Pinning Stabilizer Design for Large-Scale Probabilistic Boolean Networks

TL;DR

This paper introduces a network-structure-based pinning control method for stabilizing large-scale probabilistic Boolean networks, reducing computational complexity and enabling control with local information.

Contribution

It proposes a novel pinning control strategy that relies on local network structure, reducing complexity and applicable to large-scale, sparse networks.

Findings

The control reduces computational complexity from exponential to linear in network size.

The method successfully stabilizes a mammalian cell-cycle model with mutations.

Local in-neighbors' information suffices for effective stabilization.

Abstract

This paper investigates the stabilization of probabilistic Boolean networks (PBNs) via a novel pinning control strategy based on network structure. In a PBN, the evolution equation of each gene switches among a collection of candidate Boolean functions with probability distributions that govern the activation frequency of each Boolean function. Owing to the stochasticity, the uniform state feedback controller, independent of switching signal, might be out of work, and in this case, the non-uniform state feedback controller is required. Subsequently, a criterion is derived to determine whether uniform controllers is applicable to achieve stabilization. It is worth pointing out that the pinning control designed in this paper is based on the network structure, which only requires local in-neighbors' information, rather than global information (state transition matrix). Moreover, this pinning control strategy reduces the computational complexity from $O(2^{2n})$ to $O(n2^\alpha)$, and thus it has the ability to handle some large-scale networks, especially the networks with sparse connections. Finally, the mammalian cell-cycle encountering a mutated phenotype is modelled by a PBN to demonstrate the obtained results.