Reconstruction of large-scale regulatory networks based on perturbation graphs and transitive reduction: improved methods and their evaluation

Identification of marginal causal relationships in gene networks from observational and interventional expression data

Causal network inference is an important methodological challenge in biology as well as other areas of application. Although several causal network inference methods have been proposed in recent years, they are typically applicable for only a small number of genes, due to the large number of parameters to be estimated and the limited number of biological replicates available. In this work, we consider the specific case of transcriptomic studies made up of both observational and interventional data in which a single gene of biological interest is knocked out. We focus on a marginal causal estimation approach, based on the framework of Gaussian directed acyclic graphs, to infer causal relationships between the knocked-out gene and a large set of other genes. In a simulation study, we found that our proposed method accurately differentiates between downstream causal relationships and those that are upstream or simply associative. It also enables an estimation of the total causal effects between the gene of interest and the remaining genes. Our method performed very similarly to a classical differential analysis for experiments with a relatively large number of biological replicates, but has the advantage of providing a formal causal interpretation. Our proposed marginal causal approach is computationally efficient and may be applied to several thousands of genes simultaneously. In addition, it may help highlight subsets of genes of interest for a more thorough subsequent causal network inference. The method is implemented in an R package called MarginalCausality (available on GitHub).

TRaCE+: Ensemble inference of gene regulatory networks from transcriptional expression profiles of gene knock-out experiments

Background

The inference of gene regulatory networks (GRNs) from transcriptional expression profiles is challenging, predominantly due to its underdetermined nature. One important consequence of underdetermination is the existence of many possible solutions to this inference. Our previously proposed ensemble inference algorithm TRaCE addressed this issue by inferring an ensemble of network directed graphs (digraphs) using differential gene expressions from gene knock-out (KO) experiments. However, TRaCE could not deal with the mode of the transcriptional regulations (activation or repression), an important feature of GRNs.

Results

In this work, we developed a new algorithm called TRaCE+ for the inference of an ensemble of signed GRN digraphs from transcriptional expression data of gene KO experiments. The sign of the edges indicates whether the regulation is an activation (positive) or a repression (negative). TRaCE+ generates the upper and lower bounds of the ensemble, which define uncertain regulatory interactions that could not be verified by the data. As demonstrated in the case studies using Escherichia coli GRN and 100-gene gold-standard GRNs from DREAM 4 network inference challenge, by accounting for regulatory signs, TRaCE+ could extract more information from the KO data than TRaCE, leading to fewer uncertain edges. Importantly, iterating TRaCE+ with an optimal design of gene KOs could resolve the underdetermined issue of GRN inference in much fewer KO experiments than using TRaCE.

Conclusions

TRaCE+ expands the applications of ensemble GRN inference strategy by accounting for the mode of the gene regulatory interactions. In comparison to TRaCE, TRaCE+ enables a better utilization of gene KO data, thereby reducing the cost of tackling underdetermined GRN inference. TRaCE+ subroutines for MATLAB are freely available at the following website: http://www.cabsel.ethz.ch/tools/trace.html.

Data- and knowledge-based modeling of gene regulatory networks: an update

Gene regulatory network inference is a systems biology approach which predicts interactions between genes with the help of high-throughput data. In this review, we present current and updated network inference methods focusing on novel techniques for data acquisition, network inference assessment, network inference for interacting species and the integration of prior knowledge. After the advance of Next-Generation-Sequencing of cDNAs derived from RNA samples (RNA-Seq) we discuss in detail its application to network inference. Furthermore, we present progress for large-scale or even full-genomic network inference as well as for small-scale condensed network inference and review advances in the evaluation of network inference methods by crowdsourcing. Finally, we reflect the current availability of data and prior knowledge sources and give an outlook for the inference of gene regulatory networks that reflect interacting species, in particular pathogen-host interactions.

Joint estimation of causal effects from observational and intervention gene expression data

Background

In recent years, there has been great interest in using transcriptomic data to infer gene regulatory networks. For the time being, methodological development in this area has primarily made use of graphical Gaussian models for observational wild-type data, resulting in undirected graphs that are not able to accurately highlight causal relationships among genes. In the present work, we seek to improve the estimation of causal effects among genes by jointly modeling observational transcriptomic data with arbitrarily complex intervention data obtained by performing partial, single, or multiple gene knock-outs or knock-downs.

Results

Using the framework of causal Gaussian Bayesian networks, we propose a Markov chain Monte Carlo algorithm with a Mallows proposal model and analytical likelihood maximization to sample from the posterior distribution of causal node orderings, and in turn, to estimate causal effects. The main advantage of the proposed algorithm over previously proposed methods is its flexibility to accommodate any kind of intervention design, including partial or multiple knock-out experiments. Using simulated data as well as data from the Dialogue for Reverse Engineering Assessments and Methods (DREAM) 2007 challenge, the proposed method was compared to two alternative approaches: one requiring a complete, single knock-out design, and one able to model only observational data.

Conclusions

The proposed algorithm was found to perform as well as, and in most cases better, than the alternative methods in terms of accuracy for the estimation of causal effects. In addition, multiple knock-outs proved to contribute valuable additional information compared to single knock-outs. Finally, the simulation study confirmed that it is not possible to estimate the causal ordering of genes from observational data alone. In all cases, we found that the inclusion of intervention experiments enabled more accurate estimation of causal regulatory relationships than the use of wild-type data alone.