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On Eigen’s quasispecies model, two-valued fitness landscapes, and isometry groups acting on finite metric spacesстатья
- Авторы: Semenov Yuri S., Novozhilov Artem S.
- Журнал: Bulletin of Mathematical Biology
- Том: 78
- Номер: 5
- Год издания: 2016
- Издательство: Academic Press
- Местоположение издательства: United States
- Первая страница: 991
- Последняя страница: 1038
- DOI: 10.1007/s11538-016-0172-2
- Аннотация: A two-valued fitness landscape is introduced for the classical Eigen's quasispecies model. This fitness landscape can be considered as a direct generalization of the so-called single- or sharply peaked landscape. A general, non-permutation invariant quasispecies model is studied, and therefore the dimension of the problem is [Formula: see text], where N is the sequence length. It is shown that if the fitness function is equal to [Formula: see text] on a G-orbit A and is equal to w elsewhere, then the mean population fitness can be found as the largest root of an algebraic equation of degree at most [Formula: see text]. Here G is an arbitrary isometry group acting on the metric space of sequences of zeroes and ones of the length N with the Hamming distance. An explicit form of this exact algebraic equation is given in terms of the spherical growth function of the G-orbit A. Motivated by the analysis of the two-valued fitness landscapes, an abstract generalization of Eigen's model is introduced such that the sequences are identified with the points of a finite metric space X together with a group of isometries acting transitively on X. In particular, a simplicial analog of the original quasispecies model is discussed, which can be considered as a mathematical model of the switching of the antigenic variants for some bacteria.
- Добавил в систему: Семенов Юрий Станиславович