KMS Of Academy of mathematics and systems sciences, CAS
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 Publication | JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS |
ISSN | 0377-0427 |
Volume | 235Issue:8Pages:2242-2251 |
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 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. |
Keyword | Boolean networks Gene perturbation Perturbation matrix Probabilistic Boolean networks Steady-state probability distribution |
DOI | 10.1016/j.cam.2010.10.021 |
Language | 英语 |
Funding Project | HKRGC[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 Area | Mathematics |
WOS Subject | Mathematics, Applied |
WOS ID | WOS:000287642200029 |
Publisher | ELSEVIER SCIENCE BV |
Citation statistics | |
Document Type | 期刊论文 |
Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/12774 |
Collection | 中国科学院数学与系统科学研究院 |
Corresponding Author | Zhang, Shu-Qin |
Affiliation | 1.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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