Relaxation Property and Stability Analysis of the Quasispecies Models

	Relaxation Property and Stability Analysis of the Quasispecies Models
	Fegn Xiao-Li 1,2; Li Yu-Xiao 1; Gu Jian-Zhong 3,4; Zhuo Yi-Zhong 3
刊名	COMMUNICATIONS IN THEORETICAL PHYSICS
	2009-10
卷号	52 页码:726-734
关键词	relaxation time critical exponent error threshold
ISSN号	0253-6102
英文摘要	The relaxation property of both Eigen model and Crow-Kimura model with a single peak fitness landscape is studied from phase transition point of view. We first analyze the eigenvalue spectra of the replication mutation matrices. For sufficiently long sequences, the almost crossing point between the largest and second-largest eigenvalues locates the error threshold at which critical slowing down behavior appears. We calculate the critical exponent in the limit of infinite sequence lengths and compare it with the result from numerical curve fittings at sufficiently long sequences. We find that for both models the relaxation time diverges with exponent 1 at the error (mutation) threshold point. Results obtained from both methods agree quite well. From the unlimited correlation length feature, the first order phase transition is further confirmed. Finally with linear stability theory, we show that the two model systems are stable for all ranges of mutation rate. The Eigen model is asymptotically stable in terms of mutant classes, and the Crow-Kimura model is completely stable.
资助项目	Major State Basic Research Developing Program[2007CB815003]
WOS关键词	EIGEN EVOLUTION MODEL ; ISING QUANTUM CHAIN ; ERROR CATASTROPHE ; FITNESS LANDSCAPES ; PHASE-TRANSITIONS ; THRESHOLDS ; REPLICATION ; POPULATIONS ; SELECTION ; CANCER
WOS研究方向	Physics
语种	英语
出版者	IOP PUBLISHING LTD
WOS记录号	WOS:000271194800033
内容类型	期刊论文
源URL	[http://119.78.100.186/handle/113462/57108]
专题	中国科学院近代物理研究所
通讯作者	Fegn Xiao-Li
作者单位	1.Zhengzhou Univ, Sch Phys Engn, Zhengzhou 450052, Peoples R China 2.Chinese Acad Sci, Inst Biophys, Ctr Computat & Syst Biol, Beijing 100101, Peoples R China 3.China Inst Atom Energy, Beijing 102413, Peoples R China 4.Natl Lab Heavy Ion Accelerator Lanzhou, Ctr Theoret Nucl Phys, Lanzhou 730000, Peoples R China
推荐引用方式 GB/T 7714	Fegn Xiao-Li,Li Yu-Xiao,Gu Jian-Zhong,et al. Relaxation Property and Stability Analysis of the Quasispecies Models[J]. COMMUNICATIONS IN THEORETICAL PHYSICS,2009,52:726-734.
APA	Fegn Xiao-Li,Li Yu-Xiao,Gu Jian-Zhong,&Zhuo Yi-Zhong.(2009).Relaxation Property and Stability Analysis of the Quasispecies Models.COMMUNICATIONS IN THEORETICAL PHYSICS,52,726-734.
MLA	Fegn Xiao-Li,et al."Relaxation Property and Stability Analysis of the Quasispecies Models".COMMUNICATIONS IN THEORETICAL PHYSICS 52(2009):726-734.