  We propose new activity-dependent adaptive Boolean networks inspired by the
cis-regulatory mechanism in gene regulatory networks. We analytically show that
our model can be solved for stationary in-degree distribution for a wide class
of update rules by employing the annealed approximation of Boolean network
dynamics and that evolved Boolean networks have a preassigned average
sensitivity that can be set independently of update rules if certain conditions
are satisfied. In particular, when it is set to 1, our theory predicts that the
proposed network rewiring algorithm drives Boolean networks towards
criticality. We verify that these analytic results agree well with numerical
simulations for four representative update rules. We also discuss the
relationship between sensitivity of update rules and stationary in-degree
distributions and compare it with that in real-world gene regulatory networks.
