Effects of Antimodularity and Multiscale Influence in Random Boolean Networks

We investigate the effects of modularity, antimodularity, and multiscale influence on random Boolean networks (RBNs). On the one hand, we produced modular, antimodular, and standard RBNs and compared them to identify how antimodularity affects the dynamical behaviors of RBNs. We found that the antimodular networks showed similar dynamics to the standard networks. Confirming previous results, modular networks had more complex dynamics. On the other hand, we generated multilayer RBNs where there are different RBNs in the nodes of a higher scale RBN. We observed the dynamics of micro-and macronetworks by adjusting parameters at each scale to reveal how the behavior of lower layers affects the behavior of higher layers and vice versa. We found that the statistical properties of macro-RBNs were changed by the parameters of micro-RBNs, but not the other way around. However, the precise patterns of networks were dominated by the macro-RBNs. In other words, for statistical properties only upward causation was relevant, while for the detailed dynamics downward causation was prevalent.