State feedback control design for Boolean networks

Abstract

BackgroundDriving Boolean networks to desired states is of paramount significance toward our ultimate goal of controlling the progression of biological pathways and regulatory networks. Despite recent computational development of controllability of general complex networks and structural controllability of Boolean networks, there is still a lack of bridging the mathematical condition on controllability to real boolean operations in a network. Further, no realtime control strategy has been proposed to drive a Boolean network.ResultsIn this study, we applied semi-tensor product to represent boolean functions in a network and explored controllability of a boolean network based on the transition matrix and time transition diagram. We determined the necessary and sufficient condition for a controllable Boolean network and mapped this requirement in transition matrix to real boolean functions and structure property of a network. An efficient tool is offered to assess controllability of an arbitrary Boolean network and to determine all reachable and non-reachable states. We found six simplest forms of controllable 2-node Boolean networks and explored the consistency of transition matrices while extending these six forms to controllable networks with more nodes. Importantly, we proposed the first state feedback control strategy to drive the network based on the status of all nodes in the network. Finally, we applied our reachability condition to the major switch of P53 pathway to predict the progression of the pathway and validate the prediction with published experimental results.ConclusionsThis control strategy allowed us to apply realtime control to drive Boolean networks, which could not be achieved by the current control strategy for Boolean networks. Our results enabled a more comprehensive understanding of the evolution of Boolean networks and might be extended to output feedback control design.

Deriving a Boolean dynamics to reveal macrophage activation with in vitro temporal cytokine expression profiles

“…12. The 8 states, state transition matrix, and evolution of the 8 states for the 3-node network was computed with our own software package [151]. All codes associated with macrophage polarization can be found in our GitHub link (https://github.com/RicardoRamirez2020/Macrophage_Boolean_Network_LP).…”

Genetic Algorithm-Pid Controller for Model Order Reduction Pantographcatenary System

“…Indeed this has attracted a lot interest in the study of pantograph-catenary interaction. For example, easy nation comments control approach is viewed in (Arnold & Simenon, 2000); in (Giovanelli & Farella, 2016), an LQR is designed the use of a linear pantographcatenary model, whilst in (Liu et al, 2016) a high order sliding mode variable structure controller is built for the energetic manipulate of pantograph; an evolutionary multiobjective optimization method is utilized taking into account the perturbations brought on by means of the time-varying stiffness of catenary, differential-geometric idea is used for outputperturbation decoupling for a nonlinear pantograph-catenary model in (O'Connor et al, 1997); very recently fuzzy common sense has additionally discovered application in the active control strategies such as in (Pourzeynali, Lavasani & Modarayi, 2007). The pantograph and catenary form an oscillating gadget that is coupled by way of the contact force between the pantograph head and the contact wire.…”

Advancing Systems Biology in the International Conference on Intelligent Biology and Medicine (ICIBM) 2015

“…Liu et al explored controllability of a Boolean network based on the transition matrix and time transition diagram [10]. In their study, the authors determined the necessary and sufficient condition for a controllable Boolean network and mapped this requirement in transition matrix to real Boolean functions and structure property of a network.…”