Dissecting molecular network structures using a network subgraph approach

Biological processes are based on molecular networks, which exhibit biological functions through interactions of genetic elements or proteins. This study presents a graph-based method to characterize molecular networks by decomposing the networks into directed multigraphs: network subgraphs. Spectral graph theory, reciprocity and complexity measures were used to quantify the network subgraphs. Graph energy, reciprocity and cyclomatic complexity can optimally specify network subgraphs with some degree of degeneracy. Seventy-one molecular networks were analyzed from three network types: cancer networks, signal transduction networks, and cellular processes. Molecular networks are built from a finite number of subgraph patterns and subgraphs with large graph energies are not present, which implies a graph energy cutoff. In addition, certain subgraph patterns are absent from the three network types. Thus, the Shannon entropy of the subgraph frequency distribution is not maximal. Furthermore, frequently-observed subgraphs are irreducible graphs. These novel findings warrant further investigation and may lead to important applications. Finally, we observed that cancer-related cellular processes are enriched with subgraph-associated driver genes. Our study provides a systematic approach for dissecting biological networks and supports the conclusion that there are organizational principles underlying molecular networks.

ON THE PHYSICAL INTERPRETATION OF THE VILKOVISKY-DEWITT EFFECTIVE ACTION

This letter examines the physical interpretation of a class of reparameterization-invariant effective actions, recently introduced by DeWitt. These include as a special case the Vilkovisky and DeWitt effective action. The invariant actions are shown to share those features at the root of the utility of the standard effective action. In particular, they can be interpreted as the minimum energy in states that are subject to a reparameterization-invariant constraint. It is also shown that, contrary to standard lore, although the Vilkovisky-DeWitt action is given as the sum of one-particle-irreducible graphs it is not the generator of 1PI n-point functions.