Exact hypothesis testing for shrinkage-based Gaussian graphical models

Information-incorporated gene network construction with FDR control

MOTIVATION

Large-scale gene expression studies allow gene network construction to uncover associations among genes. To study direct associations among genes, partial correlation-based networks are preferred over marginal correlations. However, FDR control for partial correlation-based network construction is not well-studied. In addition, currently available partial correlation-based methods cannot take existing biological knowledge to help network construction while controlling FDR.

RESULTS

In this paper, we propose a method called Partial Correlation Graph with Information Incorporation (PCGII). PCGII estimates partial correlations between each pair of genes by regularized node-wise regression that can incorporate prior knowledge while controlling the effects of all other genes. It handles high-dimensional data where the number of genes can be much larger than the sample size and controls FDR at the same time. We compare PCGII with several existing approaches through extensive simulation studies and demonstrate that PCGII has better FDR control and higher power. We apply PCGII to a plant gene expression dataset where it recovers confirmed regulatory relationships and a hub node, as well as several direct associations that shed light on potential functional relationships in the system. We also introduce a method to supplement observed data with a pseudogene to apply PCGII when no prior information is available, which also allows checking FDR control and power for real data analysis.

AVAILABILITY AND IMPLEMENTATION

R package is freely available for download at https://cran.r-project.org/package=PCGII.

Childhood exposure to non-persistent endocrine disrupting chemicals and multi-omic profiles: A panel study

BACKGROUND

Individuals are exposed to environmental pollutants with endocrine disrupting activity (endocrine disruptors, EDCs) and the early stages of life are particularly susceptible to these exposures. Previous studies have focused on identifying molecular signatures associated with EDCs, but none have used repeated sampling strategy and integrated multiple omics. We aimed to identify multi-omic signatures associated with childhood exposure to non-persistent EDCs.

METHODS

We used data from the HELIX Child Panel Study, which included 156 children aged 6 to 11. Children were followed for one week, in two time periods. Twenty-two non-persistent EDCs (10 phthalate, 7 phenol, and 5 organophosphate pesticide metabolites) were measured in two weekly pools of 15 urine samples each. Multi-omic profiles (methylome, serum and urinary metabolome, proteome) were measured in blood and in a pool urine samples. We developed visit-specific Gaussian Graphical Models based on pairwise partial correlations. The visit-specific networks were then merged to identify reproducible associations. Independent biological evidence was systematically sought to confirm some of these associations and assess their potential health implications.

RESULTS

950 reproducible associations were found among which 23 were direct associations between EDCs and omics. For 9 of them, we were able to find corroborating evidence from previous literature: DEP - serotonin, OXBE - cg27466129, OXBE - dimethylamine, triclosan - leptin, triclosan - serotonin, MBzP - Neu5AC, MEHP - cg20080548, oh-MiNP - kynurenine, oxo-MiNP - 5-oxoproline. We used these associations to explore possible mechanisms between EDCs and health outcomes, and found links to health outcomes for 3 analytes: serotonin and kynurenine in relation to neuro-behavioural development, and leptin in relation to obesity and insulin resistance.

CONCLUSIONS

This multi-omics network analysis at two time points identified biologically relevant molecular signatures related to non-persistent EDC exposure in childhood, suggesting pathways related to neurological and metabolic outcomes.

DRAGON: Determining Regulatory Associations using Graphical models on multi-Omic Networks

The increasing quantity of multi-omic data, such as methylomic and transcriptomic profiles collected on the same specimen or even on the same cell, provides a unique opportunity to explore the complex interactions that define cell phenotype and govern cellular responses to perturbations. We propose a network approach based on Gaussian Graphical Models (GGMs) that facilitates the joint analysis of paired omics data. This method, called DRAGON (Determining Regulatory Associations using Graphical models on multi-Omic Networks), calibrates its parameters to achieve an optimal trade-off between the network's complexity and estimation accuracy, while explicitly accounting for the characteristics of each of the assessed omics 'layers.' In simulation studies, we show that DRAGON adapts to edge density and feature size differences between omics layers, improving model inference and edge recovery compared to state-of-the-art methods. We further demonstrate in an analysis of joint transcriptome - methylome data from TCGA breast cancer specimens that DRAGON can identify key molecular mechanisms such as gene regulation via promoter methylation. In particular, we identify Transcription Factor AP-2 Beta (TFAP2B) as a potential multi-omic biomarker for basal-type breast cancer. DRAGON is available as open-source code in Python through the Network Zoo package (netZooPy v0.8; netzoo.github.io).

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.

The 'un-shrunk' partial correlation in Gaussian graphical models

BACKGROUND

In systems biology, it is important to reconstruct regulatory networks from quantitative molecular profiles. Gaussian graphical models (GGMs) are one of the most popular methods to this end. A GGM consists of nodes (representing the transcripts, metabolites or proteins) inter-connected by edges (reflecting their partial correlations). Learning the edges from quantitative molecular profiles is statistically challenging, as there are usually fewer samples than nodes ('high dimensional problem'). Shrinkage methods address this issue by learning a regularized GGM. However, it remains open to study how the shrinkage affects the final result and its interpretation.

RESULTS

We show that the shrinkage biases the partial correlation in a non-linear way. This bias does not only change the magnitudes of the partial correlations but also affects their order. Furthermore, it makes networks obtained from different experiments incomparable and hinders their biological interpretation. We propose a method, referred to as 'un-shrinking' the partial correlation, which corrects for this non-linear bias. Unlike traditional methods, which use a fixed shrinkage value, the new approach provides partial correlations that are closer to the actual (population) values and that are easier to interpret. This is demonstrated on two gene expression datasets from Escherichia coli and Mus musculus.

CONCLUSIONS

GGMs are popular undirected graphical models based on partial correlations. The application of GGMs to reconstruct regulatory networks is commonly performed using shrinkage to overcome the 'high-dimensional problem'. Besides it advantages, we have identified that the shrinkage introduces a non-linear bias in the partial correlations. Ignoring this type of effects caused by the shrinkage can obscure the interpretation of the network, and impede the validation of earlier reported results.

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.

Network Modeling Approaches and Applications to Unravelling Non-Alcoholic Fatty Liver Disease

Non-alcoholic fatty liver disease (NAFLD) is a progressive condition of the liver encompassing a range of pathologies including steatosis, non-alcoholic steatohepatitis (NASH), cirrhosis, and hepatocellular carcinoma. Research into this disease is imperative due to its rapid growth in prevalence, economic burden, and current lack of FDA approved therapies. NAFLD involves a highly complex etiology that calls for multi-tissue multi-omics network approaches to uncover the pathogenic genes and processes, diagnostic biomarkers, and potential therapeutic strategies. In this review, we first present a basic overview of disease pathogenesis, risk factors, and remaining knowledge gaps, followed by discussions of the need and concepts of multi-tissue multi-omics approaches, various network methodologies and application examples in NAFLD research. We highlight the findings that have been uncovered thus far including novel biomarkers, genes, and biological pathways involved in different stages of NAFLD, molecular connections between NAFLD and its comorbidities, mechanisms underpinning sex differences, and druggable targets. Lastly, we outline the future directions of implementing network approaches to further improve our understanding of NAFLD in order to guide diagnosis and therapeutics.

Gene network approach reveals co-expression patterns in nasal and bronchial epithelium

Nasal gene expression profiling is a new approach to investigate the airway epithelium as a biomarker to study the activity and treatment responses of obstructive pulmonary diseases. We investigated to what extent gene expression profiling of nasal brushings is similar to that of bronchial brushings. We performed genome wide gene expression profiling on matched nasal and bronchial epithelial brushes from 77 respiratory healthy individuals. To investigate differences and similarities among regulatory modules, network analysis was performed on correlated, differentially expressed and smoking-related genes using Gaussian Graphical Models. Between nasal and bronchial brushes, 619 genes were correlated and 1692 genes were differentially expressed (false discovery rate <0.05, |Fold-change|>2). Network analysis of correlated genes showed pro-inflammatory pathways to be similar between the two locations. Focusing on smoking-related genes, cytochrome-P450 pathway related genes were found to be similar, supporting the concept of a detoxifying response to tobacco exposure throughout the airways. In contrast, cilia-related pathways were decreased in nasal compared to bronchial brushes when focusing on differentially expressed genes. Collectively, while there are substantial differences in gene expression between nasal and bronchial brushes, we also found similarities, especially in the response to the external factors such as smoking.