منابع مشابه
Quasispecies distribution of Eigen model
We study sharp peak landscapes (SPL) of Eigen model from a new perspective about how the quasispecies distribute in the sequence space. To analyze the distribution more carefully, we bring forth two tools. One tool is the variance of Hamming distance of the sequences at a given generation. It not only offers us a different avenue for accurately locating the error threshold and illustrates how t...
متن کاملVariational ansatz for quasispecies in the Eigen model
We investigate the error threshold for the emergence of quasispecies in the Eigen model. By mapping to an effective Hamiltonian ruled by the “imaginary-time” Schrödinger equation, a variational ansatz is proposed and applied to calculate various properties associated with the quasispecies. The variational ansatz gives correct prediction for the survival population of the wild-type sequence and ...
متن کاملRigorous mathematical analysis of the quasispecies model: From Manfred Eigen to the recent developments
We review the major progress in the rigorous analysis of the classical quasispecies model that usually comes in two related but different forms: the Eigen model and the Crow–Kimura model. The model itself was formulated almost 50 years ago, and in its stationary form represents an easy to formulate eigenvalue problem. Notwithstanding the simplicity of the problem statement, we still lack full u...
متن کاملThe quasispecies distribution
The quasispecies model was introduced in 1971 by Manfred Eigen to discuss the first stages of life on Earth. It provides an appealing mathematical framework to study the evolution of populations in biology, for instance viruses. We present briefly the model and we focus on its stationary solutions. These formulae have a surprisingly rich combinatorial structure, involving for instance the Euler...
متن کاملA probabilistic representation of the quasispecies distribution
We give a probabilistic representation of the stationary solutions of Eigen’s model, when the set of possible genotypes is finite and the mutation matrix is primitive. In the long chain regime, we perform a formal passage to the limit to obtain a probabilistic representation of the quasispecies distribution. We prove rigorously the validity of this representation with the help of previously kno...
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ژورنال
عنوان ژورنال: Chinese Physics
سال: 2007
ISSN: 1009-1963,1741-4199
DOI: 10.1088/1009-1963/16/9/017