Optimal Stabilization of Boolean Networks through Collective Influence

TL;DR

This paper introduces a collective influence-based method to identify minimal influential nodes for stabilizing Boolean networks efficiently, with potential applications in biological systems and disease control.

Contribution

It presents a novel, computationally efficient approach using collective influence theory to stabilize Boolean networks by targeting key nodes, outperforming existing heuristics.

Findings

The method effectively stabilizes networks with fewer nodes.

It outperforms other heuristic algorithms in stability control.

Applicable to biological systems for identifying critical genes.

Abstract

The stability of Boolean networks has attracted much attention due to its wide applications in describing the dynamics of biological systems. During the past decades, much effort has been invested in unveiling how network structure and update rules will affect the stability of Boolean networks. In this paper, we aim to identify and control a minimal set of influential nodes that is capable of stabilizing an unstable Boolean network. By minimizing the largest eigenvalue of a modified non-backtracking matrix, we propose a method using the collective influence theory to identify the influential nodes in Boolean networks with high computational efficiency. We test the performance of collective influence on four different networks. Results show that the collective influence algorithm can stabilize each network with a smaller set of nodes than other heuristic algorithms. Our work provides a new insight into the mechanism that determines the stability of Boolean networks, which may find applications in identifying the virulence genes that lead to serious disease.