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

doi:10.1016/j.cam.2010.10.021

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	A matrix perturbation method for computing the steady-state probability distributions of probabilistic Boolean networks with gene perturbations
	Xu, Wei-Wei 2; Ching, Wai-Ki 3; Zhang, Shu-Qin 1; Li, Wen 4; Chen, Xiao-Shan 4
	2011-02-15
发表期刊	JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
ISSN	0377-0427
卷号	235 期号:8 页码:2242-2251
摘要	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.
关键词	Boolean networks Gene perturbation Perturbation matrix Probabilistic Boolean networks Steady-state probability distribution
DOI	10.1016/j.cam.2010.10.021
语种	英语
资助项目	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研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000287642200029
出版者	ELSEVIER SCIENCE BV
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/12774
专题	中国科学院数学与系统科学研究院
通讯作者	Zhang, Shu-Qin
作者单位	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
推荐引用方式 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.