The mutual information of attractors in scale-free boolean networks

Boolean Network, originally developed by Kauffman in 1969, is one of the models to study genetic regulatory networks, and it has been widely applied in Bioscience. In this paper, we proposed a model of Boolean Networks in which the topological structures and updating functions were different from the classical random graph model. For topological structures, the output degree of a node obeyed power law distribution, while the input of each node remained fixed as the classical N-K model. For updating functions, two parameters '1 and '2 were used to generate various Boolean functions. By calculating the mutual information and robustness of attractors in instances of Scale-free Boolean Networks, we investigated the relationships between structure parameters and rule parameters, which were involved in different phase with respect to different parameters. Furthermore, we observed that the structure parameters determined the regions that robustness '... and mutual information belonged to, while rule parameters 1 and '2 determined the relative values of R and L.