Effect of the sos response on the mean fitness of unicellular populations: A quasispecies approach

The goal of this paper is to develop a mathematical model that analyzes the selective advantage of the SOS response in unicellular organisms. To this end, 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 λ, and that the SOS response is triggered when the total number of mismatched base-pairs is at least l_S. We further assume that the per-mismatch SOS elimination rate is characterized by a first-order rate constant κ_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.