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Register a new userThe effect of the SOS response on the mean fitness of unicellular populations: A quasispecies approach
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Added by
Emmanuel Tannenbaum
Publication date
2008
fields
Biology
and research's language is
English
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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.
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This paper develops a mathematical model describing the influence that conjugation-mediated Horizontal Gene Transfer (HGT) has on the mutation-selection balance in an asexually reproducing population of unicellular, prokaryotic organisms. It is assumed that mutation-selection balance is reached in the presence of a fixed background concentration of antibiotic, to which the population must become resistant in order to survive. We analyze the behavior of the model in the limit of low and high antibiotic-induced first-order death rate constants, and find that the highest mean fitness is obtained at low rates of bacterial conjugation. As the rate of conjugation crosses a threshold, the mean fitness decreases to a minimum, and then rises asymptotically to a limiting value as the rate of conjugation becomes infinitely large. However, this limiting value is smaller than the mean fitness obtained in the limit of low conjugation rate. This dependence of the mean fitness on the conjugation rate is fairly small for the parameter ranges we have considered, and disappears as the first-order death rate constant due to the presence of antibiotic approaches zero. For large values of the antibiotic death rate constant, we have obtained an analytical solution for the behavior of the mean fitness that agrees well with the results of simulations. The results of this paper suggest that conjugation-mediated HGT has a slightly deleterious effect on the mean fitness of a population at mutation-selection balance. Therefore, we argue that HGT confers a selective advantage by allowing for faster adaptation to a new or changing environment. The results of this paper are consistent with the observation that HGT can be promoted by environmental stresses on a population.
This Letter studies the quasispecies dynamics of a population capable of genetic repair evolving on a time-dependent fitness landscape. We develop a model that considers an asexual population of single-stranded, conservatively replicating genomes, whose only source of genetic variation is due to copying errors during replication. We consider a time-dependent, single-fitness-peak landscape where the master sequence changes by a single point mutation every time $ tau $. We are able to analytically solve for the evolutionary dynamics of the population in the point-mutation limit. In particular, our model provides an analytical expression for the fraction of mutators in the dynamic fitness landscape that agrees well with results from stochastic simulations.
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.
This paper develops simplified mathematical models describing the mutation-selection balance for the asexual and sexual replication pathways in {it Saccharomyces cerevisiae}. We assume diploid genomes consisting of two chromosomes, and we assume that each chromosome is functional if and only if its base sequence is identical to some master sequence. The growth and replication of the yeast cells is modeled as a first-order process, with first-order growth rate constants that are determined by whether a given genome consists of zero, one, or two functional chromosomes. In the asexual pathway, we assume that a given diploid cell divides into two diploids. In the sexual pathway, we assume that a given diploid cell divides into two diploids, each of which then divide into two haploids. The resulting four haploids enter a haploid pool, where they grow and replicate until they meet another haploid with which to fuse. When the cost for sex is low, we find that the selective mating strategy leads to the highest mean fitness of the population, when compared to all of the other strategies. We also show that, at low to intermediate replication fidelities, sexual replication with random mating has a higher mean fitness than asexual replication, as long as the cost for sex is low. This is consistent with previous work suggesting that sexual replication is advantageous at high population densities, low replication rates, and intermediate replication fidelities. The results of this paper also suggest that {it S. cerevisiae} switches from asexual to sexual replication when stressed, because stressful growth conditions provide an opportunity for the yeast to clear out deleterious mutations from their genomes.
We study a minimal model for the growth of a phenotypically heterogeneous population of cells subject to a fluctuating environment in which they can replicate (by exploiting available resources) and modify their phenotype within a given landscape (thereby exploring novel configurations). The model displays an exploration-exploitation trade-off whose specifics depend on the statistics of the environment. Most notably, the phenotypic distribution corresponding to maximum population fitness (i.e. growth rate) requires a non-zero exploration rate when the magnitude of environmental fluctuations changes randomly over time, while a purely exploitative strategy turns out to be optimal in two-state environments, independently of the statistics of switching times. We obtain analytical insight into the limiting cases of very fast and very slow exploration rates by directly linking population growth to the features of the environment.
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