Semiconservative quasispecies equations for polysomic genomes: The general case

This paper develops a formulation of the quasispecies equations appropriate for polysomic, semiconservatively replicating genomes. This paper is an extension of previous work on the subject, which considered the case of haploid genomes. Here, we develop a more general formulation of the quasispecies equations that is applicable to diploid and even polyploid genomes. Interestingly, with an appropriate classification of population fractions, we obtain a system of equations that is formally identical to the haploid case. As with the work for haploid genomes, we consider both random and immortal DNA strand chromosome segregation mechanisms. However, in contrast to the haploid case, we have found that an analytical solution for the mean fitness is considerably more difficult to obtain for the polyploid case. Accordingly, whereas for the haploid case we obtained expressions for the mean fitness for the case of an analogue of the single-fitness-peak landscape for arbitrary lesion repair probabilities (thereby allowing for non-complementary genomes), here we solve for the mean fitness for the restricted case of perfect lesion repair.Comment: 16 pages, 3 figure

Evolutionary dynamics of adult stem cells: Comparison of random and immortal strand segregation mechanisms

This paper develops a point-mutation model describing the evolutionary dynamics of a population of adult stem cells. Such a model may prove useful for quantitative studies of tissue aging and the emergence of cancer. We consider two modes of chromosome segregation: (1) Random segregation, where the daughter chromosomes of a given parent chromosome segregate randomly into the stem cell and its differentiating sister cell. (2) ``Immortal DNA strand'' co-segregation, for which the stem cell retains the daughter chromosomes with the oldest parent strands. Immortal strand co-segregation is a mechanism, originally proposed by Cairns (J. Cairns, {\it Nature} {\bf 255}, 197 (1975)), by which stem cells preserve the integrity of their genomes. For random segregation, we develop an ordered strand pair formulation of the dynamics, analogous to the ordered strand pair formalism developed for quasispecies dynamics involving semiconservative replication with imperfect lesion repair (in this context, lesion repair is taken to mean repair of postreplication base-pair mismatches). Interestingly, a similar formulation is possible with immortal strand co-segregation, despite the fact that this segregation mechanism is age-dependent. From our model we are able to mathematically show that, when lesion repair is imperfect, then immortal strand co-segregation leads to better preservation of the stem cell lineage than random chromosome segregation. Furthermore, our model allows us to estimate the optimal lesion repair efficiency for preserving an adult stem cell population for a given period of time. For human stem cells, we obtain that mispaired bases still present after replication and cell division should be left untouched, to avoid potentially fixing a mutation in both DNA strands.Comment: 9 pages, 3 figure

LABELING OF MURINE MASTOCYTOMA CELLS IN VITRO WITH PLASMA TRITIATED THYMIDINE-LABELED ANIMALS

40 min after injecting tritiated thymidine into an animal, 20–30% of the total plasma radioactivity is nonvolatile. This fraction decreases to about 6% 10 hr after the injection and 3% 24 hr after the injection. There appears to be material in this nonvolatile fraction that can label mastocytoma cells in culture. The labeling indices decrease with time after injection in the same way as the nonvolatile fraction. The 40 min plasma sample contains sufficient material to allow accurate assessment of the fraction of cells in S in culture after a 6 wk exposure. The circulating material is not apparently available for incorporation into those cells in cycle in the donor animal. The material appears to be related to the G0 cell-specific pool that has been described elsewhere. The trichloroacetic acid-soluble or ethanol-soluble nonvolatile activity appears to contain thymine, and some thymidine-phosphorylated compounds