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

Estimation of multiple networks with common structures in heterogeneous subgroups

Network estimation has been a critical component of high-dimensional data analysis and can provide an understanding of the underlying complex dependence structures. Among the existing studies, Gaussian graphical models have been highly popular. However, they still have limitations due to the homogeneous distribution assumption and the fact that they are only applicable to small-scale data. For example, cancers have various levels of unknown heterogeneity, and biological networks, which include thousands of molecular components, often differ across subgroups while also sharing some commonalities. In this article, we propose a new joint estimation approach for multiple networks with unknown sample heterogeneity, by decomposing the Gaussian graphical model (GGM) into a collection of sparse regression problems. A reparameterization technique and a composite minimax concave penalty are introduced to effectively accommodate the specific and common information across the networks of multiple subgroups, making the proposed estimator significantly advancing from the existing heterogeneity network analysis based on the regularized likelihood of GGM directly and enjoying scale-invariant, tuning-insensitive, and optimization convexity properties. The proposed analysis can be effectively realized using parallel computing. The estimation and selection consistency properties are rigorously established. The proposed approach allows the theoretical studies to focus on independent network estimation only and has the significant advantage of being both theoretically and computationally applicable to large-scale data. Extensive numerical experiments with simulated data and the TCGA breast cancer data demonstrate the prominent performance of the proposed approach in both subgroup and network identifications.

Application of fused graphical lasso to statistical inference for multiple sparse precision matrices

In this paper, the fused graphical lasso (FGL) method is used to estimate multiple precision matrices from multiple populations simultaneously. The lasso penalty in the FGL model is a restraint on sparsity of precision matrices, and a moderate penalty on the two precision matrices from distinct groups restrains the similar structure across multiple groups. In high-dimensional settings, an oracle inequality is provided for FGL estimators, which is necessary to establish the central limit law. We not only focus on point estimation of a precision matrix, but also work on hypothesis testing for a linear combination of the entries of multiple precision matrices. We apply a de-biasing technology, which is used to obtain a new consistent estimator with known distribution for implementing the statistical inference, and extend the statistical inference problem to multiple populations. The corresponding de-biasing FGL estimator and its asymptotic theory are provided. A simulation study and an application of the diffuse large B-cell lymphoma data show that the proposed test works well in high-dimensional situation.

DeepGRNCS: deep learning-based framework for jointly inferring gene regulatory networks across cell subpopulations

Inferring gene regulatory networks (GRNs) allows us to obtain a deeper understanding of cellular function and disease pathogenesis. Recent advances in single-cell RNA sequencing (scRNA-seq) technology have improved the accuracy of GRN inference. However, many methods for inferring individual GRNs from scRNA-seq data are limited because they overlook intercellular heterogeneity and similarities between different cell subpopulations, which are often present in the data. Here, we propose a deep learning-based framework, DeepGRNCS, for jointly inferring GRNs across cell subpopulations. We follow the commonly accepted hypothesis that the expression of a target gene can be predicted based on the expression of transcription factors (TFs) due to underlying regulatory relationships. We initially processed scRNA-seq data by discretizing data scattering using the equal-width method. Then, we trained deep learning models to predict target gene expression from TFs. By individually removing each TF from the expression matrix, we used pre-trained deep model predictions to infer regulatory relationships between TFs and genes, thereby constructing the GRN. Our method outperforms existing GRN inference methods for various simulated and real scRNA-seq datasets. Finally, we applied DeepGRNCS to non-small cell lung cancer scRNA-seq data to identify key genes in each cell subpopulation and analyzed their biological relevance. In conclusion, DeepGRNCS effectively predicts cell subpopulation-specific GRNs. The source code is available at https://github.com/Nastume777/DeepGRNCS.

Inferring cancer common and specific gene networks via multi-layer joint graphical model

Cancer is a complex disease caused primarily by genetic variants. Reconstructing gene networks within tumors is essential for understanding the functional regulatory mechanisms of carcinogenesis. Advances in high-throughput sequencing technologies have provided tremendous opportunities for inferring gene networks via computational approaches. However, due to the heterogeneity of the same cancer type and the similarities between different cancer types, it remains a challenge to systematically investigate the commonalities and specificities between gene networks of different cancer types, which is a crucial step towards precision cancer diagnosis and treatment. In this study, we propose a new sparse regularized multi-layer decomposition graphical model to jointly estimate the gene networks of multiple cancer types. Our model can handle various types of gene expression data and decomposes each cancer-type-specific network into three components, i.e., globally shared, partially shared and cancer-type-unique components. By identifying the globally and partially shared gene network components, our model can explore the heterogeneous similarities between different cancer types, and our identified cancer-type-unique components can help to reveal the regulatory mechanisms unique to each cancer type. Extensive experiments on synthetic data illustrate the effectiveness of our model in joint estimation of multiple gene networks. We also apply our model to two real data sets to infer the gene networks of multiple cancer subtypes or cell lines. By analyzing our estimated globally shared, partially shared, and cancer-type-unique components, we identified a number of important genes associated with common and specific regulatory mechanisms across different cancer types.

Interaction-based transcriptome analysis via differential network inference

Gene-based transcriptome analysis, such as differential expression analysis, can identify the key factors causing disease production, cell differentiation and other biological processes. However, this is not enough because basic life activities are mainly driven by the interactions between genes. Although there have been already many differential network inference methods for identifying the differential gene interactions, currently, most studies still only use the information of nodes in the network for downstream analyses. To investigate the insight into differential gene interactions, we should perform interaction-based transcriptome analysis (IBTA) instead of gene-based analysis after obtaining the differential networks. In this paper, we illustrated a workflow of IBTA by developing a Co-hub Differential Network inference (CDN) algorithm, and a novel interaction-based metric, pivot APC2. We confirmed the superior performance of CDN through simulation experiments compared with other popular differential network inference algorithms. Furthermore, three case studies are given using colorectal cancer, COVID-19 and triple-negative breast cancer datasets to demonstrate the ability of our interaction-based analytical process to uncover causative mechanisms.

Network-based cancer heterogeneity analysis incorporating multi-view of prior information

MOTIVATION

Cancer genetic heterogeneity analysis has critical implications for tumour classification, response to therapy and choice of biomarkers to guide personalized cancer medicine. However, existing heterogeneity analysis based solely on molecular profiling data usually suffers from a lack of information and has limited effectiveness. Many biomedical and life sciences databases have accumulated a substantial volume of meaningful biological information. They can provide additional information beyond molecular profiling data, yet pose challenges arising from potential noise and uncertainty.

RESULTS

In this study, we aim to develop a more effective heterogeneity analysis method with the help of prior information. A network-based penalization technique is proposed to innovatively incorporate a multi-view of prior information from multiple databases, which accommodates heterogeneity attributed to both differential genes and gene relationships. To account for the fact that the prior information might not be fully credible, we propose a weighted strategy, where the weight is determined dependent on the data and can ensure that the present model is not excessively disturbed by incorrect information. Simulation and analysis of The Cancer Genome Atlas glioblastoma multiforme data demonstrate the practical applicability of the proposed method.

AVAILABILITY AND IMPLEMENTATION

R code implementing the proposed method is available at https://github.com/mengyunwu2020/PECM. The data that support the findings in this paper are openly available in TCGA (The Cancer Genome Atlas) at https://portal.gdc.cancer.gov/.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

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.

Inferring Differential Networks by Integrating Gene Expression Data With Additional Knowledge

Evidences increasingly indicate the involvement of gene network rewiring in disease development and cell differentiation. With the accumulation of high-throughput gene expression data, it is now possible to infer the changes of gene networks between two different states or cell types via computational approaches. However, the distribution diversity of multi-platform gene expression data and the sparseness and high noise rate of single-cell RNA sequencing (scRNA-seq) data raise new challenges for existing differential network estimation methods. Furthermore, most existing methods are purely rely on gene expression data, and ignore the additional information provided by various existing biological knowledge. In this study, to address these challenges, we propose a general framework, named weighted joint sparse penalized D-trace model (WJSDM), to infer differential gene networks by integrating multi-platform gene expression data and multiple prior biological knowledge. Firstly, a non-paranormal graphical model is employed to tackle gene expression data with missing values. Then we propose a weighted group bridge penalty to integrate multi-platform gene expression data and various existing biological knowledge. Experiment results on synthetic data demonstrate the effectiveness of our method in inferring differential networks. We apply our method to the gene expression data of ovarian cancer and the scRNA-seq data of circulating tumor cells of prostate cancer, and infer the differential network associated with platinum resistance of ovarian cancer and anti-androgen resistance of prostate cancer. By analyzing the estimated differential networks, we find some important biological insights about the mechanisms underlying platinum resistance of ovarian cancer and anti-androgen resistance of prostate cancer.

WDNE: an integrative graphical model for inferring differential networks from multi-platform gene expression data with missing values

The mechanisms controlling biological process, such as the development of disease or cell differentiation, can be investigated by examining changes in the networks of gene dependencies between states in the process. High-throughput experimental methods, like microarray and RNA sequencing, have been widely used to gather gene expression data, which paves the way to infer gene dependencies based on computational methods. However, most differential network analysis methods are designed to deal with fully observed data, but missing values, such as the dropout events in single-cell RNA-sequencing data, are frequent. New methods are needed to take account of these missing values. Moreover, since the changes of gene dependencies may be driven by certain perturbed genes, considering the changes in gene expression levels may promote the identification of gene network rewiring. In this study, a novel weighted differential network estimation (WDNE) model is proposed to handle multi-platform gene expression data with missing values and take account of changes in gene expression levels. Simulation studies demonstrate that WDNE outperforms state-of-the-art differential network estimation methods. When applied WDNE to infer differential gene networks associated with drug resistance in ovarian tumors, cell differentiation and breast tumor heterogeneity, the hub genes in the estimated differential gene networks can provide important insights into the underlying mechanisms. Furthermore, a Matlab toolbox, differential network analysis toolbox, was developed to implement the WDNE model and visualize the estimated differential networks.

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.

Joint learning of multiple gene networks from single-cell gene expression data

Inferring gene networks from gene expression data is important for understanding functional organizations within cells. With the accumulation of single-cell RNA sequencing (scRNA-seq) data, it is possible to infer gene networks at single cell level. However, due to the characteristics of scRNA-seq data, such as cellular heterogeneity and high sparsity caused by dropout events, traditional network inference methods may not be suitable for scRNA-seq data. In this study, we introduce a novel joint Gaussian copula graphical model (JGCGM) to jointly estimate multiple gene networks for multiple cell subgroups from scRNA-seq data. Our model can deal with non-Gaussian data with missing values, and identify the common and unique network structures of multiple cell subgroups, which is suitable for scRNA-seq data. Extensive experiments on synthetic data demonstrate that our proposed model outperforms other compared state-of-the-art network inference models. We apply our model to real scRNA-seq data sets to infer gene networks of different cell subgroups. Hub genes in the estimated gene networks are found to be biological significance.