Eigen模型中误差阈展宽机制的研究
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摘要
物种演化本质上是生物群体与他们周围环境之间相互作用的一个随机过程.即演化模型中的一些物理参量是受外界环境涨落的影响.本工作中,是把模型中的适应度和突变率这2个物理参量同时处理为高斯分布随机变量,当二者同步耦合随机化时,转变区域的宽度与适应度和突变率的涨落强度分别呈线性和指数型关系;二者在非同步耦合随机化的情况下,转变区域的宽度与变量涨落强度间的关系与之前相一致.此时,不同的涨落强度下,变量与转变区域的宽度呈现出不同的趋势.当适应度和突变率二者同时随机化时,突变率随机化占据了主导地位,这就需要将突变概率矩阵中矩阵元作进一步的分析,进而研究误差阈的展宽机制.
Species evolution is essentially a random process of interaction between biological populations and their environments.As a result,some physical parameters in evolution modles are subject to statistical fluctuations.In this work,two important parameters in the Eigen model.The fitness and mutation rate are treated as Gaussian distributed random variables simultaneously.When the two are coupled by randomization,the width of the crossover region is linearly and exponentially related to the fluctuation of the fitness and the mutation rate.In the case of the random coupling,the relationship between the width of the crossover region and the fluctuating strength of the variable is consistent with the previous one.At the same time,the variable and the width of the crossover region show different trends under different fluctuation strengths.When both fitness and mutation rate are randomized,the randomization of mutation rate dominates,which requires further analysis of the matrix elements in the mutation probability matrix,and then studies the extension mechanism of the error threshold.
Species evolution is essentially a random process of interaction between biological populations and their environments.As a result,some physical parameters in evolution modles are subject to statistical fluctuations.In this work,two important parameters in the Eigen model.The fitness and mutation rate are treated as Gaussian distributed random variables simultaneously.When the two are coupled by randomization,the width of the crossover region is linearly and exponentially related to the fluctuation of the fitness and the mutation rate.In the case of the random coupling,the relationship between the width of the crossover region and the fluctuating strength of the variable is consistent with the previous one.At the same time,the variable and the width of the crossover region show different trends under different fluctuation strengths.When both fitness and mutation rate are randomized,the randomization of mutation rate dominates,which requires further analysis of the matrix elements in the mutation probability matrix,and then studies the extension mechanism of the error threshold.
引文
[1]Eigen M.Selforganization of matter and the evolution of biological macromolecules[J].Die Naturwissenschaften,1971,58(10):465-523.
[2]Eigen M,Mc Caskill J,Schuster P.Molecular quasi-species[J].The Journal of Physical Chemistry,1988,92(24):6881-6891.
[3]Eigen M,Mc Caskill J,Schuster P.The Molecular quasi-species[J].Adv Chem Phys,1989,75:149-263.
[4]Nowak M,Schuster P.Error thresholds of replication in finite populations mutation frequencies and the onset of Muller′s ratchet[J].Journal of theoretical Biology,1989,137(4):375-395.
[5]Campos P,Fontanari J.Finite-size scaling of the error threshold transition in finite populations[J].Journal of physics A:Mathematical and general,1999,32(1):L1.
[6]Feng X.Error thresholds for quasispecies on single peak gaussian-distributed fitness landscapes[J].Journal of theoretical biology,2007,246(1):28-32.
[7]Qiao Lihua,Zhao Tongjun,Gu Jianzhong,et al.Eigen model of randomness in species evolution[J].Acta Phys Sin,2014,63(10):108701.
[8]LI Duofang,CAO Tianguang,GENG Jinpeng,et al.Error threshold of fully random Eigen model[J].Chinese Physics Letters,2015,32(1):018702.
[9]Saakian D,Hu C K.Eigen model as a quantum spin chain:exact dynamics[J].Physical Review E,2004,69(2):021913.
[10]FENG Xiaoli,GU Jianzhong,LI Yuxiao,et al.Error thresholds in single-peak gaussian distributed fitness landscapes[J].Communications in Theoretical Physics,2007,48(4):763-768.
[11]Li Duofang,CAO Tianguang,GENG Jinpeng,et al.Statistical properties and error threshold of quasispecies on single-peak gaussian-distributed fitness landscapes[J].Journal of theoretical biology,2015,380:53-59.
[12]Eigen M.Error catastrophe and antiviral strategy[J].Proceedings of the National Academy of Sciences,2002,99(21):13374-13376.
[13]Manrubia S C,Domingo E,Lázaro E.Pathways to extinction:beyond the error threshold[J].Philosophical Transactions of the Royal Society B:Biological Sciences,2010,365(1548):1943-1952.
[14]Codoner Francisco M,Dar仵s Jos伢-Antonio,Sol伢Ricard V,et al.The Fittest Versus the Flattest:Experimental confirmation of the quasispecies effect with subviral pathogens[J].PLo S Pathog,2006,2(12):1187-1193.
[15]Rajamani S,Ichida J K,Antal T,et al,Effect of stalling after mismatches on the error catastrophe in nonenzymatic nucleic acid replication[J].Journal of the American Chemical Society,2010,132(16):5880-5885.
[2]Eigen M,Mc Caskill J,Schuster P.Molecular quasi-species[J].The Journal of Physical Chemistry,1988,92(24):6881-6891.
[3]Eigen M,Mc Caskill J,Schuster P.The Molecular quasi-species[J].Adv Chem Phys,1989,75:149-263.
[4]Nowak M,Schuster P.Error thresholds of replication in finite populations mutation frequencies and the onset of Muller′s ratchet[J].Journal of theoretical Biology,1989,137(4):375-395.
[5]Campos P,Fontanari J.Finite-size scaling of the error threshold transition in finite populations[J].Journal of physics A:Mathematical and general,1999,32(1):L1.
[6]Feng X.Error thresholds for quasispecies on single peak gaussian-distributed fitness landscapes[J].Journal of theoretical biology,2007,246(1):28-32.
[7]Qiao Lihua,Zhao Tongjun,Gu Jianzhong,et al.Eigen model of randomness in species evolution[J].Acta Phys Sin,2014,63(10):108701.
[8]LI Duofang,CAO Tianguang,GENG Jinpeng,et al.Error threshold of fully random Eigen model[J].Chinese Physics Letters,2015,32(1):018702.
[9]Saakian D,Hu C K.Eigen model as a quantum spin chain:exact dynamics[J].Physical Review E,2004,69(2):021913.
[10]FENG Xiaoli,GU Jianzhong,LI Yuxiao,et al.Error thresholds in single-peak gaussian distributed fitness landscapes[J].Communications in Theoretical Physics,2007,48(4):763-768.
[11]Li Duofang,CAO Tianguang,GENG Jinpeng,et al.Statistical properties and error threshold of quasispecies on single-peak gaussian-distributed fitness landscapes[J].Journal of theoretical biology,2015,380:53-59.
[12]Eigen M.Error catastrophe and antiviral strategy[J].Proceedings of the National Academy of Sciences,2002,99(21):13374-13376.
[13]Manrubia S C,Domingo E,Lázaro E.Pathways to extinction:beyond the error threshold[J].Philosophical Transactions of the Royal Society B:Biological Sciences,2010,365(1548):1943-1952.
[14]Codoner Francisco M,Dar仵s Jos伢-Antonio,Sol伢Ricard V,et al.The Fittest Versus the Flattest:Experimental confirmation of the quasispecies effect with subviral pathogens[J].PLo S Pathog,2006,2(12):1187-1193.
[15]Rajamani S,Ichida J K,Antal T,et al,Effect of stalling after mismatches on the error catastrophe in nonenzymatic nucleic acid replication[J].Journal of the American Chemical Society,2010,132(16):5880-5885.