Table 1.
Postulated mechanism of phenotypic lag for different antibiotics discussed in this work.
Fig 1.
(a) Schematic representation of a simulated experiment, in which a mutagen (e.g., UV radiation) induces resistant mutations at a particular moment in time. Mutants initially remain sensitive to the antibiotic, only becoming resistant after a few generations. (b) Two ways of determining the time to resistance: tracking a single random lineage (dotted line), and tracking the whole population. In this example, resistance emerges in generations 3 and 2, respectively. (c) The dilution mechanism: blue/brown dots denote sensitive/resistant variants of the target molecule. When a wild-type cell (blue) mutates, it initially remains sensitive (green) and becomes resistant (red) when all sensitive molecules are diluted out. (d) Probability that at least one cell in an exponentially growing population starting with 100 newly genetically mutated cells is phenotypically resistant (dilution model) as a function of the number of generations since the genetic mutation (dots: simulation; lines: theory). Phenotypic delay increases with the number of molecules n to be diluted. (e) The effective polyploidy mechanism: chromosomes are represented as black ellipses, with a sensitive/resistant allele marked blue/red. (f) Same as in (d) but for the effective polyploidy mechanism. Phenotypic delay increases with ploidy c. (g) The accumulation mechanism: blue/red dots denote sensitive/resistant mutants of the resistant-enhancing molecule. Cells become resistant (red) when the cell contains enough resistant molecules. (h) Same as in (d) but for the accumulation model. Phenotypic delay decreases with increasing ratio m of the number of molecules produced during cell cycle and the number of molecules required for resistance.
Fig 2.
Combined effect of the dilution and effective polyploidy mechanisms.
(a-b) Probability of resistance of a single mutated cell. While the long-term probability is defined by the effective polyploidy, short-term behaviour is determined by the dilution mechanism, leading to longer phenotypic delays than the effective polyploidy mechanism would produce. (c) Population-level probability of resistance versus the number of generations from the mutation event, for n = 20. The combined mechanism leads to smoother curves than the effective polyploidy mechanism and longer delays than for either mechanism individually. (d) Phenotypic penetrance (ratio of phenotypically resistant to genetically resistant cells, obtained from Eq (1)) for the different mechanisms, for c = 8, n = 8. The dashed red line indicates when the phenotypic penetrance surpasses 1/2, which is the threshold used by Sun et al. [31] to define the emergence of phenotypic resistance. With this definition, the dilution mechanism plus effective polyploidy doubles the delay (generation 6 as opposed to generation 3 compared to effective polyploidy alone).
Fig 3.
Phenotypic delay decreases the probability of a bacterial infection surviving antibiotic treatment.
(a-b) A schematic of the simulated infection: a population of exponentially replicating sensitive cells is exposed to an antibiotic when the population reaches 107 cells. Only phenotypically resistant cells survive the antibiotic. Time and antibiotic concentration in panel (b) have arbitrary units. (c) The probability of survival for the effective polyploidy mechanism is independent of the doubling time (and hence the ploidy). (d) For the dilution mechanism, the probability of survival decreases with the number of molecules n which need to be diluted out before the cell becomes phenotypically resistant. (e) In a combined dilution-and-effective polyploidy model, the survival probability increases with the doubling time.
Fig 4.
The dilution model affects the probability distribution of the number of resistant cells.
The frequency of mutants for a simulated fluctuation test with 10,000 samples, for the model with n = 0 (no delay) and n = 16. (a) Distributions for both models for a fixed μ = 10−7. (b) Distributions for the case when μ in the dilution model has been adjusted to minimize the difference to the no-delay model (values in the inset).
Fig 5.
Phenotypic delay due to the dilution mechanism explains observed discrepancy in mutation rates and provides superior fit to fluctuation experiment data.
(a) We simulated the fluctuation experiment of Ref. [46], where the authors report a factor of 9.5 difference between the values of μ obtained by DNA sequencing and fluctuation tests. For each n we simulated 1000 experiments with the sequencing-derived mutation probability μ = 3.98 × 10−9 and then used the same estimation procedure as Ref. [46] to infer μ assuming no delay exists. n = 30 sensitive molecules are required to account for the discrepancy observed. Error bars are 1.96 × standard error. (b) The experimental cumulative mutant frequency distribution reported by Boe et al. [47] (black points) and the best-fit simulated distribution (green line) for the dilution phenotypic delay model. The staircase-like shape of the simulated distribution is caused by the fixed division time and strictly synchronous division of the mutated cells. (c) Histograms of the probability of the delay model obtained by applying the approximate Bayesian computation scheme to simulated data. Our classification algorithm correctly discriminates between the models.