Optimal Stabilization of Boolean Networks through Collective Influence

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.

References in corpus (24)

• Error and attack tolerance of complex networks
• The spread of epidemic disease on networks
• Identification of influential spreaders in complex networks
• Breakdown of the Internet under intentional attack
• Influence maximization in complex networks through optimal percolation
• The Yeast Cell-Cycle Network Is Robustly Designed
• Mathematical Formulation of Multi-Layer Networks
• k-core organization of complex networks
• Searching for superspreaders of information in real-world social media
• Genetic networks with canalyzing Boolean rules are always stable
• Characterizing the dynamical importance of network nodes and links
• Spreading dynamics in complex networks
• Scaling in ordered and critical random Boolean networks
• Self-organized Networks of Competing Boolean Agents
• The effect of network topology on the stability of discrete state models of genetic control
• Boolean Chaos
• Stability of Boolean Multilevel Networks
• Efficient collective influence maximization in cascading processes with first-order transitions
• Scaling in critical random Boolean networks
• The properties of attractors of canalyzing random Boolean networks
• Binary threshold networks as a natural null model for biological networks
• Stability of Boolean networks: The joint effects of topology and update rules
• Dynamic range maximization in excitable networks
• Approximating the Largest Eigenvalue of the Modified Adjacency Matrix of Networks with Heterogeneous Node Biases

Cited by in corpus (4)

• Targeted influence maximization in complex networks
• Dynamic range maximization in excitable networks
• Backtracking activation impacts the criticality of excitable networks
• Interplay between degree and Boolean rules in the stability of Boolean networks