A generative model for protein contact networks

Abstract

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.

Right-side-stretched multifractal spectra indicate small-worldness in networks

“…• We propose to use the degree of right-sided asymmetry of multifractal spectra [10], i.e., the degree to which spectra are stretched on the right-hand side, estimated for time series generated from complex networks as a signature of small-worldness in the corresponding networks. This claim is supported by experimental results on Watts-Strogatz [43], Dorogovtsev-Goltsev-Mendes [9], Song-Havlin-Makse [41] network models and on real data describing protein contact networks [27];…”

“…coli protein molecules [27,28]. We consider network representations of folded proteins (i.e., native structures) called protein contact networks (PCNs) [8].…”

“…We consider network representations of folded proteins (i.e., native structures) called protein contact networks (PCNs) [8]. is not possible to claim that PCNs are pure small-world networks (see [27] and references therein for details). Here, we take into account four sample proteins with PDB codes 3DMQ (PCN0058), 4JOM (PCN0179), 2JGD (PCN0715), and 2QTA (PCN0110).…”

A Systematic Survey on Deep Generative Models for Graph Generation

“…Current computational modeling methods for protein design are slow and often require human oversight and intervention, which are often biased and incomplete. Inspired by recent momentum in deep graph generative models, some works [3,42,50,87] demonstrate the potential of deep graph generative modeling for fast generation of new, viable protein structures. Specifically, in these methods, the contact map/distance matrix of a protein molecule is treated as a graph, while each amino acid molecule in the protein is regarded as a node and their pairwise contacts or distance are edge weights.…”

Modelling and Recognition of Protein Contact Networks by Multiple Kernel Learning and Dissimilarity Representations

“…It is worth stressing that both nodes labels (i.e., the type of amino-acid) and edges labels (i.e., the distance between neighbour residues) are deliberately discarded in order to focus only on proteins’ topological configuration. Despite the minimalistic representation, PCNs have been successfully used in pattern recognition problems for tasks such as solubility prediction/folding propensity [ 42 , 43 ] and physiological role prediction [ 44 , 45 , 46 ]; furthermore, their structural and dynamical properties have been extensively studied in works such as [ 47 , 48 , 49 , 50 ].…”