The effect of certain Boolean functions in stability of networks with varying topology

The stability of biological organisms is a major feature which contributes to their survival in the environment. However, the study of the stability in vivo is a very hard challenge. An objective way for the stability analysis is to adopt the Boolean network model, which can qualitatively describe the behavior of biological networks as well as allows the analysis of the results in a comprehensive and global way. Besides, certain Boolean function classes play an important role in Boolean network stability. In addition to this relationship, it is expected that many classes of network topology assigns greater or lesser resistance to damage. In this work, we define “local stability” as the stability resulted from the presence of a certain Boolean function class, such as the canalyzing Boolean functions, and “global stability” as the result of a certain network topology, such as the scale-free topology. Next, we investigate the interaction between these two factors using the size of the largest basin of attraction and generalized Derrida curves as measures for network stability. Our results show that there is a “topology order” for certain Boolean function classes, and that these two factors should be jointly addressed in future analysis of network stability.