On the Consistency between Gene Expression and the Gene Regulatory Network of Corynebacterium glutamicum.

A data-driven optimization method for coarse-graining gene regulatory networks

The reverse engineering of gene regulatory network (GRN) is an important problem in systems biology. While gene expression data provide a main source of insights, other types of data are needed to elucidate the structure and dynamics of gene regulation. Epigenetic data (e.g., histone modification) show promise to provide more insights into gene regulation and on epigenetic implication in biological pathways. In this paper, we investigate how epigenetic data are incorporated into reconstruction of GRN. We encode the histone modification data as prior for Bayesian network inference of GRN. Bayesian framework provides a natural and mathematically tractable way of integrating various data and knowledge through its prior. Applying to the gene expression data of yeast cell cycle, we demonstrate that integration of epigenetic data improves the accuracy of GRN inference significantly. Furthermore, fusion of gene expression and epigenetic data shed light on the interactions between genetic and epigenetic regulations of gene expression.

Understanding gene regulatory networks (GRNs) is essential for unraveling the molecular mechanisms governing cellular behavior. With the advent of high-throughput transcriptome measurement technology, researchers have aimed to reverse engineer the biological systems, extracting gene regulatory rules from their outputs, which represented by gene expression data. Bulk RNA sequencing, a widely used method for measuring gene expression, has been employed for GRN reconstruction. However, it falls short in capturing dynamic changes in gene expression at the level of individual cells since it averages gene expression across mixed cell populations. In this review, we provide an overview of 15 GRN reconstruction tools and discuss their respective strengths and limitations, particularly in the context of single cell RNA sequencing (scRNA-seq). Recent advancements in scRNA-seq break new ground of GRN reconstruction. They offer snapshots of the individual cell transcriptomes and capturing dynamic changes. We emphasize how these technological breakthroughs have enhanced GRN reconstruction. GRN reconstructors can be classified based on their requirement for cellular trajectory, which represents a dynamical cellular process including differentiation, aging, or disease progression. Benchmarking studies support the superiority of GRN reconstructors that do not require trajectory analysis in identifying regulator-target relationships. However, methods equipped with trajectory analysis demonstrate better performance in identifying key regulatory factors. In conclusion, researchers should select a suitable GRN reconstructor based on their specific research objectives.

Author response: Heritability enrichment in context-specific regulatory networks improves phenotype-relevant tissue identification

BackgroundCellular processes are controlled by gene-regulatory networks. Several computational methods are currently used to learn the structure of gene-regulatory networks from data. This study focusses on time series gene expression and gene knock-out data in order to identify the underlying network structure. We compare the performance of different network reconstruction methods using synthetic data generated from an ensemble of reference networks. Data requirements as well as optimal experiments for the reconstruction of gene-regulatory networks are investigated. Additionally, the impact of prior knowledge on network reconstruction as well as the effect of unobserved cellular processes is studied.ResultsWe identify linear Gaussian dynamic Bayesian networks and variable selection based on F-statistics as suitable methods for the reconstruction of gene-regulatory networks from time series data. Commonly used discrete dynamic Bayesian networks perform inferior and this result can be attributed to the inevitable information loss by discretization of expression data. It is shown that short time series generated under transcription factor knock-out are optimal experiments in order to reveal the structure of gene regulatory networks. Relative to the level of observational noise, we give estimates for the required amount of gene expression data in order to accurately reconstruct gene-regulatory networks. The benefit of using of prior knowledge within a Bayesian learning framework is found to be limited to conditions of small gene expression data size. Unobserved processes, like protein-protein interactions, induce dependencies between gene expression levels similar to direct transcriptional regulation. We show that these dependencies cannot be distinguished from transcription factor mediated gene regulation on the basis of gene expression data alone.ConclusionCurrently available data size and data quality make the reconstruction of gene networks from gene expression data a challenge. In this study, we identify an optimal type of experiment, requirements on the gene expression data quality and size as well as appropriate reconstruction methods in order to reverse engineer gene regulatory networks from time series data.

Joint reconstruction of multiple gene regulatory networks (GRNs) using gene expression data from multiple tissues/conditions is very important for understanding common and tissue/condition-specific regulation. However, there are currently no computational models and methods available for directly constructing such multiple GRNs that not only share some common hub genes but also possess tissue/condition-specific regulatory edges. In this paper, we proposed a new graphic Gaussian model for joint reconstruction of multiple gene regulatory networks (JRmGRN), which highlighted hub genes, using gene expression data from several tissues/conditions. Under the framework of Gaussian graphical model, JRmGRN method constructs the GRNs through maximizing a penalized log likelihood function. We formulated it as a convex optimization problem, and then solved it with an alternating direction method of multipliers (ADMM) algorithm. The performance of JRmGRN was first evaluated with synthetic data and the results showed that JRmGRN outperformed several other methods for reconstruction of GRNs. We also applied our method to real Arabidopsis thaliana RNA-seq data from two light regime conditions in comparison with other methods, and both common hub genes and some conditions-specific hub genes were identified with higher accuracy and precision. JRmGRN is available as a R program from: https://github.com/wenpingd. Supplementary data are available at Bioinformatics online.

Reconstruction of gene regulatory networks (GRNs), which explicitly represent the causality of developmental or regulatory process, is of utmost interest and has become a challenging computational problem for understanding the complex regulatory mechanisms in cellular systems. However, all existing methods of inferring GRNs from gene expression profiles have their strengths and weaknesses. In particular, many properties of GRNs, such as topology sparseness and non-linear dependence, are generally in regulation mechanism but seldom are taken into account simultaneously in one computational method. In this work, we present a novel method for inferring GRNs from gene expression data considering the non-linear dependence and topological structure of GRNs by employing path consistency algorithm (PCA) based on conditional mutual information (CMI). In this algorithm, the conditional dependence between a pair of genes is represented by the CMI between them. With the general hypothesis of Gaussian distribution underlying gene expression data, CMI between a pair of genes is computed by a concise formula involving the covariance matrices of the related gene expression profiles. The method is validated on the benchmark GRNs from the DREAM challenge and the widely used SOS DNA repair network in Escherichia coli. The cross-validation results confirmed the effectiveness of our method (PCA-CMI), which outperforms significantly other previous methods. Besides its high accuracy, our method is able to distinguish direct (or causal) interactions from indirect associations. All the source data and code are available at: http://csb.shu.edu.cn/subweb/grn.htm. lnchen@sibs.ac.cn; zpliu@sibs.ac.cn Supplementary data are available at Bioinformatics online.

The reconstruction of gene regulatory networks (GRNs) from gene expression data has received increasing attention in recent years, due to its usefulness in the understanding of regulatory mechanisms involved in human diseases. Most of the existing methods reconstruct the network through machine learning approaches, by analyzing known examples of interactions. However, (i) they often produce poor results when the amount of labeled examples is limited, or when no negative example is available and (ii) they are not able to exploit information extracted from GRNs of other (better studied) related organisms, when this information is available. In this paper, we propose a novel machine learning method that overcomes these limitations, by exploiting the knowledge about the GRN of a source organism for the reconstruction of the GRN of the target organism, by means of a novel transfer learning technique. Moreover, the proposed method is natively able to work in the positive-unlabeled setting, where no negative example is available, by fruitfully exploiting a (possibly large) set of unlabeled examples. In our experiments, we reconstructed the human GRN, by exploiting the knowledge of the GRN of Mus musculus. Results showed that the proposed method outperforms state-of-the-art approaches and identifies previously unknown functional relationships among the analyzed genes. http://www.di.uniba.it/∼mignone/systems/biosfer/index.html. Supplementary data are available at Bioinformatics online.

Inductive inference of gene regulatory network using supervised and semi-supervised graph neural networks

BackgroundReconstruction of gene regulatory networks (GRNs), also known as reverse engineering of GRNs, aims to infer the potential regulation relationships between genes. With the development of biotechnology, such as gene chip microarray and RNA-sequencing, the high-throughput data generated provide us with more opportunities to infer the gene-gene interaction relationships using gene expression data and hence understand the underlying mechanism of biological processes. Gene regulatory networks are known to exhibit a multiplicity of interaction mechanisms which include functional and non-functional, and linear and non-linear relationships. Meanwhile, the regulatory interactions between genes and gene products are not spontaneous since various processes involved in producing fully functional and measurable concentrations of transcriptional factors/proteins lead to a delay in gene regulation. Many different approaches for reconstructing GRNs have been proposed, but the existing GRN inference approaches such as probabilistic Boolean networks and dynamic Bayesian networks have various limitations and relatively low accuracy. Inferring GRNs from time series microarray data or RNA-sequencing data remains a very challenging inverse problem due to its nonlinearity, high dimensionality, sparse and noisy data, and significant computational cost, which motivates us to develop more effective inference methods.ResultsWe developed a novel algorithm, MICRAT (Maximal Information coefficient with Conditional Relative Average entropy and Time-series mutual information), for inferring GRNs from time series gene expression data. Maximal information coefficient (MIC) is an effective measure of dependence for two-variable relationships. It captures a wide range of associations, both functional and non-functional, and thus has good performance on measuring the dependence between two genes. Our approach mainly includes two procedures. Firstly, it employs maximal information coefficient for constructing an undirected graph to represent the underlying relationships between genes. Secondly, it directs the edges in the undirected graph for inferring regulators and their targets. In this procedure, the conditional relative average entropies of each pair of nodes (or genes) are employed to indicate the directions of edges. Since the time delay might exist in the expression of regulators and target genes, time series mutual information is combined to cooperatively direct the edges for inferring the potential regulators and their targets. We evaluated the performance of MICRAT by applying it to synthetic datasets as well as real gene expression data and compare with other GRN inference methods. We inferred five 10-gene and five 100-gene networks from the DREAM4 challenge that were generated using the gene expression simulator GeneNetWeaver (GNW). MICRAT was also used to reconstruct GRNs on real gene expression data including part of the DNA-damaged response pathway (SOS DNA repair network) and experimental dataset in E. Coli. The results showed that MICRAT significantly improved the inference accuracy, compared to other inference methods, such as TDBN, etc.ConclusionIn this work, a novel algorithm, MICRAT, for inferring GRNs from time series gene expression data was proposed by taking into account dependence and time delay of expressions of a regulator and its target genes. This approach employed maximal information coefficients for reconstructing an undirected graph to represent the underlying relationships between genes. The edges were directed by combining conditional relative average entropy with time course mutual information of pairs of genes. The proposed algorithm was evaluated on the benchmark GRNs provided by the DREAM4 challenge and part of the real SOS DNA repair network in E. Coli. The experimental study showed that our approach was comparable to other methods on 10-gene datasets and outperformed other methods on 100-gene datasets in GRN inference from time series datasets.

Gene Regulatory Network (GRN) is a virtual network in a cellular context of an organism, comprising a set of genes and their internal relationships to regulate protein production rate (gene expression level) of each other through coded proteins. Computational Reconstruction of GRN from gene expression data is a widely-applied research area. Recurrent Neural Network (RNN) is a useful modeling scheme for GRN reconstruction. In this research, the RNN formulation of GRN reconstruction having single objective function has been modified to incorporate a new objective function. An existing multi-objective meta-heuristic algorithm, called Archived Multi Objective Simulated Annealing (AMOSA), has been modified and applied to this bi-objective RNN formulation. Executing the resulting algorithm (called AMOSA-GRN) on a gene expression dataset, a collection (termed as Archive) of non-dominated GRNs has been obtained. Ensemble averaging has been applied on the archives, and obtained through a sequence of executions of AMOSA-GRN. Accuracy of GRNs in the averaged archive, with respect to gold standard GRN, varies in the range 0.875 - 1.0 (87.5 - 100 percent).

The computational reconstruction of Gene Regulatory Networks (GRNs) from gene expression data has been modelled as a complex optimisation problem, which enables the use of sophisticated search methods to address it. Among these techniques, particle swarm optimisation based algorithms stand out as prominent techniques with fast convergence and accurate network inferences. A multi-objective approach for the inference of GRNs consists of optimising a given network’s topology while tuning the kinetic order parameters in an S-System, thus preventing the use of unnecessary penalty weights and enables the adoption of Pareto optimality based algorithms. In this study, we empirically assess the behaviour of a set of multi-objective particle swarm optimisers based on different archiving and leader selection strategies in the scope of the inference of GRNs. The main goal is to provide system biologists with experimental evidence about which optimisation technique performs with higher success for the inference of consistent GRNs. The experiments conducted involve time-series datasets of gene expression taken from the DREAM3/4 standard benchmarks, as well as in vivo datasets from IRMA and Melanoma cancer samples. Our study shows that multi-objective particle swarm optimiser OMOPSO obtains the best overall performance. Inferred networks show biological consistency in accordance with in vivo studies in the literature.

Reconstruction of gene regulatory networks (GRNs) from expression data is a significant open problem. Common approaches train a machine learning (ML) model to predict a gene's expression using transcription factors' (TFs') expression as features and designate important features/TFs as regulators of the gene. Here, we present an entirely different paradigm, where GRN edges are directly predicted by the ML model. The new approach, named "SPREd," is a simulation-supervised neural network for GRN inference. Its inputs comprise expression relationships (e.g. correlation, mutual information) between the target gene and each TF and between pairs of TFs. The output includes binary labels indicating whether each TF regulates the target gene. We train the neural network model using synthetic expression data generated by a biophysics-inspired simulation model that incorporates linear as well as non-linear TF-gene relationships and diverse GRN configurations. We show SPREd to outperform state-of-the-art GRN reconstruction tools GENIE3, ENNET, PORTIA, and TIGRESS on synthetic datasets with high co-expression among TFs, similar to that seen in real data. A key advantage of the new approach is its robustness to relatively small numbers of conditions (columns) in the expression matrix, which is a common problem faced by existing methods. Finally, we evaluate SPREd on real data sets in yeast that represent gold-standard benchmarks of GRN reconstruction and show it to perform significantly better than or comparably to existing methods. In addition to its high accuracy and speed, SPREd marks a first step toward incorporating biophysics principles of gene regulation into ML-based approaches to GRN reconstruction. Data and code are available from https://github.com/iiiime/SPREd.

Filter feature selection based Boolean Modelling for Genetic Network Inference

Background: The reconstruction of gene regulatory networks (GRN) using gene expression data can gain new insights into the causality of transcriptional and cellular processes that make a complex living system. Dynamic Bayesian network (DBN) modeling has been increasingly used to reconstruct GRN for the temporal pattern of transcriptional interactions in a time course, but this approach requires expression data measured at even time intervals. In practice, time points at which gene expression is recorded are usually uneven-spaced, determined on the basis of distinct phases of biological processes. We reform DBN modeling to accommodate to any possible irregularity and sparsity of time course microarray data.