The stabilization of random Boolean networks through edge immunization

Abstract

The stability of random Boolean networks (RBNs) has aroused continuous interest due to its close relationship with genetic regulatory systems. In this paper, we aim to stabilize RBNs through immunization of a minimum set of influential edges. By formulizing network stability with edge-based Hamming distance, we exploit the cavity method with the assumption of locally tree-like topology and find that the stability of RBNs is determined by the largest eigenvalue of weighted non-backtracking matrix. Combined with the collective influence theory in optimal percolation research, we quantify the contribution of each edge to the largest eigenvalue and propose an efficient edge immunization strategy. As validation we perform numerical simulations on both synthetic and real-world networks. Results show that the proposed strategy outperforms the other benchmarks and achieves stabilization with fewer immune edges. In addition, we also find that the top influential edges are rarely the most connected, which emphasizes the significance of global network topology rather than local connections. Our work sheds light on the stabilization of RBNs, and moreover, provides necessary theoretical guidance to the targeted therapy of genetic diseases.