A generative model for protein contact networks

In this paper, we present a generative model for protein contact networks (PCNs). The soundness of the proposed model is investigated by focusing primarily on mesoscopic properties elaborated from the spectra of the graph Laplacian. To complement the analysis, we also study the classical topological descriptors, such as statistics of the shortest paths and the important feature of modularity. Our experiments show that the proposed model results in a considerable improvement with respect to two suitably chosen generative mechanisms, mimicking with better approximation real PCNs in terms of diffusion properties elaborated from the normalized Laplacian spectra. However, as well as the other network models, it does not reproduce with sufficient accuracy the shortest paths structure. To compensate this drawback, we designed a second step involving a targeted edge reconfiguration process. The ensemble of reconfigured networks denotes further improvements that are statistically significant. As an important byproduct of our study, we demonstrate that modularity, a well-known property of proteins, does not entirely explain the actual network architecture characterizing PCNs. In fact, we conclude that modularity, intended as a quantification of an underlying community structure, should be considered as an emergent property of the structural organization of proteins. Interestingly, such a property is suitably optimized in PCNs together with the feature of path efficiency.