Ispolatov I, Krapivsky P L, Yuryev A
Ariadne Genomics Inc., Rockville, Maryland 20850, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2005 Jun;71(6 Pt 1):061911. doi: 10.1103/PhysRevE.71.061911. Epub 2005 Jun 22.
We investigate a very simple model describing the evolution of protein-protein interaction networks via duplication and divergence. The model exhibits a remarkably rich behavior depending on a single parameter, the probability to retain a duplicated link during divergence. When this parameter is large, the network growth is not self-averaging and an average node degree increases algebraically. The lack of self-averaging results in a great diversity of networks grown out of the same initial condition. When less than a half of links are (on average) preserved after divergence, the growth is self-averaging, the average degree increases very slowly or tends to a constant, and a degree distribution has a power-law tail. The predicted degree distributions are in a very good agreement with the distributions observed in real protein networks.
我们研究了一个非常简单的模型，该模型通过复制和分化来描述蛋白质-蛋白质相互作用网络的演化。该模型根据一个单一参数（即分化过程中保留复制链接的概率）展现出极为丰富的行为。当此参数较大时，网络增长并非自平均的，平均节点度代数增长。缺乏自平均性导致从相同初始条件生长出的网络具有极大的多样性。当分化后（平均）保留的链接少于一半时，增长是自平均的，平均度增长非常缓慢或趋于恒定，并且度分布具有幂律尾部。预测的度分布与在真实蛋白质网络中观察到的分布非常吻合。
