Hierarchical and Topological Study of the Protein–protein Interaction Networks

Abstract

We employ the random graph theory approach to analyze the protein–protein interaction database DIP. Several global topological parameters are used to characterize the protein–protein interaction networks (PINs) for seven organisms. We find that the seven PINs are well approximated by the scale-free networks, that is, the node degree cumulative distribution P cum (k) scales with the node degree k (P cum (k) ~ k-α). We also find that the logarithm of the average clustering coefficient C ave (k) scales with k (C ave (k) ~ k-β), for E. coli and S. cerevisiae. In particular, we determine that the E. coli and the S. cerevisiae PINs are better represented by the stochastic and deterministic hierarchical network models, respectively. The current fruit fly protein–protein interaction dataset does not have convincing evidence in favor of the hierarchical network model. These findings lead us to conclude that, in contrast to scale-free structure, hierarchical structure model applies for certain species' PINs only. We also demonstrate that PINs are robust when subject to random perturbation where up to 50% of the nodes are rewired. Average node degree correlation study supports the fact that nodes of low connectivity are correlated, whereas nodes of high connectivity are not directly linked.

Modular Structures and Robustness of Protein Networks

“…We notice that the C"ve(k) plot for the fruit fly PIN exhibits a rather flat plateau for a large range of k, and it falls rapidly for large k. In addition, the clustering coefficient C for fruit fly is the smallest among the seven species, where one would expect a large C value for hierarchical network model. These results 26 For the other four species (C. elegans, H. pylori, H. sapiens and M. musculus) our results indicate that their C me (k) values decrease with k (i.e. 0.49^/7^0.66) and have a less significant coefficients of determination.…”

“…Regression and correlation results of the logarithm of C me (k) vs. the logarithm of k plots (P, r 2 and p-value), the clustering coefficients C for the seven species, and the C values from Ref. 26. The results indicate that C ave (k) decreases with k for the seven species, as illustrate in Table 4 and Figures 3, and 4.…”

“…26 In Table 3, we present the regression and correlation analysis results for the node degree distribution. Regression analysis determines that a lies between 1.48 and 2.34 for the seven species.…”

“…To further characterize the network topological structures, we compute the C me (k), and consider the logarithm of the C ave (k) vs. the logarithm of node degree k plots for the seven species. 26 In Table 4, we present the regression and correlation analysis results for the average clustering function C ave (k), the clustering coefficient C, and the C values for the species, C. elegans, D. melanogaster and S. cerevisiae, given by Ref 27. Table 4.…”

Computational analysis of molecular networks using spectral graph theory, complexity measures and information theory

“…assortative/disassortative, small world etc., of molecular networks [9][10] . For instance, it has been shown that protein-protein interaction networks are well described by scale-free networks or hierarchical network models 11 .…”