Graph Neural Networks (GNNs) traditionally employ a message-passing mechanism that resembles diffusion over undirected graphs, which often leads to homogenization of node features and reduced discriminative power in tasks such as node classification. Our key insight for addressing this limitation is to assign fuzzy edge directions---that can vary continuously from node $i$ pointing to node $j$ to vice versa---to the edges of a graph so that features can preferentially flow in one direction between nodes to enable long-range information transmission across the graph. We also introduce a novel complex-valued Laplacian for directed graphs with fuzzy edges where the real and imaginary parts represent information flow in opposite directions. Using this Laplacian, we propose a general framework, called Continuous Edge Direction (CoED) GNN, for learning on graphs with fuzzy edges and prove its expressivity limits using a generalization of the Weisfeiler-Leman (WL) graph isomorphism test for directed graphs with fuzzy edges. Our architecture aggregates neighbor features scaled by the learned edge directions and processes the aggregated messages from in-neighbors and out-neighbors separately alongside the self-features of the nodes. Since continuous edge directions are differentiable, they can be learned jointly with the GNN weights via gradient-based optimization. CoED GNN is particularly well-suited for graph ensemble data where the graph structure remains fixed but multiple realizations of node features are available, such as in gene regulatory networks, web connectivity graphs, and power grids. We demonstrate through extensive experiments on both synthetic and real graph ensemble datasets that learning continuous edge directions significantly improves performance both for undirected and directed graphs compared with existing methods.

MOTIVATION: Detecting oscillations in time series remains a challenging problem even after decades of research. In chronobiology, rhythms (for instance in gene expression, eclosion, egg-laying, and feeding) tend to be low amplitude, display large variations amongst replicates, and often exhibit varying peak-to-peak distances (non-stationarity). Most currently available rhythm detection methods are not specifically designed to handle such datasets, and are also limited by their use of P-values in detecting oscillations. RESULTS: We introduce a new method, ODeGP (Oscillation Detection using Gaussian Processes), which combines Gaussian Process regression and Bayesian inference to incorporate measurement errors, non-uniformly sampled data, and a recently developed non-stationary kernel to improve detection of oscillations. By using Bayes factors, ODeGP models both the null (non-rhythmic) and the alternative (rhythmic) hypotheses, thus providing an advantage over P-values. Using synthetic datasets, we first demonstrate that ODeGP almost always outperforms eight commonly used methods in detecting stationary as well as non-stationary symmetric oscillations. Next, by analyzing existing qPCR datasets, we demonstrate that our method is more sensitive compared to the existing methods at detecting weak and noisy oscillations. Finally, we generate new qPCR data on mouse embryonic stem cells. Surprisingly, we discover using ODeGP that increasing cell-density results in rapid generation of oscillations in the Bmal1 gene, thus highlighting our method's ability to discover unexpected and new patterns. In its current implementation, ODeGP is meant only for analyzing single or a few time-trajectories, not genome-wide datasets. AVAILABILITY AND IMPLEMENTATION: ODeGP is available at https://github.com/Shaonlab/ODeGP.

MOTIVATION: Animal models are widely used in biomedical research for reasons ranging from practical to ethical. An important issue is whether rodent models are predictive of human biology. This has been addressed recently in the framework of a series of challenges designed by the systems biology verification for Industrial Methodology for Process Verification in Research (sbv IMPROVER) initiative. In particular, one of the sub-challenges was devoted to the prediction of protein phosphorylation responses in human bronchial epithelial cells, exposed to a number of different chemical stimuli, given the responses in rat bronchial epithelial cells. Participating teams were asked to make inter-species predictions on the basis of available training examples, comprising transcriptomics and phosphoproteomics data. RESULTS: Here, the two best performing teams present their data-driven approaches and computational methods. In addition, post hoc analyses of the datasets and challenge results were performed by the participants and challenge organizers. The challenge outcome indicates that successful prediction of protein phosphorylation status in human based on rat phosphorylation levels is feasible. However, within the limitations of the computational tools used, the inclusion of gene expression data does not improve the prediction quality. The post hoc analysis of time-specific measurements sheds light on the signaling pathways in both species. AVAILABILITY AND IMPLEMENTATION: A detailed description of the dataset, challenge design and outcome is available at www.sbvimprover.com. The code used by team IGB is provided under http://github.com/uci-igb/improver2013. Implementations of the algorithms applied by team AMG are available at http://bhanot.biomaps.rutgers.edu/wiki/AMG-sc2-code.zip. CONTACT: [email protected].

MOTIVATION: Using gene expression to infer changes in protein phosphorylation levels induced in cells by various stimuli is an outstanding problem. The intra-species protein phosphorylation challenge organized by the IMPROVER consortium provided the framework to identify the best approaches to address this issue. RESULTS: Rat lung epithelial cells were treated with 52 stimuli, and gene expression and phosphorylation levels were measured. Competing teams used gene expression data from 26 stimuli to develop protein phosphorylation prediction models and were ranked based on prediction performance for the remaining 26 stimuli. Three teams were tied in first place in this challenge achieving a balanced accuracy of about 70%, indicating that gene expression is only moderately predictive of protein phosphorylation. In spite of the similar performance, the approaches used by these three teams, described in detail in this article, were different, with the average number of predictor genes per phosphoprotein used by the teams ranging from 3 to 124. However, a significant overlap of gene signatures between teams was observed for the majority of the proteins considered, while Kyoto Encyclopedia of Genes and Genomes (KEGG) pathways were enriched in the union of the predictor genes of the three teams for multiple proteins. AVAILABILITY AND IMPLEMENTATION: Gene expression and protein phosphorylation data are available from ArrayExpress (E-MTAB-2091). Software implementation of the approach of Teams 49 and 75 are available at http://bioinformaticsprb.med.wayne.edu and http://people.cs.clemson.edu/∼luofeng/sbv.rar, respectively. CONTACT: [email protected] or [email protected] or [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

MOTIVATION: Translating findings in rodent models to human models has been a cornerstone of modern biology and drug development. However, in many cases, a naive 'extrapolation' between the two species has not succeeded. As a result, clinical trials of new drugs sometimes fail even after considerable success in the mouse or rat stage of development. In addition to in vitro studies, inter-species translation requires analytical tools that can predict the enriched gene sets in human cells under various stimuli from corresponding measurements in animals. Such tools can improve our understanding of the underlying biology and optimize the allocation of resources for drug development. RESULTS: We developed an algorithm to predict differential gene set enrichment as part of the sbv IMPROVER (systems biology verification in Industrial Methodology for Process Verification in Research) Species Translation Challenge, which focused on phosphoproteomic and transcriptomic measurements of normal human bronchial epithelial (NHBE) primary cells under various stimuli and corresponding measurements in rat (NRBE) primary cells. We find that gene sets exhibit a higher inter-species correlation compared with individual genes, and are potentially more suited for direct prediction. Furthermore, in contrast to a similar cross-species response in protein phosphorylation states 5 and 25 min after exposure to stimuli, gene set enrichment 6 h after exposure is significantly different in NHBE cells compared with NRBE cells. In spite of this difference, we were able to develop a robust algorithm to predict gene set activation in NHBE with high accuracy using simple analytical methods. AVAILABILITY AND IMPLEMENTATION: Implementation of all algorithms is available as source code (in Matlab) at http://bhanot.biomaps.rutgers.edu/wiki/codes_SC3_Predicting_GeneSets.zip, along with the relevant data used in the analysis. Gene sets, gene expression and protein phosphorylation data are available on request. CONTACT: [email protected].