Optimal Control of Boolean Biological Networks Modeled by Petri Nets

Koichi KOBAYASHI  Kunihiko HIRAISHI  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E96-A    No.2    pp.532-539
Publication Date: 2013/02/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E96.A.532
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Mathematical Systems Science and its Applications)
Category: Systems and Control
Keyword: 
asynchronous behavior,  Boolean networks,  integer programming,  optimal control,  Petri nets,  

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Summary: 
A Boolean network model is one of the models of gene regulatory networks, and is widely used in analysis and control. Although a Boolean network is a class of discrete-time nonlinear systems and expresses the synchronous behavior, it is important to consider the asynchronous behavior. In this paper, using a Petri net, a new modeling method of asynchronous Boolean networks with control inputs is proposed. Furthermore, the optimal control problem of Petri nets expressing asynchronous Boolean networks is formulated, and is reduced to an integer programming problem. The proposed approach will provide us one of the mathematical bases of control methods for gene regulatory networks.