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We propose a novel strategy for provenance tracing in random walk-based network diffusion algorithms, a problem that has been surprisingly overlooked in spite of the widespread use of diffusion algorithms in biological applications. Our path-based approach enables ranking paths by the magnitude of their contribution to each node’s score, offering insight into how information propagates through a network. Building on this capability, we introduce two quantitative measures: (i) path-based effective diffusion, which evaluates how well a diffusion algorithm leverages the full topology of a network, and (ii) diffusion betweenness, which quantifies a node’s importance in propagating scores. We applied our framework to SARS-CoV-2 protein interactors and human PPI networks. Provenance tracing of the Regularized Laplacian and Random Walk with Restart algorithms revealed that a substantial amount of a node’s score is contributed via multi-edge paths, demonstrating that diffusion algorithms exploit the non-local structure of the network. Analysis of diffusion betweenness identified proteins playing a critical role in score propagation; proteins with high diffusion betweenness are enriched with essential human genes and interactors of other viruses, supporting the biological interpretability of the metric. Finally, in a signaling network composed of causal interactions between human proteins, the top contributing paths showed strong overlap with COVID-19-related pathways. These results suggest that our path-based framework offers valuable insight into diffusion algorithms and can serve as a powerful tool for interpreting diffusion scores in a biologically meaningful context, complementing existing module- ornode-centric approaches in systems biology. The code is publicly available at https:// github.com/n-tasnina/provenance-tracing.git under the GNU General Public License v3.0. 

Motivation: Molecular interaction networks are powerful tools for studying cellular functions. Integrating diverse types of networks enhances performance in downstream tasks such as gene module detection and protein function prediction. The challenge lies in extracting meaningful protein feature representations due to varying levels of sparsity and noise across these heterogeneous networks. Results: We propose ICoN, a novel unsupervised graph neural network model that takes multiple protein–protein association networks as inputs and generates a feature representation for each protein that integrates the topological information from all the networks. A key contribution of ICoN is exploiting a mechanism called “co-attention” that enables cross-network communication during training. The model also incorporates a denoising training technique, introducing perturbations to each input network and training the model to reconstruct the original network from its corrupted version. Our experimental results demonstrate that ICoN surpasses individual networks across three downstream tasks: gene module detection, gene coannotation prediction, and protein function prediction. Compared to existing unsupervised network integration models, ICoN exhibits superior performance across the majority of downstream tasks and shows enhanced robustness against noise. This work introduces a promising approach for effectively integrating diverse protein–protein association networks, aiming to achieve a biologically meaningful representation of proteins. Availability and implementation: The ICoN software is available under the GNU Public License v3 at https://github.com/Murali-group/ICoN.