Controllability and observability of Boolean networks arising from biology

Li, Rui; Yang, Meng; Chu, Tianguang

doi:10.1063/1.4907708

Cited by 42 publications

(29 citation statements)

References 68 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…However, we remark that some algebraic methods allow to estimate the change in the basin size after an edge deletion, see [59]. Nonetheless, the control targets identified by the algebraic techniques described here could be used for further analysis of the system, such as for studying reachability [60], or for designing optimal control policies in a stochastic setting [29][30][31][32].…”

Section: Discussionmentioning

confidence: 98%

Identification of control targets in Boolean molecular network models via computational algebra

et al. 2016

View full text Add to dashboard Cite

BackgroundMany problems in biomedicine and other areas of the life sciences can be characterized as control problems, with the goal of finding strategies to change a disease or otherwise undesirable state of a biological system into another, more desirable, state through an intervention, such as a drug or other therapeutic treatment. The identification of such strategies is typically based on a mathematical model of the process to be altered through targeted control inputs. This paper focuses on processes at the molecular level that determine the state of an individual cell, involving signaling or gene regulation. The mathematical model type considered is that of Boolean networks. The potential control targets can be represented by a set of nodes and edges that can be manipulated to produce a desired effect on the system.ResultsThis paper presents a method for the identification of potential intervention targets in Boolean molecular network models using algebraic techniques. The approach exploits an algebraic representation of Boolean networks to encode the control candidates in the network wiring diagram as the solutions of a system of polynomials equations, and then uses computational algebra techniques to find such controllers. The control methods in this paper are validated through the identification of combinatorial interventions in the signaling pathways of previously reported control targets in two well studied systems, a p53-mdm2 network and a blood T cell lymphocyte granular leukemia survival signaling network. Supplementary data is available online and our code in Macaulay2 and Matlab are available via http://www.ms.uky.edu/~dmu228/ControlAlg.ConclusionsThis paper presents a novel method for the identification of intervention targets in Boolean network models. The results in this paper show that the proposed methods are useful and efficient for moderately large networks.Electronic supplementary materialThe online version of this article (doi:10.1186/s12918-016-0332-x) contains supplementary material, which is available to authorized users.

show abstract

Section: Discussionmentioning

confidence: 98%

Identification of control targets in Boolean molecular network models via computational algebra

et al. 2016

View full text Add to dashboard Cite

show abstract

“…In 2007, Akutsu et al [AHCN07] proved that it is NP-hard to verify whether a BCN is controllable in the number of nodes (hence there exists no polynomial-time algorithm for determining controllability of BCNs unless P=NP), and pointed out that "One of the major goals of systems biology is to develop a control theory for complex biological systems". Since then, especially since a control-theoretic framework for BCNs based on the STP of matrices (proposed by Cheng [Che01] in 2001) was established by Cheng et al [CQ09] in 2009, the study on control problems in the area of BCNs has drawn vast attention, e.g., controllability [CQ09,ZQC10], observability [CQ09,FV13,ZZ16,LYC15], reconstructibility [FV13,ZZS16], identifiability [CZ11,ZLZ17], invertibility [ZZX15], Kalman decomposition [ZZ15], and related aspects [Li16, WS18, GZW + 18, LCW18,LW13]. Although some of these results are based on an algebraic method [LYC15], finite automata [ZZ16,ZZS16], graph theory [FV13], and symbolic dynamics [ZZX15], most of them are mainly based on the STP framework.…”

Section: Introductionmentioning

confidence: 99%

“…Since then, especially since a control-theoretic framework for BCNs based on the STP of matrices (proposed by Cheng [Che01] in 2001) was established by Cheng et al [CQ09] in 2009, the study on control problems in the area of BCNs has drawn vast attention, e.g., controllability [CQ09,ZQC10], observability [CQ09,FV13,ZZ16,LYC15], reconstructibility [FV13,ZZS16], identifiability [CZ11,ZLZ17], invertibility [ZZX15], Kalman decomposition [ZZ15], and related aspects [Li16, WS18, GZW + 18, LCW18,LW13]. Although some of these results are based on an algebraic method [LYC15], finite automata [ZZ16,ZZS16], graph theory [FV13], and symbolic dynamics [ZZX15], most of them are mainly based on the STP framework. Besides, as a powerful tool, the STP has been applied to many fields, e.g., symmetry of dynamical systems [CYX07], differential geometry and Lie algebras [CZ03], finite games [Che14, CQL17,Zha17], engineering problems [SWS17,ZW18].…”

Section: Introductionmentioning

confidence: 99%

Synthesis for controllability and observability of logical control networks

Zhang

Johansson

2019

2019 IEEE 58th Conference on Decision and Control (CDC)

View full text Add to dashboard Cite

Finite-state systems have applications in systems biology, formal verification and synthesis problems of infinite-state (hybrid) systems, etc. As deterministic finite-state systems, logical control networks (LCNs) consist of a finite number of nodes which can be in a finite number of states and update their states. In this paper, we investigate the synthesis problem for controllability and observability of LCNs by state feedback under the semitensor product framework. We show that state feedback can never enforce controllability of an LCN, but sometimes can enforce its observability. We prove that for an LCN Σ and another LCN Σ ′ obtained by feeding a state-feedback controller into Σ, (1) if Σ is controllable, then Σ ′ can be either controllable or not; (2) if Σ is not controllable, then Σ ′ is not controllable either; (3) if Σ is observable, then Σ ′ can be either observable or not; (4) if Σ is not observable, Σ ′ can also be observable or not. We also prove that if an unobservable LCN can be synthesized to be observable by state feedback, then it can also be synthesized to be observable by closed-loop state feedback (i.e., state feedback without any input). Furthermore, we give an upper bound for the number of closed-loop state-feedback controllers that are needed to verify whether an unobservable LCN can be synthesized to be observable by state feedback.

show abstract

“…Like nonlinear systems, BCNs are polynomial systems over F 2 , the Galois field of two elements [16]. This explains why the observability proposed in [6], [7] that rely on initial states and inputs are important for BCNs.…”

Section: Introductionmentioning

confidence: 99%

Observability of Boolean Control Networks: A Unified Approach Based on Finite Automata

Zhang

2016

IEEE Trans. Automat. Contr.

152

View full text Add to dashboard Cite

The problem on how to determine the observability of Boolean control networks (BCNs) has been open for five years already. In this paper, we propose a unified approach to determine all the four types of observability of BCNs in the literature. We define the concept of weighted pair graphs for BCNs. In the sense of each observability, we use the so-called weighted pair graph to transform a BCN to a finite automaton, and then we use the automaton to determine observability. In particular, the two types of observability that rely on initial states and inputs in the literature are determined. Finally, we show that no pairs of the four types of observability are equivalent, which reveals the essence of nonlinearity of BCNs.Index Terms-Boolean control network, observability, weighted pair graph, finite automaton, formal language, semi-tensor product of matrices K. Zhang is with College of Automation, Harbin Engineering University,

show abstract

Controllability and observability of Boolean networks arising from biology

Cited by 42 publications

References 68 publications

Identification of control targets in Boolean molecular network models via computational algebra

Identification of control targets in Boolean molecular network models via computational algebra

Synthesis for controllability and observability of logical control networks

Observability of Boolean Control Networks: A Unified Approach Based on Finite Automata

Contact Info

Product

Resources

About