An Approximation Method for Solving the Steady-state Probability Distribution of Probabilistic Boolean Networks. Export

@article{citeulike:1319068, 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 2(n)-by-2(n) 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 paper, we propose an approximation method for computing the steady-state probability distribution of a PBN based on neglecting some BNs with very small probabilities during the construction of the transition probability matrix. An error analysis of this approximation method is given and theoretical results 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.}, address = {Advanced Modeling and Applied Computing Laboratory, Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong, Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong and Bioinformatics Center, Institute for Chemical Research, Kyoto University, Uji-city, Kyoto 611-0011, Japan.}, author = {Ching, Wai-Ki K. and Zhang, Shu-Qin Q. and Ng, Michael K K. and Akutsu, Tatsuya}, citeulike-article-id = {1319068}, citeulike-linkout-0 = {http://dx.doi.org/10.1093/bioinformatics/btm142}, citeulike-linkout-1 = {http://bioinformatics.oxfordjournals.org/cgi/content/abstract/23/12/1511}, citeulike-linkout-2 = {http://view.ncbi.nlm.nih.gov/pubmed/17463027}, citeulike-linkout-3 = {http://www.hubmed.org/display.cgi?uids=17463027}, day = {26}, doi = {10.1093/bioinformatics/btm142}, issn = {1460-2059}, journal = {Bioinformatics}, keywords = {boolean, booleannet, booleannets, booleannetworks, pbn, probabilistic}, month = {April}, posted-at = {2007-05-22 10:46:34}, priority = {1}, title = {An Approximation Method for Solving the Steady-state Probability Distribution of Probabilistic Boolean Networks.}, url = {http://dx.doi.org/10.1093/bioinformatics/btm142}, year = {2007} }

TY - JOUR ID - citeulike:1319068 L3 - citeulike-article-id:1319068 N2 - 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 2(n)-by-2(n) 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 paper, we propose an approximation method for computing the steady-state probability distribution of a PBN based on neglecting some BNs with very small probabilities during the construction of the transition probability matrix. An error analysis of this approximation method is given and theoretical results 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. JF - Bioinformatics SN - 1460-2059 AD - Advanced Modeling and Applied Computing Laboratory, Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong, Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong and Bioinformatics Center, Institute for Chemical Research, Kyoto University, Uji-city, Kyoto 611-0011, Japan. TI - An Approximation Method for Solving the Steady-state Probability Distribution of Probabilistic Boolean Networks. KW - boolean KW - booleannet KW - booleannets KW - booleannetworks KW - pbn KW - probabilistic AU - Ching, Wai-Ki AU - Zhang, Shu-Qin AU - Ng, Michael K AU - Akutsu, Tatsuya PY - 2007/04/26/ UR - http://dx.doi.org/10.1093/bioinformatics/btm142 ER -