Evolutionary Mechanisms of Network Motifs in PPI Networks
Duplication and divergence are two basic evolutionary mechanisms of bio-molecular networks. Real-world bio-molecular networks and their statistical characteristics can be well mimicked by artificial algorithms based on the two mechanisms. Bio-molecular ne
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Evolutionary Mechanisms of Network Motifs in PPI Networks
Abstract Duplication and divergence are two basic evolutionary mechanisms of bio-molecular networks. Real-world bio-molecular networks and their statistical characteristics can be well mimicked by artificial algorithms based on the two mechanisms. Bio-molecular networks consist of network motifs, which act as building blocks of large-scale networks. A fundamental question is how network motifs are evolved from long time evolution and natural selection. By considering the effect of various duplication and divergence strategies, it is founded that the underlying duplication scheme of the real-world undirected bio-molecular networks would rather follow the anti-preference strategy than the random one. The antipreference duplication mechanism and the dimerization can lead to the formation of various motifs and robustly conserve proper quantities of motifs in the artificial networks as that in the real-world ones. Furthermore, the anti-preference mechanism and edge deletion divergence can robustly preserve the sparsity of the networks. The investigations reveal the possible evolutionary mechanisms of network motifs and have potential implications in the design, synthesis, and reengineering of biological networks for biomedical purpose.
6.1 Backgrounds Structures and functions of complex networks arising from various disciplines have been extensively investigated in the last several decades [1–3]. In 2002, Milo et al. [4–11] found that complex networks consist of network motifs. Network motifs are small subgraphs that more frequently appear in a network than in its random counterparts, where the random networks are permuted from the investigated networks, which keep the same node degrees as the concerned network. Milo et al. mainly considered various directed networks and found that the 3-node FFLs, the 4-node bi-fan, and bi-parallel subgraphs are typical motifs in various systems. Since then, structures and functions of network motifs have been extensively investigated both theoretically and experimentally [11–14]. It has been found that the FFLs, the bi-fan, and the bi-parallel subgraphs are with crucial © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2020 J. Lü, P. Wang, Modeling and Analysis of Bio-molecular Networks, https://doi.org/10.1007/978-981-15-9144-0_6
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6 Evolutionary Mechanisms of Network Motifs in PPI Networks
functions in bio-systems [11–15]. For example, in 2003, Mangan et al. [12] found the relation between topological structures and functional characteristics of the FFLs. In 2012, through dynamical analysis, Wang et al. [13, 14] answered the question that why FFLs with certain structures can be selected by evolution. PPI networks are typical undirected networks. Many works have been reported that PPI networks consist of modulars acting as basic functional building blocks [6–9]. In 2003, Wuchty et al. [8] investigated the evolutionary conservation of motif constituents
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