GeneNetTools: tests for Gaussian graphical models with shrinkage

MOTIVATION

Gaussian graphical models (GGMs) are network representations of random variables (as nodes) and their partial correlations (as edges). GGMs overcome the challenges of high-dimensional data analysis by using shrinkage methodologies. Therefore, they have become useful to reconstruct gene regulatory networks from gene-expression profiles. However, it is often ignored that the partial correlations are 'shrunk' and that they cannot be compared/assessed directly. Therefore, accurate (differential) network analyses need to account for the number of variables, the sample size, and also the shrinkage value, otherwise, the analysis and its biological interpretation would turn biased. To date, there are no appropriate methods to account for these factors and address these issues.

RESULTS

We derive the statistical properties of the partial correlation obtained with the Ledoit-Wolf shrinkage. Our result provides a toolbox for (differential) network analyses as (i) confidence intervals, (ii) a test for zero partial correlation (null-effects) and (iii) a test to compare partial correlations. Our novel (parametric) methods account for the number of variables, the sample size and the shrinkage values. Additionally, they are computationally fast, simple to implement and require only basic statistical knowledge. Our simulations show that the novel tests perform better than DiffNetFDR-a recently published alternative-in terms of the trade-off between true and false positives. The methods are demonstrated on synthetic data and two gene-expression datasets from Escherichia coli and Mus musculus.

AVAILABILITY AND IMPLEMENTATION

The R package with the methods and the R script with the analysis are available in https://github.com/V-Bernal/GeneNetTools.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Inferring Gene Co-Expression Networks by Incorporating Prior Protein-Protein Interaction Networks

Inferring gene co-expression networks from high-throughput gene expression data is an important task in bioinformatics. Many gene networks often exhibit modular structures. Although several Gaussian graphical model-based methods have been developed to estimate gene co-expression networks by incorporating the modular structural prior, none of them takes into account the modular structures captured by the prior networks (e.g., protein interaction networks). In this study, we propose a novel prior network-dependent gene network inference (pGNI) method to estimate gene co-expression networks by integrating gene expression data and prior protein interaction network data. The underlying modular structure is learned from both sets of data. Through simulation studies, we demonstrate the feasibility and effectiveness of our method. We also apply our method to two real datasets. The modular structures in the networks estimated by our method are biological significant.

Identifying Gene Network Rewiring Based on Partial Correlation

It is an important task to learn how gene regulatory networks change under different conditions. Several Gaussian graphical model-based methods have been proposed to deal with this task by inferring differential networks from gene expression data. However, most existing methods define the differential networks as the difference of precision matrices, which may include false differential edges caused by the change of conditional variances. In addition, prior information about the condition-specific networks and the differential networks can be obtained from other domains. It is useful to incorporate prior information into differential network analysis. In this study, we propose a new differential network analysis method to address the above challenges. Instead of using the precision matrices, we define the differential networks as the difference of partial correlations, which can exclude the spurious differential edges due to the variants of conditional variances. Furthermore, prior information from multiple hypothesis testing is incorporated using a weighted fused penalty. Simulation studies show that our method outperforms the competing methods. We also apply our method to identify the differential network between luminal A and basal-like subtypes of breast cancers and the differential network between acute myeloid leukemia tumors and normal samples. The hub genes in the differential networks identified by our method carry out important biological functions.

Differential network analysis by simultaneously considering changes in gene interactions and gene expression

MOTIVATION

Differential network analysis is an important tool to investigate the rewiring of gene interactions under different conditions. Several computational methods have been developed to estimate differential networks from gene expression data, but most of them do not consider that gene network rewiring may be driven by the differential expression of individual genes. New differential network analysis methods that simultaneously take account of the changes in gene interactions and changes in expression levels are needed.

RESULTS

In this paper, we propose a differential network analysis method that considers the differential expression of individual genes when identifying differential edges. First, two hypothesis test statistics are used to quantify changes in partial correlations between gene pairs and changes in expression levels for individual genes. Then, an optimization framework is proposed to combine the two test statistics so that the resulting differential network has a hierarchical property, where a differential edge can be considered only if at least one of the two involved genes is differentially expressed. Simulation results indicate that our method outperforms current state-of-the-art methods. We apply our method to identify the differential networks between the luminal A and basal-like subtypes of breast cancer and those between acute myeloid leukemia and normal samples. Hub nodes in the differential networks estimated by our method, including both differentially and non-differentially expressed genes, have important biological functions.

AVAILABILITY

The source code is available at https://github.com/Zhangxf-ccnu/chNet.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Time-Varying Differential Network Analysis for Revealing Network Rewiring over Cancer Progression

To reveal how gene regulatory networks change over cancer development, multiple time-varying differential networks between adjacent cancer stages should be estimated simultaneously. Since the network rewiring may be driven by the perturbation of certain individual genes, there may be some hub nodes shared by these differential networks. Although several methods have been developed to estimate differential networks from gene expression data, most of them are designed for estimating a single differential network, which neglect the similarities between different differential networks. In this article, we propose a new Gaussian graphical model-based method to jointly estimate multiple time-varying differential networks for identifying network rewiring over cancer development. A D-trace loss is used to determine the differential networks. A tree-structured group Lasso penalty is designed to identify the common hub nodes shared by different differential networks and the specific hub nodes unique to individual differential networks. Simulation experiment results demonstrate that our method outperforms other state-of-the-art techniques in most cases. We also apply our method to The Cancer Genome Atlas data to explore gene network rewiring over different breast cancer stages. Hub nodes in the estimated differential networks rediscover well known genes associated with the development and progression of breast cancer.

A Joint Graphical Model for Inferring Gene Networks Across Multiple Subpopulations and Data Types

Reconstructing gene networks from gene expression data is a long-standing challenge. In most applications, the observations can be divided into several distinct but related subpopulations and the gene expression measurements can be collected from multiple data types. Most existing methods are designed to estimate a single gene network from a single dataset. These methods may be suboptimal since they do not exploit the similarities and differences among different subpopulations and data types. In this article, we propose a joint graphical model to estimate the multiple gene networks simultaneously. Our model decomposes each subpopulation-specific gene network as a sum of common and unique components and imposes a group lasso penalty on gene networks corresponding to different data types. The gene network variations across subpopulations can be learned automatically by the decompositions of networks, and the similarities and differences among data types can be captured by the group lasso penalty. The simulation studies demonstrate that our method outperforms the state-of-the-art methods. We also apply our method to the cancer genome atlas breast cancer datasets to reconstruct subtype-specific gene networks. Hub nodes in the estimated subnetworks unique to individual cancer subtypes rediscover well-known genes associated with breast cancer subtypes and provide interesting predictions.

Joint reconstruction of multiple gene networks by simultaneously capturing inter-tumor and intra-tumor heterogeneity

MOTIVATION

Reconstruction of cancer gene networks from gene expression data is important for understanding the mechanisms underlying human cancer. Due to heterogeneity, the tumor tissue samples for a single cancer type can be divided into multiple distinct subtypes (inter-tumor heterogeneity) and are composed of non-cancerous and cancerous cells (intra-tumor heterogeneity). If tumor heterogeneity is ignored when inferring gene networks, the edges specific to individual cancer subtypes and cell types cannot be characterized. However, most existing network reconstruction methods do not simultaneously take inter-tumor and intra-tumor heterogeneity into account.

RESULTS

In this article, we propose a new Gaussian graphical model-based method for jointly estimating multiple cancer gene networks by simultaneously capturing inter-tumor and intra-tumor heterogeneity. Given gene expression data of heterogeneous samples for different cancer subtypes, a non-cancerous network shared across different cancer subtypes and multiple subtype-specific cancerous networks are estimated jointly. Tumor heterogeneity can be revealed by the difference in the estimated networks. The performance of our method is first evaluated using simulated data, and the results indicate that our method outperforms other state-of-the-art methods. We also apply our method to The Cancer Genome Atlas breast cancer data to reconstruct non-cancerous and subtype-specific cancerous gene networks. Hub nodes in the networks estimated by our method perform important biological functions associated with breast cancer development and subtype classification.

AVAILABILITY AND IMPLEMENTATION

The source code is available at https://github.com/Zhangxf-ccnu/NETI2.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

DiNeR: a Differential graphical model for analysis of co-regulation Network Rewiring

BACKGROUND

During transcription, numerous transcription factors (TFs) bind to targets in a highly coordinated manner to control the gene expression. Alterations in groups of TF-binding profiles (i.e. "co-binding changes") can affect the co-regulating associations between TFs (i.e. "rewiring the co-regulator network"). This, in turn, can potentially drive downstream expression changes, phenotypic variation, and even disease. However, quantification of co-regulatory network rewiring has not been comprehensively studied.

RESULTS

To address this, we propose DiNeR, a computational method to directly construct a differential TF co-regulation network from paired disease-to-normal ChIP-seq data. Specifically, DiNeR uses a graphical model to capture the gained and lost edges in the co-regulation network. Then, it adopts a stability-based, sparsity-tuning criterion -- by sub-sampling the complete binding profiles to remove spurious edges -- to report only significant co-regulation alterations. Finally, DiNeR highlights hubs in the resultant differential network as key TFs associated with disease. We assembled genome-wide binding profiles of 104 TFs in the K562 and GM12878 cell lines, which loosely model the transition between normal and cancerous states in chronic myeloid leukemia (CML). In total, we identified 351 significantly altered TF co-regulation pairs. In particular, we found that the co-binding of the tumor suppressor BRCA1 and RNA polymerase II, a well-known transcriptional pair in healthy cells, was disrupted in tumors. Thus, DiNeR successfully extracted hub regulators and discovered well-known risk genes.

CONCLUSIONS

Our method DiNeR makes it possible to quantify changes in co-regulatory networks and identify alterations to TF co-binding patterns, highlighting key disease regulators. Our method DiNeR makes it possible to quantify changes in co-regulatory networks and identify alterations to TF co-binding patterns, highlighting key disease regulators.

DiffNetFDR: differential network analysis with false discovery rate control

SUMMARY

To identify biological network rewiring under different conditions, we develop a user-friendly R package, named DiffNetFDR, to implement two methods developed for testing the difference in different Gaussian graphical models. Compared to existing tools, our methods have the following features: (i) they are based on Gaussian graphical models which can capture the changes of conditional dependencies; (ii) they determine the tuning parameters in a data-driven manner; (iii) they take a multiple testing procedure to control the overall false discovery rate; and (iv) our approach defines the differential network based on partial correlation coefficients so that the spurious differential edges caused by the variants of conditional variances can be excluded. We also develop a Shiny application to provide easier analysis and visualization. Simulation studies are conducted to evaluate the performance of our methods. We also apply our methods to two real gene expression datasets. The effectiveness of our methods is validated by the biological significance of the identified differential networks.

AVAILABILITY AND IMPLEMENTATION

R package and Shiny app are available at https://github.com/Zhangxf-ccnu/DiffNetFDR.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Identifying Gene Network Rewiring Using Robust Differential Graphical Model with Multivariate t-Distribution

Identifying gene network rewiring under different biological conditions is important for understanding the mechanisms underlying complex diseases. Gaussian graphical models, which assume the data follow the multivariate normal distribution, are widely used to identify gene network rewiring. However, the normality assume often fails in reality since the data are contaminated by extreme outliers in general. In this study, we propose a new robust differential graphical model to identify gene network rewiring between two conditions based on the multivariate t-distribution. The multivariate t-distribution is more robust to outliers than the normal distribution since it has heavy tails and allows values far from the mean. A fused lasso penalty is used to borrow information across conditions to improve the results. We develop an expectation maximization algorithm to solve the optimization model. Experiment results on simulated data show that our method outperforms the state-of-the-art methods. Our method is also applied to identify gene network rewiring between luminal A and basal-like subtypes of breast cancer, and gene network rewiring between the proneural and mesenchymal subtypes of glioblastoma. Several key genes which drive gene network rewiring are discovered.