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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. 

Abstract BackgroundNetwork propagation has been widely used for nearly 20 years to predict gene functions and phenotypes. Despite the popularity of this approach, little attention has been paid to the question of provenance tracing in this context, e.g., determining how much any experimental observation in the input contributes to the score of every prediction. ResultsWe design a network propagation framework with 2 novel components and apply it to predict human proteins that directly or indirectly interact with SARS-CoV-2 proteins. First, we trace the provenance of each prediction to its experimentally validated sources, which in our case are human proteins experimentally determined to interact with viral proteins. Second, we design a technique that helps to reduce the manual adjustment of parameters by users. We find that for every top-ranking prediction, the highest contribution to its score arises from a direct neighbor in a human protein-protein interaction network. We further analyze these results to develop functional insights on SARS-CoV-2 that expand on known biology such as the connection between endoplasmic reticulum stress, HSPA5, and anti-clotting agents. ConclusionsWe examine how our provenance-tracing method can be generalized to a broad class of network-based algorithms. We provide a useful resource for the SARS-CoV-2 community that implicates many previously undocumented proteins with putative functional relationships to viral infection. This resource includes potential drugs that can be opportunistically repositioned to target these proteins. We also discuss how our overall framework can be extended to other, newly emerging viruses.