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A matrix perturbation method for computing the steady-state probability distributions of probabilistic Boolean networks with gene perturbations
Xu, Wei-Wei2; Ching, Wai-Ki3; Zhang, Shu-Qin1; Li, Wen4; Chen, Xiao-Shan4
2011-02-15
Source PublicationJOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
ISSN0377-0427
Volume235Issue:8Pages:2242-2251
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 2(n) x 2(n) 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. (C) 2010 Elsevier B.V. All rights reserved.
KeywordBoolean networks Gene perturbation Perturbation matrix Probabilistic Boolean networks Steady-state probability distribution
DOI10.1016/j.cam.2010.10.021
Language英语
Funding ProjectHKRGC[7017/07P] ; HKU Strategy Research Theme fund on Computational Sciences ; Hung Hing Ying Physical Research Sciences Research Grant ; National Natural Science Foundation of China[10971075] ; National Natural Science Foundation of China[10901042] ; Guangdong Provincial Natural Science Foundations[9151063101000021] ; Ministry of Education of China ; Shanghai Municipal Education Commission ; Shanghai Education Development Foundation ; Guangdong Provincial Natural Science Foundations, PR China[9151063101000021]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000287642200029
PublisherELSEVIER SCIENCE BV
Citation statistics
Cited Times:8[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/12774
Collection中国科学院数学与系统科学研究院
Affiliation1.Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China
2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100080, Peoples R China
3.Univ Hong Kong, Adv Modeling & Appl Comp Lab, Dept Math, Hong Kong, Hong Kong, Peoples R China
4.S China Normal Univ, Sch Math Sci, Guangzhou 510631, Guangdong, Peoples R China
Recommended Citation
GB/T 7714
Xu, Wei-Wei,Ching, Wai-Ki,Zhang, Shu-Qin,et al. A matrix perturbation method for computing the steady-state probability distributions of probabilistic Boolean networks with gene perturbations[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS,2011,235(8):2242-2251.
APA Xu, Wei-Wei,Ching, Wai-Ki,Zhang, Shu-Qin,Li, Wen,&Chen, Xiao-Shan.(2011).A matrix perturbation method for computing the steady-state probability distributions of probabilistic Boolean networks with gene perturbations.JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS,235(8),2242-2251.
MLA Xu, Wei-Wei,et al."A matrix perturbation method for computing the steady-state probability distributions of probabilistic Boolean networks with gene perturbations".JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 235.8(2011):2242-2251.
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