Interplay between degree and Boolean rules in the stability of Boolean networks

Empirical evidence has revealed that biological regulatory systems are controlled by high-level coordination between topology and Boolean rules. In this study, we study the joint effects of degree and Boolean functions on the stability of Boolean networks. To elucidate these effects, we focus on i) the correlation between the sensitivity of Boolean variables and the degree, and ii) the coupling between canalizing inputs and degree. We find that negatively correlated sensitivity with respect to local degree enhances the stability of Boolean networks against external perturbations. We also demonstrate that the effects of canalizing inputs can be amplified when they coordinate with high in-degree nodes. Numerical simulations confirm the accuracy of our analytical predictions at both the node and network levels.