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Article: A matrix perturbation method for computing the steady-state probability distributions of probabilistic Boolean networks with gene perturbations
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TitleA matrix perturbation method for computing the steady-state probability distributions of probabilistic Boolean networks with gene perturbations
 
AuthorsXu, WW1
Ching, WK3
Zhang, SQ4
Li, W2
Chen, XS2
 
KeywordsBoolean networks
Gene perturbation
Perturbation matrix
Probabilistic Boolean networks
Steady-state probability distribution
 
Issue Date2011
 
PublisherElsevier BV. The Journal's web site is located at http://www.elsevier.com/locate/cam
 
CitationJournal Of Computational And Applied Mathematics, 2011, v. 235 n. 8, p. 2242-2251 [How to Cite?]
DOI: http://dx.doi.org/10.1016/j.cam.2010.10.021
 
AbstractModeling genetic regulatory interactions is an important issue in systems biology. Probabilistic Boolean networks (PBNs) have been proved to be a useful tool for the task. The steady-state probability distribution of a PBN gives important information about the captured genetic network. The computation of the steady-state probability distribution involves the construction of the transition probability matrix of the PBN. The size of the transition probability matrix is 2n×2n where n is the number of genes. Although given the number of genes and the perturbation probability in a perturbed PBN, the perturbation matrix is the same for different PBNs, the storage requirement for this matrix is huge if the number of genes is large. Thus an important issue is developing computational methods from the perturbation point of view. In this paper, we analyze and estimate the steady-state probability distribution of a PBN with gene perturbations. We first analyze the perturbation matrix. We then give a perturbation matrix analysis for the captured PBN problem and propose a method for computing the steady-state probability distribution. An approximation method with error analysis is then given for further reducing the computational complexity. Numerical experiments are given to demonstrate the efficiency of the proposed methods. © 2010 Elsevier B.V. All rights reserved.
 
ISSN0377-0427
2013 Impact Factor: 1.077
2013 SCImago Journal Rankings: 1.148
 
DOIhttp://dx.doi.org/10.1016/j.cam.2010.10.021
 
ISI Accession Number IDWOS:000287642200029
Funding AgencyGrant Number
HKRGC7017/07P
HKU Strategy Research Theme fund on Computational Sciences
Hung Hing Ying Physical Research Sciences Research Grant
National Natural Science Foundation of China10971075
10901042
Guangdong Provincial Natural Science Foundations9151063101000021
Ministry of Education of China
Shanghai Municipal Education Commission
Shanghai Education Development Foundation
Guangdong Provincial Natural Science Foundations, PR China9151063101000021
Funding Information:

This work was supported in part by HKRGC Grant No. 7017/07P, HKUCRGC Grants, HKU Strategy Research Theme fund on Computational Sciences, Hung Hing Ying Physical Research Sciences Research Grant, National Natural Science Foundation of China Grant No. 10971075 and Guangdong Provincial Natural Science Foundations No. 9151063101000021 (W. Ching), National Natural Science Foundation of China Grant No. 10901042, 10971075, Doctoral Fund of Ministry of Education of China, 'Chen Guang' project supported by Shanghai Municipal Education Commission and Shanghai Education Development Foundation (S. Zhang), National Natural Science Foundation of China Grant No. 10971075 and Guangdong Provincial Natural Science Foundations No. 9151063101000021, PR China (W. Li).

 
ReferencesReferences in Scopus
 
DC FieldValue
dc.contributor.authorXu, WW
 
dc.contributor.authorChing, WK
 
dc.contributor.authorZhang, SQ
 
dc.contributor.authorLi, W
 
dc.contributor.authorChen, XS
 
dc.date.accessioned2011-10-28T02:44:17Z
 
dc.date.available2011-10-28T02:44:17Z
 
dc.date.issued2011
 
dc.description.abstractModeling genetic regulatory interactions is an important issue in systems biology. Probabilistic Boolean networks (PBNs) have been proved to be a useful tool for the task. The steady-state probability distribution of a PBN gives important information about the captured genetic network. The computation of the steady-state probability distribution involves the construction of the transition probability matrix of the PBN. The size of the transition probability matrix is 2n×2n where n is the number of genes. Although given the number of genes and the perturbation probability in a perturbed PBN, the perturbation matrix is the same for different PBNs, the storage requirement for this matrix is huge if the number of genes is large. Thus an important issue is developing computational methods from the perturbation point of view. In this paper, we analyze and estimate the steady-state probability distribution of a PBN with gene perturbations. We first analyze the perturbation matrix. We then give a perturbation matrix analysis for the captured PBN problem and propose a method for computing the steady-state probability distribution. An approximation method with error analysis is then given for further reducing the computational complexity. Numerical experiments are given to demonstrate the efficiency of the proposed methods. © 2010 Elsevier B.V. All rights reserved.
 
dc.description.naturelink_to_subscribed_fulltext
 
dc.identifier.citationJournal Of Computational And Applied Mathematics, 2011, v. 235 n. 8, p. 2242-2251 [How to Cite?]
DOI: http://dx.doi.org/10.1016/j.cam.2010.10.021
 
dc.identifier.citeulike8184662
 
dc.identifier.doihttp://dx.doi.org/10.1016/j.cam.2010.10.021
 
dc.identifier.epage2251
 
dc.identifier.hkuros184281
 
dc.identifier.isiWOS:000287642200029
Funding AgencyGrant Number
HKRGC7017/07P
HKU Strategy Research Theme fund on Computational Sciences
Hung Hing Ying Physical Research Sciences Research Grant
National Natural Science Foundation of China10971075
10901042
Guangdong Provincial Natural Science Foundations9151063101000021
Ministry of Education of China
Shanghai Municipal Education Commission
Shanghai Education Development Foundation
Guangdong Provincial Natural Science Foundations, PR China9151063101000021
Funding Information:

This work was supported in part by HKRGC Grant No. 7017/07P, HKUCRGC Grants, HKU Strategy Research Theme fund on Computational Sciences, Hung Hing Ying Physical Research Sciences Research Grant, National Natural Science Foundation of China Grant No. 10971075 and Guangdong Provincial Natural Science Foundations No. 9151063101000021 (W. Ching), National Natural Science Foundation of China Grant No. 10901042, 10971075, Doctoral Fund of Ministry of Education of China, 'Chen Guang' project supported by Shanghai Municipal Education Commission and Shanghai Education Development Foundation (S. Zhang), National Natural Science Foundation of China Grant No. 10971075 and Guangdong Provincial Natural Science Foundations No. 9151063101000021, PR China (W. Li).

 
dc.identifier.issn0377-0427
2013 Impact Factor: 1.077
2013 SCImago Journal Rankings: 1.148
 
dc.identifier.issue8
 
dc.identifier.openurl
 
dc.identifier.scopuseid_2-s2.0-79251593423
 
dc.identifier.spage2242
 
dc.identifier.urihttp://hdl.handle.net/10722/142364
 
dc.identifier.volume235
 
dc.languageeng
 
dc.publisherElsevier BV. The Journal's web site is located at http://www.elsevier.com/locate/cam
 
dc.publisher.placeNetherlands
 
dc.relation.ispartofJournal of Computational and Applied Mathematics
 
dc.relation.referencesReferences in Scopus
 
dc.subjectBoolean networks
 
dc.subjectGene perturbation
 
dc.subjectPerturbation matrix
 
dc.subjectProbabilistic Boolean networks
 
dc.subjectSteady-state probability distribution
 
dc.titleA matrix perturbation method for computing the steady-state probability distributions of probabilistic Boolean networks with gene perturbations
 
dc.typeArticle
 
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Author Affiliations
  1. Academy of Mathematics and System Sciences Chinese Academy of Sciences
  2. South China Normal University
  3. The University of Hong Kong
  4. Fudan University