Article: A matrix perturbation method for computing the steady-state probability distributions of probabilistic Boolean networks with gene perturbations
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| Title | A matrix perturbation method for computing the steady-state probability distributions of probabilistic Boolean networks with gene perturbations | ||||||||||||||||||||
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| Authors | Xu, WW1 Ching, WK3 Zhang, SQ4 Li, W2 Chen, XS2 | ||||||||||||||||||||
| Keywords | Boolean networks Gene perturbation Perturbation matrix Probabilistic Boolean networks Steady-state probability distribution | ||||||||||||||||||||
| Issue Date | 2011 | ||||||||||||||||||||
| Publisher | Elsevier 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?] DOI: http://dx.doi.org/10.1016/j.cam.2010.10.021 | ||||||||||||||||||||
| Abstract | Modeling 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. | ||||||||||||||||||||
| ISSN | 0377-0427 2011 Impact Factor: 1.112 2011 SCImago Journal Rankings: 0.056 | ||||||||||||||||||||
| DOI | http://dx.doi.org/10.1016/j.cam.2010.10.021 | ||||||||||||||||||||
| ISI Accession Number ID | WOS:000287642200029
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 | References in Scopus |
| dc.contributor.author | Xu, WW | ||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| dc.contributor.author | Ching, WK | ||||||||||||||||||||
| dc.contributor.author | Zhang, SQ | ||||||||||||||||||||
| dc.contributor.author | Li, W | ||||||||||||||||||||
| dc.contributor.author | Chen, XS | ||||||||||||||||||||
| dc.date.accessioned | 2011-10-28T02:44:17Z | ||||||||||||||||||||
| dc.date.available | 2011-10-28T02:44:17Z | ||||||||||||||||||||
| dc.date.issued | 2011 | ||||||||||||||||||||
| dc.description.abstract | Modeling 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.nature | Link_to_subscribed_fulltext | ||||||||||||||||||||
| dc.identifier.citation | Journal 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.citeulike | 8184662 | ||||||||||||||||||||
| dc.identifier.doi | http://dx.doi.org/10.1016/j.cam.2010.10.021 | ||||||||||||||||||||
| dc.identifier.epage | 2251 | ||||||||||||||||||||
| dc.identifier.hkuros | 184281 | ||||||||||||||||||||
| dc.identifier.isi | WOS:000287642200029
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.issn | 0377-0427 2011 Impact Factor: 1.112 2011 SCImago Journal Rankings: 0.056 | ||||||||||||||||||||
| dc.identifier.issue | 8 | ||||||||||||||||||||
| dc.identifier.openurl | | ||||||||||||||||||||
| dc.identifier.scopus | eid_2-s2.0-79251593423 | ||||||||||||||||||||
| dc.identifier.spage | 2242 | ||||||||||||||||||||
| dc.identifier.uri | http://hdl.handle.net/10722/142364 | ||||||||||||||||||||
| dc.identifier.volume | 235 | ||||||||||||||||||||
| dc.language | eng | ||||||||||||||||||||
| dc.publisher | Elsevier BV. The Journal's web site is located at http://www.elsevier.com/locate/cam | ||||||||||||||||||||
| dc.publisher.place | Netherlands | ||||||||||||||||||||
| dc.relation.ispartof | Journal of Computational and Applied Mathematics | ||||||||||||||||||||
| dc.relation.references | References in Scopus | ||||||||||||||||||||
| dc.subject | Boolean networks | ||||||||||||||||||||
| dc.subject | Gene perturbation | ||||||||||||||||||||
| dc.subject | Perturbation matrix | ||||||||||||||||||||
| dc.subject | Probabilistic Boolean networks | ||||||||||||||||||||
| dc.subject | Steady-state probability distribution | ||||||||||||||||||||
| dc.title | A matrix perturbation method for computing the steady-state probability distributions of probabilistic Boolean networks with gene perturbations | ||||||||||||||||||||
| dc.type | Article |
Author Affiliations
- Academy of Mathematics and System Sciences Chinese Academy of Sciences
- South China Normal University
- The University of Hong Kong
- Fudan University