Optimization-Based Approaches to Control of Probabilistic Boolean Networks

Kobayashi, Koichi; Hiraishi, Kunihiko

doi:10.3390/a10010031

Cited by 15 publications

(9 citation statements)

References 61 publications

(93 reference statements)

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“…While this model is quite simple, it is still useful in developing a control method for gene regulatory networks. A BN has been extended to a probabilistic BN (PBN) and a context-sensitive PBN (see, e.g., [14][15][16][17]).…”

Section: Introductionmentioning

confidence: 99%

Design of Fixed Points in Boolean Networks Using Feedback Vertex Sets and Model Reduction

Kobayashi

2019

Complexity

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Fixed points in Boolean networks (BNs) represent cell types or states of cells and are important to decide characteristics of cells. As the control problem on fixed points, it is important to consider the problem of changing fixed points by using external stimuli (i.e., control inputs). In this paper, we propose two methods for designing fixed points. First, a design method using model reduction is proposed. Using the reduced model, the problem of placing fixed points can be rewritten as an integer linear programming problem. Next, we consider the design problem using only the graph structure of a given BN and derive some results. In both methods, a feedback vertex set of a directed graph plays an important role. Finally, a biological example is presented.

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Section: Introductionmentioning

confidence: 99%

Design of Fixed Points in Boolean Networks Using Feedback Vertex Sets and Model Reduction

Kobayashi

2019

Complexity

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“…Model reduction has also been studied in [11][12][13]. For a PBN, controllability/reachability analysis [14][15][16][17] and optimal control [18][19][20][21][22] have been studied (see also the survey paper [23]).…”

Section: Introductionmentioning

confidence: 99%

Construction Method of Probabilistic Boolean Networks Based on Imperfect Information

2019

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A probabilistic Boolean network (PBN) is well known as one of the mathematical models of gene regulatory networks. In a Boolean network, expression of a gene is approximated by a binary value, and its time evolution is expressed by Boolean functions. In a PBN, a Boolean function is probabilistically chosen from candidates of Boolean functions. One of the authors has proposed a method to construct a PBN from imperfect information. However, there is a weakness that the number of candidates of Boolean functions may be redundant. In this paper, this construction method is improved to efficiently utilize given information. To derive Boolean functions and those selection probabilities, the linear programming problem is solved. Here, we introduce the objective function to reduce the number of candidates. The proposed method is demonstrated by a numerical example.

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“…Finite horizon optimal control problems for PBNs and stochastic logical networks were investigated in [28] and [32], respectively. Integer programming algorithm [29] and polynomial optimization algorithm for the finite horizon optimal control problem of a PBN were developed by Kobayashi and Hiraishi [33] to reduce the computational complexity.…”

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confidence: 99%

Policy Iteration Approach to the Infinite Horizon Average Optimal Control of Probabilistic Boolean Networks

Guo

Toyoda

2021

IEEE Trans. Neural Netw. Learning Syst.

111

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This article studies the optimal control of probabilistic Boolean control networks (PBCNs) with the infinite horizon average cost criterion. By resorting to the semitensor product (STP) of matrices, a nested optimality equation for the optimal control problem of PBCNs is proposed. The Laurent series expression technique and the Jordan decomposition method derive a novel policy iteration-type algorithm, where finite iteration steps can provide the optimal state feedback law, which is presented. Finally, the intervention problem of the probabilistic Ara operon in E. coil, as a biological application, is solved to demonstrate the effectiveness and feasibility of the proposed theoretical approach and algorithms. Index Terms-Boolean networks (BNs), infinite horizon problem, logical networks, optimal control, probabilistic BNs (PBNs), semitensor product (STP) of matrix. I. INTRODUCTIONB OOLEAN networks (BNs), as a special kind of discrete (logical) dynamical models with Boolean-valued variables, were first proposed by a theoretical biologist Kauffman [1] in 1969 to model and analyze the complex biological behavior in biological systems, including gene regularity networks [2]- [4]. Since BNs modeling may be the simplest representation of the relevant biological and physical concepts for some finite-state systems, BNs have been also used in various theoretical and practical applications, such as fault detection in logic circuits [5], [6], game theory [7], [8], combustion engines [9], and many other areas.After introducing the semitensor product (STP) of matrix [10] to BNs, as an effective approach, some fundamental Manuscript

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Optimization-Based Approaches to Control of Probabilistic Boolean Networks

Cited by 15 publications

References 61 publications

Design of Fixed Points in Boolean Networks Using Feedback Vertex Sets and Model Reduction

Design of Fixed Points in Boolean Networks Using Feedback Vertex Sets and Model Reduction

Construction Method of Probabilistic Boolean Networks Based on Imperfect Information

Policy Iteration Approach to the Infinite Horizon Average Optimal Control of Probabilistic Boolean Networks

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