Semiconservative replication in the quasispecies model II:   Generalization to arbitrary lesion repair probabilities
  This paper extends the semiconservative quasispecies equations to account for arbitrary post-replication lesion repair efficiency. Such an extension could be an important tool for understanding processes such as cancer development and stem cell growth. Starting from the quasispecies dynamics over the space of genomes, we derive an equivalent dynamics over the space of ordered sequence pairs. From this set of equations, we are able to derive the infinite sequence length form of the dynamics for a class of ``master-genome''-based fitness landscapes. We use these equations to solve for a ``generalized'' single-fitness-peak landscape, where the master genome can sustain a maximum number of lesions and remain viable. The central pattern that emerges from our studies is that imperfect lesion repair often leads to increased mutational robustness over semiconservative replication with completely efficient lesion repair. The reason for this is that imperfect lesion repair breaks some of the correlation between the parent and daughter strands, thereby preventing replication errors from destroying the information in the original genome. The result is a delayed error catastrophe over that expected from the original semiconservative quasispecies model. In particular, we show that when only of the strands is necessary for conferring viability, then, when lesion repair is turned off, a semiconservatively replicating system becomes an effectively conservatively replicating one. 
Emmanuel Tannenbaum, James L. Sherley, Eugene I. Shakhnovich