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

Wai Ki Ching, Shuqin Zhang*, Kwok Po NG, Tatsuya Akutsu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

67 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)1511-1518
Number of pages8
JournalBioinformatics
Volume23
Issue number12
DOIs
Publication statusPublished - 15 Jun 2007

Scopus Subject Areas

  • Statistics and Probability
  • Biochemistry
  • Molecular Biology
  • Computer Science Applications
  • Computational Theory and Mathematics
  • Computational Mathematics

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