Inferring regulatory networks by combining perturbation screens and steady state gene expression profiles

Perturbation graphs, invariant causal prediction and causal relations in psychology

Networks (graphs) in psychology are often restricted to settings without interventions. Here we consider a framework borrowed from biology that involves multiple interventions from different contexts (observations and experiments) in a single analysis. The method is called perturbation graphs. In gene regulatory networks, the induced change in one gene is measured on all other genes in the analysis, thereby assessing possible causal relations. This is repeated for each gene in the analysis. A perturbation graph leads to the correct set of causes (not nec-essarily direct causes). Subsequent pruning of paths in the graph (called transitive reduction) should reveal direct causes. We show that transitive reduction will not in general lead to the correct underlying graph. We also show that invariant causal prediction is a generalisation of the perturbation graph method and does reveal direct causes, thereby replacing transitive re-duction. We conclude that perturbation graphs provide a promising new tool for experimental designs in psychology, and combined with invariant causal prediction make it possible to re-veal direct causes instead of causal paths. As an illustration we apply these ideas to a data set about attitudes on meat consumption and to a time series of a patient diagnosed with major depression disorder.

Non-Asymptotic Guarantees for Reliable Identification of Granger Causality via the LASSO

Granger causality is among the widely used data-driven approaches for causal analysis of time series data with applications in various areas including economics, molecular biology, and neuroscience. Two of the main challenges of this methodology are: 1) over-fitting as a result of limited data duration, and 2) correlated process noise as a confounding factor, both leading to errors in identifying the causal influences. Sparse estimation via the LASSO has successfully addressed these challenges for parameter estimation. However, the classical statistical tests for Granger causality resort to asymptotic analysis of ordinary least squares, which require long data duration to be useful and are not immune to confounding effects. In this work, we address this disconnect by introducing a LASSO-based statistic and studying its non-asymptotic properties under the assumption that the true models admit sparse autoregressive representations. We establish fundamental limits for reliable identification of Granger causal influences using the proposed LASSO-based statistic. We further characterize the false positive error probability and test power of a simple thresholding rule for identifying Granger causal effects and provide two methods to set the threshold in a data-driven fashion. We present simulation studies and application to real data to compare the performance of our proposed method to ordinary least squares and existing LASSO-based methods in detecting Granger causal influences, which corroborate our theoretical results.

A novel probabilistic generator for large-scale gene association networks

MOTIVATION

Gene expression data provide an opportunity for reverse-engineering gene-gene associations using network inference methods. However, it is difficult to assess the performance of these methods because the true underlying network is unknown in real data. Current benchmarks address this problem by subsampling a known regulatory network to conduct simulations. But the topology of regulatory networks can vary greatly across organisms or tissues, and reference-based generators-such as GeneNetWeaver-are not designed to capture this heterogeneity. This means, for example, benchmark results from the E. coli regulatory network will not carry over to other organisms or tissues. In contrast, probabilistic generators do not require a reference network, and they have the potential to capture a rich distribution of topologies. This makes probabilistic generators an ideal approach for obtaining a robust benchmarking of network inference methods.

RESULTS

We propose a novel probabilistic network generator that (1) provides an alternative to address the inherent limitation of reference-based generators and (2) is able to create realistic gene association networks, and (3) captures the heterogeneity found across gold-standard networks better than existing generators used in practice. Eight organism-specific and 12 human tissue-specific gold-standard association networks are considered. Several measures of global topology are used to determine the similarity of generated networks to the gold-standards. Along with demonstrating the variability of network structure across organisms and tissues, we show that the commonly used "scale-free" model is insufficient for replicating these structures.

AVAILABILITY

This generator is implemented in the R package "SeqNet" and is available on CRAN (https://cran.r-project.org/web/packages/SeqNet/index.html).

Identifying Dynamical Time Series Model Parameters from Equilibrium Samples, with Application to Gene Regulatory Networks

Gene regulatory network reconstruction is an essential task of genomics in order to further our understanding of how genes interact dynamically with each other. The most readily available data, however, are from steady state observations. These data are not as informative about the relational dynamics between genes as knockout or over-expression experiments, which attempt to control the expression of individual genes. We develop a new framework for network inference using samples from the equilibrium distribution of a vector autoregressive (VAR) time-series model which can be applied to steady state gene expression data. We explore the theoretical aspects of our method and apply the method to synthetic gene expression data generated using GeneNetWeaver.

Inference of gene regulatory networks with multi-objective cellular genetic algorithm

Reverse engineering of biochemical networks remains an important open challenge in computational systems biology. The goal of model inference is to, based on time-series gene expression data, obtain the sparse topological structure and parameters that quantitatively understand and reproduce the dynamics of biological systems. In this paper, we propose a multi-objective approach for the inference of S-System structures for Gene Regulatory Networks (GRNs) based on Pareto dominance and Pareto optimality theoretical concepts instead of the conventional single-objective evaluation of Mean Squared Error (MSE). Our motivation is that, using a multi-objective formulation for the GRN, it is possible to optimize the sparse topology of a given GRN as well as the kinetic order and rate constant parameters in a decoupled S-System, yet avoiding the use of additional penalty weights. A flexible and robust Multi-Objective Cellular Evolutionary Algorithm is adapted to perform the tasks of parameter learning and network topology inference for the proposed approach. The resulting software, called MONET, is evaluated on real-based academic and synthetic time-series of gene expression taken from the DREAM3 challenge and the IRMA in vivo datasets. The ability to reproduce biological behavior and robustness to noise is assessed and compared. The results obtained are competitive and indicate that the proposed approach offers advantages over previously used methods. In addition, MONET is able to provide experts with a set of trade-off solutions involving GRNs with different typologies and MSEs.

The Reduced PC-Algorithm: Improved Causal Structure Learning in Large Random Networks

We consider the task of estimating a high-dimensional directed acyclic graph, given observations from a linear structural equation model with arbitrary noise distribution. By exploiting properties of common random graphs, we develop a new algorithm that requires conditioning only on small sets of variables. The proposed algorithm, which is essentially a modified version of the PC-Algorithm, offers significant gains in both computational complexity and estimation accuracy. In particular, it results in more efficient and accurate estimation in large networks containing hub nodes, which are common in biological systems. We prove the consistency of the proposed algorithm, and show that it also requires a less stringent faithfulness assumption than the PC-Algorithm. Simulations in low and high-dimensional settings are used to illustrate these findings. An application to gene expression data suggests that the proposed algorithm can identify a greater number of clinically relevant genes than current methods.

Causal Queries from Observational Data in Biological Systems via Bayesian Networks: An Empirical Study in Small Networks

Biological networks are a very convenient modeling and visualization tool to discover knowledge from modern high-throughput genomics and post-genomics data sets. Indeed, biological entities are not isolated but are components of complex multilevel systems. We go one step further and advocate for the consideration of causal representations of the interactions in living systems. We present the causal formalism and bring it out in the context of biological networks, when the data is observational. We also discuss its ability to decipher the causal information flow as observed in gene expression. We also illustrate our exploration by experiments on small simulated networks as well as on a real biological data set.

Inference of Gene Regulatory Networks Using Bayesian Nonparametric Regression and Topology Information

Gene regulatory networks (GRNs) play an important role in cellular systems and are important for understanding biological processes. Many algorithms have been developed to infer the GRNs. However, most algorithms only pay attention to the gene expression data but do not consider the topology information in their inference process, while incorporating this information can partially compensate for the lack of reliable expression data. Here we develop a Bayesian group lasso with spike and slab priors to perform gene selection and estimation for nonparametric models. B-spline basis functions are used to capture the nonlinear relationships flexibly and penalties are used to avoid overfitting. Further, we incorporate the topology information into the Bayesian method as a prior. We present the application of our method on DREAM3 and DREAM4 datasets and two real biological datasets. The results show that our method performs better than existing methods and the topology information prior can improve the result.

A posterior probability approach for gene regulatory network inference in genetic perturbation data

Inferring gene regulatory networks is an important problem in systems biology. However, these networks can be hard to infer from experimental data because of the inherent variability in biological data as well as the large number of genes involved. We propose a fast, simple method for inferring regulatory relationships between genes from knockdown experiments in the NIH LINCS dataset by calculating posterior probabilities, incorporating prior information. We show that the method is able to find previously identified edges from TRANSFAC and JASPAR and discuss the merits and limitations of this approach.

Integrative random forest for gene regulatory network inference

Motivation: Gene regulatory network (GRN) inference based on genomic data is one of the most actively pursued computational biological problems. Because different types of biological data usually provide complementary information regarding the underlying GRN, a model that integrates big data of diverse types is expected to increase both the power and accuracy of GRN inference. Towards this goal, we propose a novel algorithm named iRafNet: integrative random forest for gene regulatory network inference.

Results: iRafNet is a flexible, unified integrative framework that allows information from heterogeneous data, such as protein–protein interactions, transcription factor (TF)-DNA-binding, gene knock-down, to be jointly considered for GRN inference. Using test data from the DREAM4 and DREAM5 challenges, we demonstrate that iRafNet outperforms the original random forest based network inference algorithm (GENIE3), and is highly comparable to the community learning approach. We apply iRafNet to construct GRN in Saccharomyces cerevisiae and demonstrate that it improves the performance in predicting TF-target gene regulations and provides additional functional insights to the predicted gene regulations.

Availability and implementation: The R code of iRafNet implementation and a tutorial are available at: http://research.mssm.edu/tulab/software/irafnet.html

Contact:zhidong.tu@mssm.edu

Supplementary information: Supplementary data are available at Bioinformatics online.

A full bayesian approach for boolean genetic network inference

Boolean networks are a simple but efficient model for describing gene regulatory systems. A number of algorithms have been proposed to infer Boolean networks. However, these methods do not take full consideration of the effects of noise and model uncertainty. In this paper, we propose a full Bayesian approach to infer Boolean genetic networks. Markov chain Monte Carlo algorithms are used to obtain the posterior samples of both the network structure and the related parameters. In addition to regular link addition and removal moves, which can guarantee the irreducibility of the Markov chain for traversing the whole network space, carefully constructed mixture proposals are used to improve the Markov chain Monte Carlo convergence. Both simulations and a real application on cell-cycle data show that our method is more powerful than existing methods for the inference of both the topology and logic relations of the Boolean network from observed data.

Comparative study of computational methods for reconstructing genetic networks of cancer-related pathways

Network reconstruction is an important yet challenging task in systems biology. While many methods have been recently proposed for reconstructing biological networks from diverse data types, properties of estimated networks and differences between reconstruction methods are not well understood. In this paper, we conduct a comprehensive empirical evaluation of seven existing network reconstruction methods, by comparing the estimated networks with different sparsity levels for both normal and tumor samples. The results suggest substantial heterogeneity in networks reconstructed using different reconstruction methods. Our findings also provide evidence for significant differences between networks of normal and tumor samples, even after accounting for the considerable variability in structures of networks estimated using different reconstruction methods. These differences can offer new insight into changes in mechanisms of genetic interaction associated with cancer initiation and progression.

Network reconstruction using nonparametric additive ODE models

Network representations of biological systems are widespread and reconstructing unknown networks from data is a focal problem for computational biologists. For example, the series of biochemical reactions in a metabolic pathway can be represented as a network, with nodes corresponding to metabolites and edges linking reactants to products. In a different context, regulatory relationships among genes are commonly represented as directed networks with edges pointing from influential genes to their targets. Reconstructing such networks from data is a challenging problem receiving much attention in the literature. There is a particular need for approaches tailored to time-series data and not reliant on direct intervention experiments, as the former are often more readily available. In this paper, we introduce an approach to reconstructing directed networks based on dynamic systems models. Our approach generalizes commonly used ODE models based on linear or nonlinear dynamics by extending the functional class for the functions involved from parametric to nonparametric models. Concomitantly we limit the complexity by imposing an additive structure on the estimated slope functions. Thus the submodel associated with each node is a sum of univariate functions. These univariate component functions form the basis for a novel coupling metric that we define in order to quantify the strength of proposed relationships and hence rank potential edges. We show the utility of the method by reconstructing networks using simulated data from computational models for the glycolytic pathway of Lactocaccus Lactis and a gene network regulating the pluripotency of mouse embryonic stem cells. For purposes of comparison, we also assess reconstruction performance using gene networks from the DREAM challenges. We compare our method to those that similarly rely on dynamic systems models and use the results to attempt to disentangle the distinct roles of linearity, sparsity, and derivative estimation.

Review on statistical methods for gene network reconstruction using expression data

Network modeling has proven to be a fundamental tool in analyzing the inner workings of a cell. It has revolutionized our understanding of biological processes and made significant contributions to the discovery of disease biomarkers. Much effort has been devoted to reconstruct various types of biochemical networks using functional genomic datasets generated by high-throughput technologies. This paper discusses statistical methods used to reconstruct gene regulatory networks using gene expression data. In particular, we highlight progress made and challenges yet to be met in the problems involved in estimating gene interactions, inferring causality and modeling temporal changes of regulation behaviors. As rapid advances in technologies have made available diverse, large-scale genomic data, we also survey methods of incorporating all these additional data to achieve better, more accurate inference of gene networks.