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Article: Generating probabilistic Boolean networks from a prescribed stationary distribution

TitleGenerating probabilistic Boolean networks from a prescribed stationary distribution
Authors
KeywordsBoolean networks
Genetic networks
Inverse problem
Probabilistic Boolean networks
Stationary distribution
Issue Date2010
PublisherElsevier Inc. The Journal's web site is located at http://www.elsevier.com/locate/ins
Citation
Information Sciences, 2010, v. 180 n. 13, p. 2560-2570 How to Cite?
AbstractModeling gene regulation is an important problem in genomic research. Boolean networks (BN) and its generalization probabilistic Boolean networks (PBNs) have been proposed to model genetic regulatory interactions. BN is a deterministic model while PBN is a stochastic model. In a PBN, on one hand, its stationary distribution gives important information about the long-run behavior of the network. On the other hand, one may be interested in system synthesis which requires the construction of networks from the observed stationary distribution. This results in an inverse problem which is ill-posed and challenging. Because there may be many networks or no network having the given properties and the size of the inverse problem is huge. In this paper, we consider the problem of constructing PBNs from a given stationary distribution and a set of given Boolean Networks (BNs). We first formulate the inverse problem as a constrained least squares problem. We then propose a heuristic method based on Conjugate Gradient (CG) algorithm, an iterative method, to solve the resulting least squares problem. We also introduce an estimation method for the parameters of the PBNs. Numerical examples are then given to demonstrate the effectiveness of the proposed methods. © 2010 Elsevier Inc. All rights reserved.
Persistent Identifierhttp://hdl.handle.net/10722/75296
ISSN
2015 Impact Factor: 3.364
2015 SCImago Journal Rankings: 2.513
ISI Accession Number ID
Funding AgencyGrant Number
HKRGC7017/07P
HKUCRGC
HKU
Hung Hing Ying Physical Research Sciences
National Natural Science Foundation of China10971075
10901042
National Natural Science Foundation of Guangdong915102240-1000002
Ministry of Education of China
Shanghai Municipal Education Commission
Shanghai Education Development Foundation
Funding Information:

The authors thank the three anonymous reviewers for their helpful comments and suggestions. Wai-Ki Ching is 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 National Natural Science Foundation of Guangdong Grant No. 915102240-1000002. Shu-Qin Zhang is supported by 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.

References

 

DC FieldValueLanguage
dc.contributor.authorZhang, SQen_HK
dc.contributor.authorChing, WKen_HK
dc.contributor.authorChen, Xen_HK
dc.contributor.authorTsing, NKen_HK
dc.date.accessioned2010-09-06T07:09:47Z-
dc.date.available2010-09-06T07:09:47Z-
dc.date.issued2010en_HK
dc.identifier.citationInformation Sciences, 2010, v. 180 n. 13, p. 2560-2570en_HK
dc.identifier.issn0020-0255en_HK
dc.identifier.urihttp://hdl.handle.net/10722/75296-
dc.description.abstractModeling gene regulation is an important problem in genomic research. Boolean networks (BN) and its generalization probabilistic Boolean networks (PBNs) have been proposed to model genetic regulatory interactions. BN is a deterministic model while PBN is a stochastic model. In a PBN, on one hand, its stationary distribution gives important information about the long-run behavior of the network. On the other hand, one may be interested in system synthesis which requires the construction of networks from the observed stationary distribution. This results in an inverse problem which is ill-posed and challenging. Because there may be many networks or no network having the given properties and the size of the inverse problem is huge. In this paper, we consider the problem of constructing PBNs from a given stationary distribution and a set of given Boolean Networks (BNs). We first formulate the inverse problem as a constrained least squares problem. We then propose a heuristic method based on Conjugate Gradient (CG) algorithm, an iterative method, to solve the resulting least squares problem. We also introduce an estimation method for the parameters of the PBNs. Numerical examples are then given to demonstrate the effectiveness of the proposed methods. © 2010 Elsevier Inc. All rights reserved.en_HK
dc.languageengen_HK
dc.publisherElsevier Inc. The Journal's web site is located at http://www.elsevier.com/locate/insen_HK
dc.relation.ispartofInformation Sciencesen_HK
dc.rightsInformation Sciences. Copyright © Elsevier Inc.en_HK
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.rightsNOTICE: this is the author’s version of a work that was accepted for publication in Information Sciences. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Information Sciences, 2010, v. 180 n. 13, p. 2560-2570. DOI: 10.1016/j.ins.2010.03.014-
dc.subjectBoolean networksen_HK
dc.subjectGenetic networksen_HK
dc.subjectInverse problemen_HK
dc.subjectProbabilistic Boolean networksen_HK
dc.subjectStationary distributionen_HK
dc.titleGenerating probabilistic Boolean networks from a prescribed stationary distributionen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=0020-0255&volume=180&issue=13&spage=2560&epage=2570&date=2010&atitle=Generating+probabilistic+boolean+networks+from+a+prescribed+stationary+distributionen_HK
dc.identifier.emailChing, WK:wching@hku.hken_HK
dc.identifier.emailTsing, NK:nktsing@hku.hken_HK
dc.identifier.authorityChing, WK=rp00679en_HK
dc.identifier.authorityTsing, NK=rp00794en_HK
dc.description.naturepostprint-
dc.identifier.doi10.1016/j.ins.2010.03.014en_HK
dc.identifier.scopuseid_2-s2.0-77950863180en_HK
dc.identifier.hkuros169673en_HK
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-77950863180&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume180en_HK
dc.identifier.issue13en_HK
dc.identifier.spage2560en_HK
dc.identifier.epage2570en_HK
dc.identifier.eissn1872-6291-
dc.identifier.isiWOS:000277850100005-
dc.publisher.placeUnited Statesen_HK
dc.identifier.scopusauthoridZhang, SQ=10143093600en_HK
dc.identifier.scopusauthoridChing, WK=13310265500en_HK
dc.identifier.scopusauthoridChen, X=35772404700en_HK
dc.identifier.scopusauthoridTsing, NK=6602663351en_HK
dc.identifier.citeulike6912995-

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