood was applied. We analyzed identifiability and precision of the estimates by calculating the profile likelihood. Furthermore, the profiles provided a way to uncover a selection of most informative experiments, from which the optimal one was chosen using additional criteria at every step of the design process. In conclusion, we provide a strategy for optimal experimental design and show its successful application on three highly nonlinear dynamic models. Although presented in the context of the GRNs to be inferred for the DREAM6 challenge, the approach is generic and applicable to most types of quantitative models in systems biology and other disciplines.     

A novel algorithm for alignment of multiple PPI networks based on simulated annealing

Background

To infer gene regulatory networks (GRNs) from gene-expression data is still a fundamental and challenging problem in systems biology. Several existing algorithms formulate GRNs inference as a regression problem and obtain the network with an ensemble strategy. Recent studies on data driven dynamic network construction provide us a new perspective to solve the regression problem.

Results

In this study, we propose a data driven dynamic network construction method to infer gene regulatory network (D3GRN), which transforms the regulatory relationship of each target gene into functional decomposition problem and solves each sub problem by using the Algorithm for Revealing Network Interactions (ARNI). To remedy the limitation of ARNI in constructing networks solely from the unit level, a bootstrapping and area based scoring method is taken to infer the final network. On DREAM4 and DREAM5 benchmark datasets, D3GRN performs competitively with the state-of-the-art algorithms in terms of AUPR.

Conclusions

We have proposed a novel data driven dynamic network construction method by combining ARNI with bootstrapping and area based scoring strategy. The proposed method performs well on the benchmark datasets, contributing as a competitive method to infer gene regulatory networks in a new perspective.

     

IPCA-CMI: An Algorithm for Inferring Gene Regulatory Networks based on a Combination of PCA-CMI and MIT Score

Inferring gene regulatory networks (GRNs) is a major issue in systems biology, which explicitly characterizes regulatory processes in the cell. The Path Consistency Algorithm based on Conditional Mutual Information (PCA-CMI) is a well-known method in this field. In this study, we introduce a new algorithm (IPCA-CMI) and apply it to a number of gene expression data sets in order to evaluate the accuracy of the algorithm to infer GRNs. The IPCA-CMI can be categorized as a hybrid method, using the PCA-CMI and Hill-Climbing algorithm (based on MIT score). The conditional dependence between variables is determined by the conditional mutual information test which can take into account both linear and nonlinear genes relations. IPCA-CMI uses a score and search method and defines a selected set of variables which is adjacent to one of or Y. This set is used to determine the dependency between X and Y. This method is compared with the method of evaluating dependency by PCA-CMI in which the set of variables adjacent to both X and Y, is selected. The merits of the IPCA-CMI are evaluated by applying this algorithm to the DREAM3 Challenge data sets with n variables and n samples () and to experimental data from Escherichia coil containing 9 variables and 9 samples. Results indicate that applying the IPCA-CMI improves the precision of learning the structure of the GRNs in comparison with that of the PCA-CMI.     

Inferring Gene Regulatory Networks by Singular Value Decomposition and Gravitation Field Algorithm

Reconstruction of gene regulatory networks (GRNs) is of utmost interest and has become a challenge computational problem in system biology. However, every existing inference algorithm from gene expression profiles has its own advantages and disadvantages. In particular, the effectiveness and efficiency of every previous algorithm is not high enough. In this work, we proposed a novel inference algorithm from gene expression data based on differential equation model. In this algorithm, two methods were included for inferring GRNs. Before reconstructing GRNs, singular value decomposition method was used to decompose gene expression data, determine the algorithm solution space, and get all candidate solutions of GRNs. In these generated family of candidate solutions, gravitation field algorithm was modified to infer GRNs, used to optimize the criteria of differential equation model, and search the best network structure result. The proposed algorithm is validated on both the simulated scale-free network and real benchmark gene regulatory network in networks database. Both the Bayesian method and the traditional differential equation model were also used to infer GRNs, and the results were used to compare with the proposed algorithm in our work. And genetic algorithm and simulated annealing were also used to evaluate gravitation field algorithm. The cross-validation results confirmed the effectiveness of our algorithm, which outperforms significantly other previous algorithms.     

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.     

Progressive search in tandem mass spectrometry

A cell exhibits a variety of responses to internal and external cues. These responses are possible, in part, due to the presence of an elaborate gene regulatory network (GRN) in every single cell. In the past 20 years, many groups worked on reconstructing the topological structure of GRNs from large-scale gene expression data using a variety of inference algorithms. Insights gained about participating players in GRNs may ultimately lead to therapeutic benefits. Mutual information (MI) is a widely used metric within this inference/reconstruction pipeline as it can detect any correlation (linear and non-linear) between any number of variables (n-dimensions). However, the use of MI with continuous data (for example, normalized fluorescence intensity measurement of gene expression levels) is sensitive to data size, correlation strength and underlying distributions, and often requires laborious and, at times, ad hoc optimization. In this work, we first show that estimating MI of a bi- and tri-variate Gaussian distribution using k-nearest neighbor (kNN) MI estimation results in significant error reduction as compared to commonly used methods based on fixed binning. Second, we demonstrate that implementing the MI-based kNN Kraskov–Stoögbauer–Grassberger (KSG) algorithm leads to a significant improvement in GRN reconstruction for popular inference algorithms, such as Context Likelihood of Relatedness (CLR). Finally, through extensive in-silico benchmarking we show that a new inference algorithm CMIA (Conditional Mutual Information Augmentation), inspired by CLR, in combination with the KSG-MI estimator, outperforms commonly used methods. Using three canonical datasets containing 15 synthetic networks, the newly developed method for GRN reconstruction—which combines CMIA, and the KSG-MI estimator—achieves an improvement of 20–35% in precision-recall measures over the current gold standard in the field. This new method will enable researchers to discover new gene interactions or better choose gene candidates for experimental validations.     

Integrating heterogeneous gene expression data for gene regulatory network modelling

Gene regulatory networks (GRNs) are complex biological systems that have a large impact on protein levels, so that discovering network interactions is a major objective of systems biology. Quantitative GRN models have been inferred, to date, from time series measurements of gene expression, but at small scale, and with limited application to real data. Time series experiments are typically short (number of time points of the order of ten), whereas regulatory networks can be very large (containing hundreds of genes). This creates an under-determination problem, which negatively influences the results of any inferential algorithm. Presented here is an integrative approach to model inference, which has not been previously discussed to the authors' knowledge. Multiple heterogeneous expression time series are used to infer the same model, and results are shown to be more robust to noise and parameter perturbation. Additionally, a wavelet analysis shows that these models display limited noise over-fitting within the individual datasets.     

From knockouts to networks: establishing direct cause-effect relationships through graph analysis

Background

Reverse-engineering gene networks from expression profiles is a difficult problem for which a multitude of techniques have been developed over the last decade. The yearly organized DREAM challenges allow for a fair evaluation and unbiased comparison of these methods.

Results

We propose an inference algorithm that combines confidence matrices, computed as the standard scores from single-gene knockout data, with the down-ranking of feed-forward edges. Substantial improvements on the predictions can be obtained after the execution of this second step.

Conclusions

Our algorithm was awarded the best overall performance at the DREAM4 In Silico 100-gene network sub-challenge, proving to be effective in inferring medium-size gene regulatory networks. This success demonstrates once again the decisive importance of gene expression data obtained after systematic gene perturbations and highlights the usefulness of graph analysis to increase the reliability of inference.     

Entropic Biological Score: a cell cycle investigation for GRNs inference

Inference of gene regulatory networks (GRNs) is one of the most challenging research problems of Systems Biology. In this investigation, a new GRNs inference methodology, called Entropic Biological Score (EBS), which linearly combines the mean conditional entropy (MCE) from expression levels and a Biological Score (BS), obtained by integrating different biological data sources, is proposed. The EBS is validated with the Cell Cycle related functional annotation information, available from Munich Information Center for Protein Sequences (MIPS), and compared with some existing methods like MRNET, ARACNE, CLR and MCE for GRNs inference. For real networks, the performance of EBS, which uses the concept of integrating different data sources, is found to be superior to the aforementioned inference methods. The best results for EBS are obtained by considering the weights w₁ = 0.2 and w₂ = 0.8 for MCE and BS values, respectively, where approximately 40% of the inferred connections are found to be correct and significantly better than related methods. The results also indicate that expression profile is able to recover some true connections, that are not present in biological annotations, thus leading to the possibility of discovering new relations between its genes.     

Improved Reconstruction of In Silico Gene Regulatory Networks by Integrating Knockout and Perturbation Data

We performed computational reconstruction of the in silico gene regulatory networks in the DREAM3 Challenges. Our task was to learn the networks from two types of data, namely gene expression profiles in deletion strains (the ‘deletion data’) and time series trajectories of gene expression after some initial perturbation (the ‘perturbation data’). In the course of developing the prediction method, we observed that the two types of data contained different and complementary information about the underlying network. In particular, deletion data allow for the detection of direct regulatory activities with strong responses upon the deletion of the regulator while perturbation data provide richer information for the identification of weaker and more complex types of regulation. We applied different techniques to learn the regulation from the two types of data. For deletion data, we learned a noise model to distinguish real signals from random fluctuations using an iterative method. For perturbation data, we used differential equations to model the change of expression levels of a gene along the trajectories due to the regulation of other genes. We tried different models, and combined their predictions. The final predictions were obtained by merging the results from the two types of data. A comparison with the actual regulatory networks suggests that our approach is effective for networks with a range of different sizes. The success of the approach demonstrates the importance of integrating heterogeneous data in network reconstruction.     

Petri Nets with Fuzzy Logic (PNFL): Reverse Engineering and Parametrization

Background

The recent DREAM4 blind assessment provided a particularly realistic and challenging setting for network reverse engineering methods. The in silico part of DREAM4 solicited the inference of cycle-rich gene regulatory networks from heterogeneous, noisy expression data including time courses as well as knockout, knockdown and multifactorial perturbations.

Methodology and Principal Findings

We inferred and parametrized simulation models based on Petri Nets with Fuzzy Logic (PNFL). This completely automated approach correctly reconstructed networks with cycles as well as oscillating network motifs. PNFL was evaluated as the best performer on DREAM4 in silico networks of size 10 with an area under the precision-recall curve (AUPR) of 81%. Besides topology, we inferred a range of additional mechanistic details with good reliability, e.g. distinguishing activation from inhibition as well as dependent from independent regulation. Our models also performed well on new experimental conditions such as double knockout mutations that were not included in the provided datasets.

Conclusions

The inference of biological networks substantially benefits from methods that are expressive enough to deal with diverse datasets in a unified way. At the same time, overly complex approaches could generate multiple different models that explain the data equally well. PNFL appears to strike the balance between expressive power and complexity. This also applies to the intuitive representation of PNFL models combining a straightforward graphical notation with colloquial fuzzy parameters.     

Gene regulatory network inference: Data integration in dynamic models—A review

Systems biology aims to develop mathematical models of biological systems by integrating experimental and theoretical techniques. During the last decade, many systems biological approaches that base on genome-wide data have been developed to unravel the complexity of gene regulation. This review deals with the reconstruction of gene regulatory networks (GRNs) from experimental data through computational methods. Standard GRN inference methods primarily use gene expression data derived from microarrays. However, the incorporation of additional information from heterogeneous data sources, e.g. genome sequence and protein–DNA interaction data, clearly supports the network inference process. This review focuses on promising modelling approaches that use such diverse types of molecular biological information. In particular, approaches are discussed that enable the modelling of the dynamics of gene regulatory systems. The review provides an overview of common modelling schemes and learning algorithms and outlines current challenges in GRN modelling.