Information-Theoretic Inference of Large Transcriptional Regulatory Networks

The paper presents MRNET, an original method for inferring genetic networks from microarray data. The method is based on maximum relevance/minimum redundancy (MRMR), an effective information-theoretic technique for feature selection in supervised learning. The MRMR principle consists in selecting among the least redundant variables the ones that have the highest mutual information with the target. MRNET extends this feature selection principle to networks in order to infer gene-dependence relationships from microarray data. The paper assesses MRNET by benchmarking it against RELNET, CLR, and ARACNE, three state-of-the-art information-theoretic methods for large (up to several thousands of genes) network inference. Experimental results on thirty synthetically generated microarray datasets show that MRNET is competitive with these methods.     

Investigating meta-approaches for reconstructing gene networks in a mammalian cellular context

The output of state-of-the-art reverse-engineering methods for biological networks is often based on the fitting of a mathematical model to the data. Typically, different datasets do not give single consistent network predictions but rather an ensemble of inconsistent networks inferred under the same reverse-engineering method that are only consistent with the specific experimentally measured data. Here, we focus on an alternative approach for combining the information contained within such an ensemble of inconsistent gene networks called meta-analysis, to make more accurate predictions and to estimate the reliability of these predictions. We review two existing meta-analysis approaches; the Fisher transformation combined coefficient test (FTCCT) and Fisher's inverse combined probability test (FICPT); and compare their performance with five well-known methods, ARACNe, Context Likelihood or Relatedness network (CLR), Maximum Relevance Minimum Redundancy (MRNET), Relevance Network (RN) and Bayesian Network (BN). We conducted in-depth numerical ensemble simulations and demonstrated for biological expression data that the meta-analysis approaches consistently outperformed the best gene regulatory network inference (GRNI) methods in the literature. Furthermore, the meta-analysis approaches have a low computational complexity. We conclude that the meta-analysis approaches are a powerful tool for integrating different datasets to give more accurate and reliable predictions for biological networks.     

Inferring connectivity of genetic regulatory networks using information-theoretic criteria

Recently, the concept of mutual information has been proposed for inferring the structure of genetic regulatory networks from gene expression profiling. After analyzing the limitations of mutual information in inferring the gene-to-gene interactions, this paper introduces the concept of conditional mutual information and based on it proposes two novel algorithms to infer the connectivity structure of genetic regulatory networks. One of the proposed algorithms exhibits a better accuracy while the other algorithm excels in simplicity and flexibility. By exploiting the mutual information and conditional mutual information, a practical metric is also proposed to assess the likeliness of direct connectivity between genes. This novel metric resolves a common limitation associated with the current inference algorithms, namely the situations where the gene connectivity is established in terms of the dichotomy of being either connected or disconnected. Based on the data sets generated by synthetic networks, the performance of the proposed algorithms is compared favorably relative to existing state-of-the-art schemes. The proposed algorithms are also applied on realistic biological measurements, such as the cutaneous melanoma data set, and biological meaningful results are inferred.     

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.     

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.     

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.     

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.     

Integration of Steady-State and Temporal Gene Expression Data for the Inference of Gene Regulatory Networks

We develop a new regression algorithm, cMIKANA, for inference of gene regulatory networks from combinations of steady-state and time-series gene expression data. Using simulated gene expression datasets to assess the accuracy of reconstructing gene regulatory networks, we show that steady-state and time-series data sets can successfully be combined to identify gene regulatory interactions using the new algorithm. Inferring gene networks from combined data sets was found to be advantageous when using noisy measurements collected with either lower sampling rates or a limited number of experimental replicates. We illustrate our method by applying it to a microarray gene expression dataset from human umbilical vein endothelial cells (HUVECs) which combines time series data from treatment with growth factor TNF and steady state data from siRNA knockdown treatments. Our results suggest that the combination of steady-state and time-series datasets may provide better prediction of RNA-to-RNA interactions, and may also reveal biological features that cannot be identified from dynamic or steady state information alone. Finally, we consider the experimental design of genomics experiments for gene regulatory network inference and show that network inference can be improved by incorporating steady-state measurements with time-series data.     

Influence of statistical estimators of mutual information and data heterogeneity on the inference of gene regulatory networks

The inference of gene regulatory networks from gene expression data is a difficult problem because the performance of the inference algorithms depends on a multitude of different factors. In this paper we study two of these. First, we investigate the influence of discrete mutual information (MI) estimators on the global and local network inference performance of the C3NET algorithm. More precisely, we study 4 different MI estimators (Empirical, Miller-Madow, Shrink and Schürmann-Grassberger) in combination with 3 discretization methods (equal frequency, equal width and global equal width discretization). We observe the best global and local inference performance of C3NET for the Miller-Madow estimator with an equal width discretization. Second, our numerical analysis can be considered as a systems approach because we simulate gene expression data from an underlying gene regulatory network, instead of making a distributional assumption to sample thereof. We demonstrate that despite the popularity of the latter approach, which is the traditional way of studying MI estimators, this is in fact not supported by simulated and biological expression data because of their heterogeneity. Hence, our study provides guidance for an efficient design of a simulation study in the context of network inference, supporting a systems approach.     

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.

     

Function approximation approach to the inference of reduced NGnet models of genetic networks

Background  

The inference of a genetic network is a problem in which mutual interactions among genes are deduced using time-series of gene expression patterns. While a number of models have been proposed to describe genetic regulatory networks, this study focuses on a set of differential equations since it has the ability to model dynamic behavior of gene expression. When we use a set of differential equations to describe genetic networks, the inference problem can be defined as a function approximation problem. On the basis of this problem definition, we propose in this study a new method to infer reduced NGnet models of genetic networks.     

DREAM4: Combining genetic and dynamic information to identify biological networks and dynamical models

Background

Current technologies have lead to the availability of multiple genomic data types in sufficient quantity and quality to serve as a basis for automatic global network inference. Accordingly, there are currently a large variety of network inference methods that learn regulatory networks to varying degrees of detail. These methods have different strengths and weaknesses and thus can be complementary. However, combining different methods in a mutually reinforcing manner remains a challenge.

Methodology

We investigate how three scalable methods can be combined into a useful network inference pipeline. The first is a novel t-test–based method that relies on a comprehensive steady-state knock-out dataset to rank regulatory interactions. The remaining two are previously published mutual information and ordinary differential equation based methods (tlCLR and Inferelator 1.0, respectively) that use both time-series and steady-state data to rank regulatory interactions; the latter has the added advantage of also inferring dynamic models of gene regulation which can be used to predict the system''s response to new perturbations.

Conclusion/Significance

Our t-test based method proved powerful at ranking regulatory interactions, tying for first out of methods in the DREAM4 100-gene in-silico network inference challenge. We demonstrate complementarity between this method and the two methods that take advantage of time-series data by combining the three into a pipeline whose ability to rank regulatory interactions is markedly improved compared to either method alone. Moreover, the pipeline is able to accurately predict the response of the system to new conditions (in this case new double knock-out genetic perturbations). Our evaluation of the performance of multiple methods for network inference suggests avenues for future methods development and provides simple considerations for genomic experimental design. Our code is publicly available at http://err.bio.nyu.edu/inferelator/.     

Sparse and Compositionally Robust Inference of Microbial Ecological Networks

16S ribosomal RNA (rRNA) gene and other environmental sequencing techniques provide snapshots of microbial communities, revealing phylogeny and the abundances of microbial populations across diverse ecosystems. While changes in microbial community structure are demonstrably associated with certain environmental conditions (from metabolic and immunological health in mammals to ecological stability in soils and oceans), identification of underlying mechanisms requires new statistical tools, as these datasets present several technical challenges. First, the abundances of microbial operational taxonomic units (OTUs) from amplicon-based datasets are compositional. Counts are normalized to the total number of counts in the sample. Thus, microbial abundances are not independent, and traditional statistical metrics (e.g., correlation) for the detection of OTU-OTU relationships can lead to spurious results. Secondly, microbial sequencing-based studies typically measure hundreds of OTUs on only tens to hundreds of samples; thus, inference of OTU-OTU association networks is severely under-powered, and additional information (or assumptions) are required for accurate inference. Here, we present SPIEC-EASI (SParse InversE Covariance Estimation for Ecological Association Inference), a statistical method for the inference of microbial ecological networks from amplicon sequencing datasets that addresses both of these issues. SPIEC-EASI combines data transformations developed for compositional data analysis with a graphical model inference framework that assumes the underlying ecological association network is sparse. To reconstruct the network, SPIEC-EASI relies on algorithms for sparse neighborhood and inverse covariance selection. To provide a synthetic benchmark in the absence of an experimentally validated gold-standard network, SPIEC-EASI is accompanied by a set of computational tools to generate OTU count data from a set of diverse underlying network topologies. SPIEC-EASI outperforms state-of-the-art methods to recover edges and network properties on synthetic data under a variety of scenarios. SPIEC-EASI also reproducibly predicts previously unknown microbial associations using data from the American Gut project.     

The mutual information: detecting and evaluating dependencies between variables

MOTIVATION: Clustering co-expressed genes usually requires the definition of 'distance' or 'similarity' between measured datasets, the most common choices being Pearson correlation or Euclidean distance. With the size of available datasets steadily increasing, it has become feasible to consider other, more general, definitions as well. One alternative, based on information theory, is the mutual information, providing a general measure of dependencies between variables. While the use of mutual information in cluster analysis and visualization of large-scale gene expression data has been suggested previously, the earlier studies did not focus on comparing different algorithms to estimate the mutual information from finite data. RESULTS: Here we describe and review several approaches to estimate the mutual information from finite datasets. Our findings show that the algorithms used so far may be quite substantially improved upon. In particular when dealing with small datasets, finite sample effects and other sources of potentially misleading results have to be taken into account.