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Analysis and evaluation of the entropy indices of a static network structure.

ABSTRACT: Although degree distribution entropy (DDE), SD structure entropy (SDSE), Wu structure entropy (WSE) and FB structure entropy (FBSE) are four static network structure entropy indices widely used to quantify the heterogeneity of a complex network, previous studies have paid little attention to their differing abilities to describe network structure. We calculate these four structure entropies for four benchmark networks and compare the results by measuring the ability of each index to characterize network heterogeneity. We find that SDSE and FBSE more accurately characterize network heterogeneity than WSE and DDE. We also find that existing benchmark networks fail to distinguish SDSE and FBSE because they cannot discriminate local and global network heterogeneity. We solve this problem by proposing an evolving caveman network that reveals the differences between structure entropy indices by comparing the sensitivities during the network evolutionary process. Mathematical analysis and computational simulation both indicate that FBSE describes the global topology variation in the evolutionary process of a caveman network, and that the other three structure entropy indices reflect only local network heterogeneity. Our study offers an expansive view of the structural complexity of networks and expands our understanding of complex network behavior.

SUBMITTER: Cai M

PROVIDER: S-EPMC5570930 | biostudies-literature |

REPOSITORIES: biostudies-literature

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Project description:Prediction of protein folding and specific interactions from only the sequence (ab initio) is a major challenge in bioinformatics. It is believed that such prediction will prove possible if Anfinsen's thermodynamic principle is correct for all kinds of proteins, and all the information necessary to form a concrete 3D structure is indeed present in the sequence.We indexed the 200 possible amino acid pairs for their compatibility regarding the three major physicochemical properties--size, charge and hydrophobicity--and constructed Size, Charge and Hydropathy Compatibility Indices and Matrices (SCI & SCM, CCI & CCM, and HCI & HCM). Each index characterized the expected strength of interaction (compatibility) of two amino acids by numbers from 1 (not compatible) to 20 (highly compatible). We found statistically significant positive correlations between these indices and the propensity for amino acid co-locations in real protein structures (a sample containing total 34630 co-locations in 80 different protein structures): for HCI: p < 0.01, n = 400 in 10 subgroups; for SCI p < 1.3E-08, n = 400 in 10 subgroups; for CCI: p < 0.01, n = 175). Size compatibility between residues (well known to exist in nucleic acids) is a novel observation for proteins. Regression analyzes indicated at least 7 well distinguished clusters regarding size compatibility and 5 clusters of charge compatibility. We tried to predict or reconstruct simple 2D representations of 3D structures from the sequence using these matrices by applying a dot plot-like method. The location and pattern of the most compatible subsequences was very similar or identical when the three fundamentally different matrices were used, which indicates the consistency of physicochemical compatibility. However, it was not sufficient to choose one preferred configuration between the many possible predicted options.Indexing of amino acids for major physico-chemical properties is a powerful approach to understanding and assisting protein design. However, it is probably insufficient itself for complete ab initio structure prediction.

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Analysis and evaluation of the entropy indices of a static network structure.

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