title: The rich phase structure of a mutator model.
abstract: We propose a modification of the Crow-Kimura and Eigen models of biological molecular evolution to include a mutator gene that causes both an increase in the mutation rate and a change in the fitness landscape. This mutator effect relates to a wide range of biomedical problems. There are three possible phases: mutator phase, mixed phase and non-selective phase. We calculate the phase structure, the mean fitness and the fraction of the mutator allele in the population, which can be applied to describe cancer development and RNA viruses. We find that depending on the genome length, either the normal or the mutator allele dominates in the mixed phase. We analytically solve the model for a general fitness function. We conclude that the random fitness landscape is an appropriate choice for describing the observed mutator phenomenon in the case of a small fraction of mutators. It is shown that the increase in the mutation rates in the regular and the mutator parts of the genome should be set independently; only some combinations of these increases can push the complex biomedical system to the non-selective phase, potentially related to the eradication of tumors.
authors.affiliation: Institute of Physics, Academia Sinica, Nankang, Taipei 11529, Taiwan.|A.I. Alikhanyan National Science Laboratory (Yerevan Physics Institute) Foundation, Alikhanian Brothers St. 2, Yerevan 375036, Armenia.
authors.forename: David B
authors.initials: DB
authors.lastname: Saakian
authors.affiliation: National Research University Higher School of Economics, Moscow, 101000, Myasnitskaya Street 20, Russia.
authors.forename: Tatiana
authors.initials: T
authors.lastname: Yakushkina
authors.affiliation: Institute of Physics, Academia Sinica, Nankang, Taipei 11529, Taiwan.|National Center for Theoretical Sciences, National Tsing Hua University, Hsinchu 30013, Taiwan.|Business School, University of Shanghai for Science and Technology, Shanghai 200093, China.
authors.forename: Chin-Kun
authors.initials: CK
authors.lastname: Hu
mesh_terms: D019143:Evolution, Molecular; D008957:Models, Genetic; D009154:Mutation; D059645:Mutation Rate; D012641:Selection, Genetic