iDDN: determining trans-omics network structure and rewiring with integrative differential dependency networks

Abstract

Motivation: Mapping the gene networks that drive disease progression allows identifying molecules that rectify the network by normalizing pivotal regulatory elements. Upon mechanistic validation, these upstream normalizers represent attractive targets for developing therapeutic interventions to prevent the initiation or interrupt the pathways of disease progression. Differential network analysis aims to detect significant rewiring of regulatory network structures under different conditions. With few exceptions, most existing tools are limited to inferring differential networks from single-omics data that could be incomplete and prone to collapse when trans-omics multifactorial regulatory mechanisms are involved.

Results: We previously developed an efficient differential network analysis method-Differential Dependency Networks (DDN), that enables joint learning of common network structure and rewiring under different conditions. We now introduce the integrative DDN (iDDN) tool that extends this framework with biologically principled designs to make robust multi-omics differential network inferences. The comparative experimental evaluations on both realistic simulations and case studies show that iDDN can help biologists more accurately identify, in a study-specific and often unknown trans-omics regulatory circuitry, a network of differentially wired molecules potentially responsible for phenotypic transitions.

Availability and implementation: The Python package of iDDN is available at https://github.com/cbil-vt/iDDN. A user's guide is provided at https://iddn.readthedocs.io/.

Figure 1.

Overview of the iDDN workflow and key features. (A) iDDN workflow. iDDN is designed to accurately and efficiently infer common and differential networks (top left) from multi-omics data under two conditions (top right). It is a user-friendly Python package that enables users to define omics layers, incorporate prior constraints (bottom left), efficiently infer networks, tune hyperparameters, and visualize the results (bottom right). (B) Multi-omics data integration. iDDN models relationships among molecules both within and across multiple omics layers. The figure illustrates a network integrating three types of omics data. (C) Incorporating prior constraints. iDDN allows for the inclusion of prior known regulatory relationships as constraints in the optimization process. The example highlights the specification of known TF-target gene relationships as allowable edges in iDDN.

Figure 2.

Simulation studies of iDDN. (A) Integration of multiple layers improves the estimation accuracy of mRNA layer. Each line represents one combination of layers. For the first case, results using DDN3.0 are shown. Top: Partial Receiver Operating Characteristic (pROC) curves for estimating the common network between two conditions. These curves are generated by varying the ${\lambda }_1$ values, with ${\lambda }_2$ selected to achieve the best $F_1$ score for each ${\lambda }_1$. The annotated number represents the area under the pROC curve [normalized by the false positive rate (FPR) cutoff]. Bottom: $F_1$ scores versus ${\lambda }_1$ values for estimating the differential network. The highest $F_1$ score for each method is annotated, corresponding to the order in the top figure. (B) Incorporation of prior constraints enhances performance. A higher “mask out” ratio corresponds to stronger constraints. Results from DDN3.0 are shown when no constraints are applied. Top: pROC results for common network inference. Bottom: Results for differential network inference. (C) Comparison of iDDN, JGL, and iDINGO. Constraints used by iDDN are post-applied to JGL and iDINGO. Top: pROC results for common network inference, Bottom: Differential network results. Note that the differential network results for iDINGO fall below the y-axis range in the bottom figures.

Figure 3.

Application of iDDN on CPTAC ovarian cancer data with HRD+ and HRD− samples. (A) The common and differential networks inferred by iDDN. Common edges (static dependencies), as well as differential edges for each HRD group, are depicted. TFs are shown as triangles, and target mRNAs are displayed as circles. The thickness of each edge corresponds to the weight of the connection. (B) A focused subset of (A) highlighting biologically significant network rewiring. Hub nodes are marked with thick outlines. Two key genes, HDAC2 and RBBP4, are emphasized with arrows.

Figure 4.

Application of iDDN on GPAA coronary artery RNA-seq and proteomics data. (A) Differential network estimated by iDDN. TFs are shown on the left, while signature gene mRNAs are on the right. The size of each node corresponds to its degree. Lines with different colors are used to represent edges only in the NL (normal) condition or edges only in the FP (disease) condition. (B) Cluster-gram linking hub TFs in the differential network to their corresponding enriched pathways, based on the BioPlanet 2019 database in Enrichr. Columns represent enriched terms, and rows correspond to input genes. Each matrix element indicates whether a gene is associated with a specific term. (C) Top hub TFs in the differential network derived from GPAA data. Only TFs with at least six rewired edges between the two conditions are shown.