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Bioinformatics Advance Access originally published online on April 26, 2007
Bioinformatics 2007 23(12):1511-1518; doi:10.1093/bioinformatics/btm142
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© The Author 2007. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

An approximation method for solving the steady-state probability distribution of probabilistic Boolean networks

Wai-Ki Ching 1, Shuqin Zhang 1,*, Michael K. Ng 2 and Tatsuya Akutsu 3

1Advanced Modeling and Applied Computing Laboratory, Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong, 2Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong and 3Bioinformatics Center, Institute for Chemical Research, Kyoto University, Uji-city, Kyoto 611-0011, Japan

*To whom correspondence should be addressed.


  Abstract

Motivation: Probabilistic Boolean networks (PBNs) have been proposed to model genetic regulatory interactions. The steady-state probability distribution of a PBN gives important information about the captured genetic network. The computation of the steady-state probability distribution usually includes construction of the transition probability matrix and computation of the steady-state probability distribution. The size of the transition probability matrix is 2n-by-2n where n is the number of genes in the genetic network. Therefore, the computational costs of these two steps are very expensive and it is essential to develop a fast approximation method.

Results: In this article, we propose an approximation method for computing the steady-state probability distribution of a PBN based on neglecting some Boolean networks (BNs) with very small probabilities during the construction of the transition probability matrix. An error analysis of this approximation method is given and theoretical result on the distribution of BNs in a PBN with at most two Boolean functions for one gene is also presented. These give a foundation and support for the approximation method. Numerical experiments based on a genetic network are given to demonstrate the efficiency of the proposed method.

Contact: sqzhang{at}hkusua.hku.hk

Supplementary information: Supplementary data are available at Bioinformatics online.

Associate Editor: Trey Ideker

Received on September 25, 2006; revised on April 6, 2007; accepted on April 6, 2007

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