Eur. Phys. J. B (2013) 86: 245
https://doi.org/10.1140/epjb/e2013-30746-7

Regular Article

Optimal finite horizon control in gene regulatory networks

School of Mathematical Sciences, South China Normal University, Guangzhou 510631, P.R. China

^a e-mail: liuql2007@aliyun.com

Received: 14 August 2012
Received in final form: 27 January 2013
Published online: 3 June 2013

Abstract

As a paradigm for modeling gene regulatory networks, probabilistic Boolean networks (PBNs) form a subclass of Markov genetic regulatory networks. To date, many different stochastic optimal control approaches have been developed to find therapeutic intervention strategies for PBNs. A PBN is essentially a collection of constituent Boolean networks via a probability structure. Most of the existing works assume that the probability structure for Boolean networks selection is known. Such an assumption cannot be satisfied in practice since the presence of noise prevents the probability structure from being accurately determined. In this paper, we treat a case in which we lack the governing probability structure for Boolean network selection. Specifically, in the framework of PBNs, the theory of finite horizon Markov decision process is employed to find optimal constituent Boolean networks with respect to the defined objective functions. In order to illustrate the validity of our proposed approach, an example is also displayed.