PathWeigh II: Graph Based Belief Propagation for Pathway Activity Analysis

Pathway analysis is essential for understanding cellular phenotypes from gene expression data. However, existing methods struggle with feedback loops and fail to integrate gene-level evidence throughout pathway topology. We present PathWeigh II, an enhanced pathway analysis tool that employs graph decomposition and Gaussian-scaled belief propagation to model pathways as directed multi-graphs. Unlike previous approaches that average interaction activities, PathWeigh II propagates probabilistic beliefs through the network structure, naturally handling cyclic dependencies and combining observed expression data with topological inference. Using 357 curated pathways from KEGG and BioCarta, PathWeigh II provides biologically meaningful activity scores while maintaining computational efficiency. We demonstrate that PathWeigh II correctly converges on pathways with feedback loops where traditional methods fail and show how integrating internal gene evidence with propagated beliefs improves pathway characterization. PathWeigh II is open source and available at <ext-link xmlns:xlink="http://www.w3.org/1999/xlink" ext-link-type="uri" xlink:href="https://github.com/zurkin1/PathWeigh/tree/master/v2">https://github.com/zurkin1/PathWeigh/tree/master/v2</ext-link> .