Mean field theory for biology inspired duplication-divergence network model.
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.
Faculty of Science, Jiangsu University, Zhenjiang 212013, China.
Shuiming
S
Cai
Institute of Systems Biology, Shanghai University, Shanghai 200444, China.
Zengrong
Z
Liu
Institute of Systems Biology and Bioinformatics, National Central University, Zhongli, 32001 Taiwan.
H C
HC
Lee
D003198:Computer Simulation; D008954:Models, Biological; D009716:Numerical Analysis, Computer-Assisted; D060066:Protein Interaction Maps