On the distribution of randomly generated boolean networks as models for genetic regulation

Gene regulatory networks play an important role in cells internal regulation and responses to external stimuli. Many computational models for these networks have been developed, but among those, Boolean networks (BNs) have attracted significant interest because of the balance between their fit to the underlying biological processes and their mathematical properties that allow for prediction, inference and control. A great effort was done regarding the random generation of Boolean Network to study average behavior, under desired constrains. A significant drawback of these algorithms is that they do not address the important question about the distributional properties of the networks they generate. There is no analysis of the distribution of the generated networks, nor any analysis of the existence of isomorphs among them. In this work we show how the most novel approach for random generation of Boolean Networks do not generate the networks uniformly, neither for the network or the equivalence classes based on isomorphism between networks.