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BioMed Research International
Volume 2013 (2013), Article ID 246761, 11 pages
http://dx.doi.org/10.1155/2013/246761
Research Article

Optimal Control of Gene Regulatory Networks with Effectiveness of Multiple Drugs: A Boolean Network Approach

School of Information Science, Japan Advanced Institute of Science and Technology, Ishikawa 923-1292, Japan

Received 30 April 2013; Revised 25 June 2013; Accepted 12 July 2013

Academic Editor: Lei Chen

Copyright © 2013 Koichi Kobayashi and Kunihiko Hiraishi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Developing control theory of gene regulatory networks is one of the significant topics in the field of systems biology, and it is expected to apply the obtained results to gene therapy technologies in the future. In this paper, a control method using a Boolean network (BN) is studied. A BN is widely used as a model of gene regulatory networks, and gene expression is expressed by a binary value (0 or 1). In the control problem, we assume that the concentration level of a part of genes is arbitrarily determined as the control input. However, there are cases that no gene satisfying this assumption exists, and it is important to consider structural control via external stimuli. Furthermore, these controls are realized by multiple drugs, and it is also important to consider multiple effects such as duration of effect and side effects. In this paper, we propose a BN model with two types of the control inputs and an optimal control method with duration of drug effectiveness. First, a BN model and duration of drug effectiveness are discussed. Next, the optimal control problem is formulated and is reduced to an integer linear programming problem. Finally, numerical simulations are shown.