Single-Input Pinning Controller Design for Reachability of Boolean Networks

Pinning Control for the p53-Mdm2 Network Dynamics Regulated by p14ARF

p53 regulates the cellular response to genotoxic damage and prevents carcinogenic events. Theoretical and experimental studies state that the p53-Mdm2 network constitutes the core module of regulatory interactions activated by cellular stress induced by a variety of signaling pathways. In this paper, a strategy to control the p53-Mdm2 network regulated by p14ARF is developed, based on the pinning control technique, which consists into applying local feedback controllers to a small number of nodes (pinned ones) in the network. Pinned nodes are selected on the basis of their importance level in a topological hierarchy, their degree of connectivity within the network, and the biological role they perform. In this paper, two cases are considered. For the first case, the oscillatory pattern under gamma-radiation is recovered; afterward, as the second case, increased expression of p53 level is taken into account. For both cases, the control law is applied to p14ARF (pinned node based on a virtual leader methodology), and overexpressed Mdm2-mediated p53 degradation condition is considered as carcinogenic initial behavior. The approach in this paper uses a computational algorithm, which opens an alternative path to understand the cellular responses to stress, doing it possible to model and control the gene regulatory network dynamics in two different biological contexts. As the main result of the proposed control technique, the two mentioned desired behaviors are obtained.

Pinning Controllers for Activation Output Tracking of Boolean Network Under One-Bit Perturbation

This paper studies pinning controllers for activation output tracking (AOT) of Boolean network under one-bit perturbation, based on the semitensor product of matrices. First, the definition of AOT with respect to an activation number is presented, where the activation number means the number of active outputs whose logical variables are 1 s. Then, several criteria are established for AOT issue. Further, the impact of one-bit perturbation on AOT is studied, where one-bit perturbation means that only one logical function has one-bit change of its truth table by flipping the value from 1 to 0 or 0 to 1. In addition, if a one-bit perturbation is a valid perturbation on AOT, an output feedback pinning control is designed to recover AOT. The obtained results are effectively illustrated by a D. melanogaster segmentation polarity gene network and a reduced signal transduction network.