Faculty of Science, Jiangsu University, Zhenjiang 212013, China.
Institute of Systems Biology, Shanghai University, Shanghai 200444, China.
Chaos. 2015 Aug;25(8):083106. doi: 10.1063/1.4928212.
The duplication-divergence network model is generally thought to incorporate key ingredients underlying the growth and evolution of protein-protein interaction networks. Properties of the model have been elucidated through numerous simulation studies. However, a comprehensive theoretical study of the model is lacking. Here, we derived analytic expressions for quantities describing key characteristics of the network-the average degree, the degree distribution, the clustering coefficient, and the neighbor connectivity-in the mean-field, large-N limit of an extended version of the model, duplication-divergence complemented with heterodimerization and addition. We carried out extensive simulations and verified excellent agreement between simulation and theory except for one partial case. All four quantities obeyed power-laws even at moderate network size ( N∼10(4)), except the degree distribution, which had an additional exponential factor observed to obey power-law. It is shown that our network model can lead to the emergence of scale-free property and hierarchical modularity simultaneously, reproducing the important topological properties of real protein-protein interaction networks.
复制-分歧网络模型通常被认为包含了蛋白质-蛋白质相互作用网络增长和进化的关键要素。通过大量的模拟研究已经阐明了该模型的特性。然而，该模型的综合理论研究仍然缺乏。在这里，我们推导出了描述网络关键特征的数量的解析表达式-平均度数、度数分布、聚类系数和邻居连接性-在扩展模型的平均场、大 N 极限中，复制-分歧与异二聚化和添加相结合。我们进行了广泛的模拟，并验证了模拟与理论之间的极好一致性，除了一个部分情况。除了观察到服从幂律的附加指数因子的度数分布外，所有四个数量都服从幂律，即使在中等网络大小（N∼10(4)）下也是如此。结果表明，我们的网络模型可以同时导致无标度特性和层次模块性的出现，再现了真实蛋白质-蛋白质相互作用网络的重要拓扑特性。
