Gene Network: Model, Dynamics and Simulation

A gene network is modeled as a dynamical random graph whose vertices and edges represent genes and gene-gene interactions, respectively. The network grows through three biological mechanisms: (1) gene duplication and loss; (2) gene-gene interaction adding and removing; and (3) genome duplication. The evolutionary dynamics of gene networks is discussed. It is shown that: (1) the vertex degree distribution (i.e., the distribution of the number of the gene-gene interactions per gene) always follows power laws and the power law exponents may be changed by genome duplications; and (2) the network degree distribution (i.e., the distribution of the total number of the gene-gene interactions in the network) has a complex behavior: If no genome duplication occurs, it follows a power law. If a genome duplication occurs, it may be away from the power law state. However, after a sufficient long evolutionary time, it approaches to a power law tail. The dynamics is confirmed by computer simulations. By allowing genome duplications, our model and dynamics (describing the dynamic behavior of gene networks) are more realistic than other previous ones (containing only static behavior).