TABLE 2

Model parameters and their settings in simulation experimentsa

VariableDescriptionDefault value
(simulation expt I)
Sampling range
(simulation expt II)
Value(s)b
kCarrying capacity
(maximal attainable cell density)
11109 expt→1 for modeling (28)
ψMaximal bacterial growth10–20.1–1c (39), 0.19–1.23d (40), 0.74e (22)
αPlasmid costs0.20–10.2f (41), 0.14–0.19g (4), 0.06–0.21h (5),
0.21i (8), 0.03–0.58 (28), 0.32–0.64j (6)
βAmelioration strength0.90–10.1–0.25g,l (4), 0.65–1i,l (8), 1h,j,k (5, 6)
ωDilution rate
(washout/mortality/predation)
0.10–10.1 (26, 41)
υAntibiotic action (killing rate)0|10−1|10−2|10−310−4–1p0.1 (8)
τSegregation rate0.0010.5–10−6q10−4i (8), 10−3e (22)
γConjugation rate0.020–10.025m (28), 10−9e,n (22), ≈10−11–10−9n (42)
χMutation rater10−610−9–10−3p10−6 (8), ≈10−9–10−3 (43), ≈10 − 10o (39)
  • a Simulation experiment I was performed using the parameter defaults in combination with one of the rates for antibiotic action. For simulation experiment II, the sampling range of each parameter defines the parameter space that was used for a random sampling, which generated a compilation of 100,000 parameter sets. Each parameter set was used for simulations with the differential equation model described by the model matrix (Table 1) considering “no mutation” (χ = 0), “chromosomal mutation,” and “plasmid mutation.” To perform simulations in the absence of antibiotics, but under otherwise identical conditions, υ was set to 0, without performing a new sampling.

  • b Reference numbers are shown in parentheses.

  • c Estimated for most bacteria in the wild.

  • d For Escherichia coli, growth on glucose at 17.4 to 40°C.

  • e Used as simulation standard.

  • f For plasmid pQBR103.

  • g For plasmid pBR322.

  • h For plasmids R1 and RP4.

  • i For plasmid pNUK73.

  • j For plasmid R1.

  • k For coadaptation of host chromosome and plasmid.

  • l For adaptation of host chromosome.

  • m Considering relative cell densities.

  • n Considering absolute cell densities (which can be converted to relative values as used in this study by a multiplication with the respective maximum attainable cell density, k [e.g., assuming k =10−9]).

  • o Laboratory estimates for different species, but mutation rates in the wild are assumed to be higher (39).

  • p Sampled on a logarithmic scale to prevent an overrepresentation of high values (retransformed by anti-log for simulations).

  • q Results from uniformly sampling x in the range from 1 to 20 and calculating probabilities using function 0.5x. In this way, τ can also be interpreted as the segregation probability for a certain plasmid copy number x (11).

  • r Referring to a specific compensatory mutation occurring in the first place in the population evolution, but not to neutral, deleterious, or secondary compensatory mutations.