Title: Multilayer flows in molecular networks identify biological modules in the human proteome,
Abstract: A variety of complex systems exhibit different types of relationships
simultaneously that can be modeled by multiplex networks. A typical problem is
to determine the community structure of such systems that, in general, depend
on one or more parameters to be tuned. In this study we propose one measure,
grounded on information theory, to find the optimal value of the relax rate
characterizing Multiplex Infomap, the generalization of the Infomap algorithm
to the realm of multilayer networks. We evaluate our methodology on synthetic
networks, to show that the most representative community structure can be
reliably identified when the most appropriate relax rate is used. Capitalizing
on these results, we use this measure to identify the most reliable meso-scale
functional organization in the human protein-protein interaction multiplex
network and compare the observed clusters against a collection of independently
annotated gene sets from the Molecular Signatures Database (MSigDB). Our
analysis reveals that modules obtained with the optimal value of the relax rate
are biologically significant and, remarkably, with higher functional content
than the ones obtained from the aggregate representation of the human proteome.
Our framework allows us to characterize the meso-scale structure of those
multilayer systems whose layers are not explicitly interconnected each other --
as in the case of edge-colored models -- the ones describing most biological
networks, from proteomes to connectomes.