  This paper develops a quasispecies model that incorporates the SOS response.
We consider a unicellular, asexually replicating population of organisms, whose
genomes consist of a single, double-stranded DNA molecule, i.e. one chromosome.
We assume that repair of post-replication mismatched base-pairs occurs with
probability $ \lambda $, and that the SOS response is triggered when the total
number of mismatched base-pairs exceeds $ l_S $. We further assume that the
per-mismatch SOS elimination rate is characterized by a first-order rate
constant $ \kappa_{SOS} $. For a single fitness peak landscape where the master
genome can sustain up to $ l $ mismatches and remain viable, this model is
analytically solvable in the limit of infinite sequence length. The results,
which are confirmed by stochastic simulations, indicate that the SOS response
does indeed confer a fitness advantage to a population, provided that it is
only activated when DNA damage is so extensive that a cell will die if it does
not attempt to repair its DNA.
