Compressibility Of Random Networks And Bio-molecular Networks Based On Duplication-Divergence Mechanism

Bio-molecular systems can be modeled via complex network theory.The life system transmits genetic information and external signals through complex biological molecular networks,thereby regulating the environmental adaptability and phenotype of organisms.Due to the influence of internal and external noise,bio-molecular duplication and divergence,there is inevitably some information distortion during the transmission process in bio-molecular networks.The rate distortion theory in information theory provides a theoretical basis for the study of source coding when there is some distortion during the process of information transmission,and becomes a powerful tool to study the compressibility of complex networks from the perspective of information transmission efficiency.Based on the rate distortion theory,this paper mainly studies the compressibility of random networks and bio-molecular networks.This paper focuses on the relationship between the compressibility of various networks and the network topology,in order to providing guidance for biological networks to maintain the efficiency of information transmission during the process of coarse-graining structure of complex networks.First,we consider the compressibility of regular networks,Erdos-Renyi(ER)random networks,small world networks and scale-free network.Real bio-molecular networks have characteristics such as sparsity,scale-free,heterogeneity,small-world,modularity,etc.The study of random networks with different topological structure properties can provide guidance for the study of real bio-molecular networks.It is found that the compressibility of regular networks increases with the increasing of network sizes and node degrees.For fixed network average degree,the compressibility of random networks decreases with the increasing of network sizes,and increases with the increasing of edge connection probabilities.In the scale-free networks with adjustable power-law index,when the powerlaw index is small,the compressibility of the network increases with the increasing of the network sizes;However,with the increasing of power index,the compressibility of scale-free network becomes weaker due to the influence of network size.The higher the heterogeneity of discovery,the greater the impact of network size on compressibility.Then,we consider the compressibility of artificial bio-molecular networks based on duplication-divergence mechanism.By considering three duplication mechanisms:random,preference,and anti-preference,as well as different divergence mechanisms such as dimerization,edge addition,and edge deletion,a large number of artificial bio-molecular networks that have similar topological characteristics with actual bio-molecular networks have been generated.Based on the rate distortion theory,the effects of different duplication and divergence mechanisms on the compressibility of artificial bio-molecular networks are studied in the generated networks.It is found that duplication mechanism,dimerization and edge divergence increase the compressibility of the networks,while the increasing of edge deletion probabilities decreases the compressibility of the networks.Finally,this paper studies the compressibility of the real yeast protein-protein interaction network(PPI).Since the real network is static,it is impossible to study the statical properties of compressibility changing with network scales.In order to overcome this problem,this paper sampled the real PPI network,and randomly sampled a large number of subnetworks with different scales from the real network to investigate the change law of its compressibility.It is found that the compressibility of the network increases with the average degrees of the networks.From random networks to artificial bio-molecular networks,and then to real PPI networks,we find that:(1)The more regular the network structure is,the greater the compressibility is affected by the network sizes.(2)The compressibility of the network increases with the average degree of the networks.(3)The compressibility of network is related to its Degree distribution.The relevant research layed a theoretical foundation for understanding the relationship between the structures and functions of bio-molecular networks from the perspective of information transmission,and is of great significance for coarse-graining of bio-molecular networks and understanding their evolution patterns.