Abstract
Protein-protein interaction networks (PINs) are scale-free networks with a small-world property. In a small-world network, the average cluster coefficient (<C>) is much higher than in a random network, but the average shortest path length (<L>) is similar between the two networks. To understand the evolutionary mechanisms shaping the structure of PINs, simulation studies using various network growth models have been performed. It has been reported that the heterodimerization (HD) model, in which a new link is added between duplicated nodes with a uniform probability, could reproduce scale-freeness and a high <C>. In this paper, however, we show that the HD model is unsatisfactory, because (i) to reproduce the high <C> in the yeast PIN, a much larger number (n HI) of HD links (links between duplicated nodes) are required than the estimated number of n HI in the yeast PIN and (ii) the spatial distribution of triangles in the yeast PIN is highly skewed but the HD model cannot reproduce the skewed distribution. To resolve these discrepancies, we here propose a new model named the non-uniform heterodimerization (NHD) model. In this model, an HD link is preferentially attached between duplicated nodes when they share many common neighbors. Simulation studies demonstrated that the NHD model can successfully reproduce the high <C>, the low n HI, and the skewed distribution of triangles in the yeast PIN. These results suggest that the survival rate of HD links is not uniform in the evolution of PINs, and that an HD link between high-degree nodes tends to be evolutionarily conservative. The non-uniform survival rate of HD links can be explained by assuming a low mutation rate for a high-degree node, and thus this model appears to be biologically plausible.
Highlights
The information of protein-protein interaction networks (PINs) at the whole-genome level is available from several organisms, including Saccharomyces cerevisiae [1,2,3], Caenorhabditis elegans [4], and Drosophila melanogaster [5]
The number of interactions between homologous nodes is much larger than that in the yeast PIN (175). This observation is consistent with the investigation of the fly PIN by Ispolatov et al [29], in which it was reported that the HD model requires a much larger number of HD links (270) than the actual number in the fly PIN (142) [32] to generate the 1,405 triangles present in the fly PIN
We showed that the non-uniform heterodimerization (NHD) model can successfully reproduce both a high,C. and a low nHI in the yeast PIN, whereas the HD model cannot regenerate the value of nHI
Summary
The information of protein-protein interaction networks (PINs) at the whole-genome level is available from several organisms, including Saccharomyces cerevisiae [1,2,3], Caenorhabditis elegans [4], and Drosophila melanogaster [5]. Is the average degree and N is the number of nodes.) Scale-free and small-world properties are commonly observed in various complex networks such as the Internet [9], coauthorship of scientific papers [14], metabolic pathways [15], and functional connections in the human brain [16]. In a network showing a hierarchical structure, ,C(k)., the average cluster coefficient of k-degree nodes, decays as a power law ,C(k).,k2m [17,18] This indicates that a node with a small number of links has a high C and belongs to a small subnetwork in which all nodes are densely connected, while a hub has a low C and links different subnetworks. The connections between a hub and a low-degree node are favored, while those between hubs and those between low-degree nodes are suppressed [19,20,21,22]
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