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 mutatio...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 seeond-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 Igigen model is asymptotically stable in terms of mutant classes, and the Crow-Kimura model is completely stable.展开更多
脑小血管病常见于中老年人,可导致老年人行动障碍、情感障碍和认知功能下降或血管性痴呆,严重影响老年人的生活质量。脑血管内皮细胞功能障碍是脑小血管病(cerebral small vessel disease,CSVD)的使动因素之一。常见的口腔慢性口腔感染...脑小血管病常见于中老年人,可导致老年人行动障碍、情感障碍和认知功能下降或血管性痴呆,严重影响老年人的生活质量。脑血管内皮细胞功能障碍是脑小血管病(cerebral small vessel disease,CSVD)的使动因素之一。常见的口腔慢性口腔感染包括龋病、根尖周病,牙龈炎和牙周炎,所致的炎症状态和内皮细胞功能障碍或与脑小血管病的发生发展密切相关。本文旨在对口腔慢性感染性疾病与CSVD之间的潜在联系和研究现状做一综述。展开更多
Based on the Eigen and Crow-Kimura models with a single-peak fitness landscape, we propose the fitness values of all sequence types to be Gausslan distributed random variables to incorporate the effects of the fluctua...Based on the Eigen and Crow-Kimura models with a single-peak fitness landscape, we propose the fitness values of all sequence types to be Gausslan distributed random variables to incorporate the effects of the fluctuations of the fitness landscapes （noise of environments） and investigate the concentration distribution and error threshold of quasispecies by performing an ensemble average within this theoretical framework. We find that a small fluctuation of the fitness landscape causes only a slight change in the concentration distribution and error threshold, which implies that the error threshold is stable against small perturbations. However, for a sizable fluctuation, quite different from the previous deterministic models, our statistical results show that the transition from quasi-species to error catastrophe is not so sharp, indicating that the error threshold is located within a certain range and has a shift toward a larger value. Our results are qualitatively in agreement with the experimental data and provide a new implication for antiviral strategies.展开更多
基金Supported in part by the National natural Science Foundation of China under Grant No.10675170Major State Basic Research Developing Program under Gant No.2007CB815003
文摘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 seeond-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 Igigen model is asymptotically stable in terms of mutant classes, and the Crow-Kimura model is completely stable.
文摘脑小血管病常见于中老年人,可导致老年人行动障碍、情感障碍和认知功能下降或血管性痴呆,严重影响老年人的生活质量。脑血管内皮细胞功能障碍是脑小血管病(cerebral small vessel disease,CSVD)的使动因素之一。常见的口腔慢性口腔感染包括龋病、根尖周病,牙龈炎和牙周炎,所致的炎症状态和内皮细胞功能障碍或与脑小血管病的发生发展密切相关。本文旨在对口腔慢性感染性疾病与CSVD之间的潜在联系和研究现状做一综述。
基金The project supported by National Natural Science Foundation of China under Grant Nos. 10475008, 10675170, and 10435020, and the Department of Nuclear Physics of China Institute of Atomic Energy under Grant Nos. 11SZZ-200501 and 11SZZ-200601
文摘Based on the Eigen and Crow-Kimura models with a single-peak fitness landscape, we propose the fitness values of all sequence types to be Gausslan distributed random variables to incorporate the effects of the fluctuations of the fitness landscapes （noise of environments） and investigate the concentration distribution and error threshold of quasispecies by performing an ensemble average within this theoretical framework. We find that a small fluctuation of the fitness landscape causes only a slight change in the concentration distribution and error threshold, which implies that the error threshold is stable against small perturbations. However, for a sizable fluctuation, quite different from the previous deterministic models, our statistical results show that the transition from quasi-species to error catastrophe is not so sharp, indicating that the error threshold is located within a certain range and has a shift toward a larger value. Our results are qualitatively in agreement with the experimental data and provide a new implication for antiviral strategies.
