Gene co-expression networks capture biologically important patterns in gene expression data, enabling functional analyses of genes, discovery of biomarkers, and interpretation of genetic variants. Most network analyses to date have been limited to assessing correlation between total gene expression levels in a single tissue or small sets of tissues. Here, we built networks that additionally capture the regulation of relative isoform abundance and splicing, along with tissue-specific connections unique to each of a diverse set of tissues. We used the Genotype-Tissue Expression (GTEx) project v6 RNA sequencing data across 50 tissues and 449 individuals. First, we developed a framework called Transcriptome-Wide Networks (TWNs) for combining total expression and relative isoform levels into a single sparse network, capturing the interplay between the regulation of splicing and transcription. We built TWNs for 16 tissues and found that hubs in these networks were strongly enriched for splicing and RNA binding genes, demonstrating their utility in unraveling regulation of splicing in the human transcriptome. Next, we used a Bayesian biclustering model that identifies network edges unique to a single tissue to reconstruct Tissue-Specific Networks (TSNs) for 26 distinct tissues and 10 groups of related tissues. Finally, we found genetic variants associated with pairs of adjacent nodes in our networks, supporting the estimated network structures and identifying 20 genetic variants with distant regulatory impact on transcription and splicing. Our networks provide an improved understanding of the complex relationships of the human transcriptome across tissues.

Graph Neural Networks (GNNs) have achieved state-of-the-art results on many graph analysis tasks such as node classification and link prediction. However, important unsupervised problems on graphs, such as graph clustering, have proved more resistant to advances in GNNs. In this paper, we study unsupervised training of GNN pooling in terms of their clustering capabilities. We start by drawing a connection between graph clustering and graph pooling: intuitively, a good graph clustering is what one would expect from a GNN pooling layer. Counterintuitively, we show that this is not true for state-of-the-art pooling methods, such as MinCut pooling. To address these deficiencies, we introduce Deep Modularity Networks (DMON), an unsupervised pooling method inspired by the modularity measure of clustering quality, and show how it tackles recovery of the challenging clustering structure of real-world graphs. In order to clarify the regimes where existing methods fail, we carefully design a set of experiments on synthetic data which show that DMON is able to jointly leverage the signal from the graph structure and node attributes. Similarly, on real-world data, we show that DMON produces high quality clusters which correlate strongly with ground truth labels, achieving state-of-the-art results.

Summary The study of expression Quantitative Trait Loci (eQTL) is an important problem in genomics and biomedicine. While detection (testing) of eQTL associations has been widely studied, less work has been devoted to the estimation of eQTL effect size. To reduce false positives, detection methods frequently rely on linear modeling of rank-based normalized or log-transformed gene expression data. Unfortunately, these approaches do not correspond to the simplest model of eQTL action, and thus yield estimates of eQTL association that can be uninterpretable and inaccurate. In this paper we propose a new, log-of-linear model for eQTL action, termed ACME, that captures allelic contributions to cis-acting eQTLs in an additive fashion, yielding effect size estimates that correspond to a biologically coherent model of cis-eQTLs. We describe a non-linear least-squares algorithm to fit the model by maximum likelihood, and obtain corresponding p-values. We perform careful investigation of the model using a combination of simulated data and data from the Genotype Tissue Expression (GTEx) project. Our results reveal little evidence for dominance effects, a parsimonious result that accords with a simple biological model for allele-specific expression and supports use of the ACME model. We show that Type-I error is well-controlled under our approach in a realistic setting, so that rank-based normalizations are unnecessary. Furthermore, we show that such normalizations can be detrimental to power and estimation accuracy under the proposed model. We then provide summaries of ACME effect sizes for whole-genome cis-eQTLs in the GTEx data.

In scientific problems involving systems that can be modeled as a network (or “graph”), it is often of interest to find network communities - strongly connected node subsets - for unsupervised learning, feature discovery, anomaly detection, or scientific study. The vast majority of community detection methods proceed via optimization of a quality function, which is possible even on random networks without communities. Therefore there is usually not an easy way to tell if a community is “significant”, in this context meaning more internally connected than would be expected under a random graph model without communities. This paper generalizes existing null models and statistical tests for this purpose to bipartite graphs, and introduces a new significance scoring algorithm called Fast Optimized Community Significance (FOCS) that is highly scalable and agnostic to the type of graph. Compared with existing methods on unipartite graphs, FOCS is more numerically stable and better balances the trade-off between detection power and false positives. On a large-scale bipartite graph derived from the Internet Movie Database (IMDB), the significance scores provided by FOCS correlate strongly with meaningful actor/director collaborations on serial cinematic projects.

Community detection is the process of grouping strongly connected nodes in a network. Many community detection methods for un-weighted networks have a theoretical basis in a null model. Communities discovered by these methods therefore have interpretations in terms of statistical significance. In this paper, we introduce a null for weighted networks called the continuous configuration model. We use the model both as a tool for community detection and for simulating weighted networks with null nodes. First, we propose a community extraction algorithm for weighted networks which incorporates iterative hypothesis testing under the null. We prove a central limit theorem for edge-weight sums and asymptotic consistency of the algorithm under a weighted stochastic block model. We then incorporate the algorithm in a community detection method called CCME. To benchmark the method, we provide a simulation framework incorporating the null to plant "background" nodes in weighted networks with communities. We show that the empirical performance of CCME on these simulations is competitive with existing methods, particularly when overlapping communities and background nodes are present. To further validate the method, we present two real-world networks with potential background nodes and analyze them with CCME, yielding results that reveal macro-features of the corresponding systems.