Semiconservative quasispecies equations for polysomic genomes: The haploid case

This paper develops the semiconservative quasispecies equations for genomes consisting of an arbitrary number of chromosomes. We assume that the chromosomes are distinguishable, so that we are effectively considering haploid genomes. We derive the quasispecies equations under the assumption of arbitrary lesion repair efficiency, and consider the cases of both random and immortal strand chromosome segregation. We solve the model in the limit of infinite sequence length for the case of the static single fitness peak landscape, where the master genome has a first-order growth rate constant of k > 1 , and all other genomes have a first-order growth rate constant of 1. If we assume that each chromosome can tolerate an arbitrary number of lesions, so that only one master copy of the strands is necessary for a functional chromosome, then for random chromosome segregation we obtain an equilibrium mean fitness of t = ∞ ) = k 2 e - ( 1 / N ) μ λ / 2 + e - ( 1 / N ) μ ( 1 - λ / 2 ) 2 N - 1 , below the error catastrophe, while for immortal strand co-segregation we obtain κ ¯ ( t = ∞ ) = k [ e - μ ( 1 - λ / 2 ) + e - μ λ / 2 - 1 ] (N denotes the number of chromosomes, λ denotes the lesion repair efficiency, and μ ≡ ε L , where ε is the per base-pair mismatch probability, and L is the total genome length). It follows that immortal strand co-segregation leads to significantly better preservation of the master genome than random segregation when lesion repair is imperfect. Based on this result, we conjecture that certain classes of tumor cells exhibit immortal strand co-segregation.