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Article: A matrix perturbation method for computing the steady-state probability distributions of probabilistic Boolean networks with gene perturbations

TitleA matrix perturbation method for computing the steady-state probability distributions of probabilistic Boolean networks with gene perturbations
Authors
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
Citation
Journal Of Computational And Applied Mathematics, 2011, v. 235 n. 8, p. 2242-2251 How to Cite?
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.
Persistent Identifierhttp://hdl.handle.net/10722/142364
ISSN
2015 Impact Factor: 1.328
2015 SCImago Journal Rankings: 1.089
ISI Accession Number ID
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).

References

 

DC FieldValueLanguage
dc.contributor.authorXu, WWen_HK
dc.contributor.authorChing, WKen_HK
dc.contributor.authorZhang, SQen_HK
dc.contributor.authorLi, Wen_HK
dc.contributor.authorChen, XSen_HK
dc.date.accessioned2011-10-28T02:44:17Z-
dc.date.available2011-10-28T02:44:17Z-
dc.date.issued2011en_HK
dc.identifier.citationJournal Of Computational And Applied Mathematics, 2011, v. 235 n. 8, p. 2242-2251en_HK
dc.identifier.issn0377-0427en_HK
dc.identifier.urihttp://hdl.handle.net/10722/142364-
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.en_HK
dc.languageengen_US
dc.publisherElsevier BV. The Journal's web site is located at http://www.elsevier.com/locate/camen_HK
dc.relation.ispartofJournal of Computational and Applied Mathematicsen_HK
dc.subjectBoolean networksen_HK
dc.subjectGene perturbationen_HK
dc.subjectPerturbation matrixen_HK
dc.subjectProbabilistic Boolean networksen_HK
dc.subjectSteady-state probability distributionen_HK
dc.titleA matrix perturbation method for computing the steady-state probability distributions of probabilistic Boolean networks with gene perturbationsen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=0377-0427&volume=235&spage=2242&epage=2251&date=2011&atitle=A+Matrix+Perturbation+Method+for+Computing+the+Steady-state+Probability+Distributions+of+Probabilistic+Boolean+Networks+with+Gene+Perturbationsen_US
dc.identifier.emailChing, WK:wching@hku.hken_HK
dc.identifier.authorityChing, WK=rp00679en_HK
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1016/j.cam.2010.10.021en_HK
dc.identifier.scopuseid_2-s2.0-79251593423en_HK
dc.identifier.hkuros184281en_US
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-79251593423&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume235en_HK
dc.identifier.issue8en_HK
dc.identifier.spage2242en_HK
dc.identifier.epage2251en_HK
dc.identifier.isiWOS:000287642200029-
dc.publisher.placeNetherlandsen_HK
dc.identifier.scopusauthoridXu, WW=36509451500en_HK
dc.identifier.scopusauthoridChing, WK=13310265500en_HK
dc.identifier.scopusauthoridZhang, SQ=10143093600en_HK
dc.identifier.scopusauthoridLi, W=36068145000en_HK
dc.identifier.scopusauthoridChen, XS=15031964800en_HK
dc.identifier.citeulike8184662-

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