Compensation of fitness costs and reversibility of antibiotic resistance mutations

Abstract

Strains of bacterial pathogens that have acquired mutations conferring antibiotic resistance often have a lower growth rate and are less invasive or transmissible initially than their susceptible counterparts. However, fitness costs of resistance mutations can be ameliorated by secondary site mutations. These so-called compensatory mutations may restore fitness in the absence and/or presence of antimicrobials. We review literature data and show that the fitness gains in the absence and presence of antibiotic treatment need not be correlated. The aim of this study is to gain a better conceptual grasp of how compensatory mutations with different fitness gains affect evolutionary trajectories, in particular reversibility. To this end, we developed a theoretical model with which we consider both a resistance and a compensation locus. We propose an intuitively understandable parameterization for the fitness values of the four resulting genotypes (wild type, resistance mutation only, compensatory mutation only, and both mutations) in the absence and presence of treatment. The differential fitness gains, together with the turnover rate and the mutation rate, strongly affected the success of antibacterial treatment, reversibility, and long-term abundance of resistant strains. We therefore propose that experimental studies of compensatory mutations should include fitness measurements of all possible genotypes in both the absence and presence of an antibiotic.

FIG. 1.

Diagram of model 1. We consider two loci, a resistance and a compensation locus, resulting in four possible genotypes: wild type (++), resistance mutation only (R+), compensatory mutation only (+C), and resistant-compensated genotype (RC). Each genotype is represented by a box. Strains of all genotypes die with a rate d (see solid lines leaving the boxes) and replicate depending on their individual fitness levels in the current environment, w_ij,A, and a density-dependent term, D(n), which corresponds to 1 minus the total population size divided by the carrying capacity (see circular arrows). Mutations occur at rates μ_→ and μ_← at the resistance locus and at rates ν_→ and ν_← at the compensatory locus (see dotted lines between the boxes). In this notation, the subscript arrows denote the direction of mutation.

FIG. 2.

Types of compensatory mutations. The x axis shows how many mutations the genotype has compared to the wild type. The y axis shows the replicative fitness compared to that of the wild type. The fitness in the absence of drugs is shown in black, and the fitness in the presence of antibiotic treatment is shown in red. ++ denotes the wild type (wt), R+ the genotype with only the resistance mutation, C+ the genotype carrying only the compensatory mutation, and RC the resistant-compensated genotype. Three extreme types of compensation are possible. (A) The compensatory mutation may be beneficial only in the absence of drugs (e_{C,no drug} = 1 and e_C,drug = 0). (B) Conversely, compensation may occur only in the presence of treatment (e_{C,no drug} = 0 and e_C,drug = 1). (C) Finally, compensation may have the same efficiency in both environments (e_{C,no drug} = 1 and e_C,drug = 1). Other parameters take the following values: a = 0.9, c_C = 0.1, c_R = 0.2, and e_R = 0.9.

FIG. 3.

Compensation in absence versus compensation in presence of antibiotics. The equations in Table 1 were used to derive e_{C,no drug} and e_C,drug from the data set of Paulander et al. (63). The blue empty circles indicate resistant compensated strains that evolved in the absence of drugs, and the red empty triangles indicate resistant compensated strains that evolved in the presence of an antibiotic. The filled symbols indicate the means with standard deviations.

FIG. 4.

RC fitness in the presence of treatment and extinction. In order to escape extinction during treatment, the fitness of the RC genotype needs to be above a certain threshold. This plot shows the maximal cost of resistance for a given e_R and c_R that permits long-term survival of the RC genotype. It was created by solving rw_RC > d for c_R, yielding c_R < 1/(1 − e_C,drug) − d/[r(1 − a + ae_R)(1 − e_C,drug)] as the condition for the bacteria to persist. The antimicrobial activity (a) has a value of 1.

FIG. 5.

Fitness of R+ and RC genotypes and minimal population size during treatment. In this plot, the color scale indicates the minimal population sizes during treatment for different c_R and e_C,drug values upon treatment initiation in a naive bacterial population of 10⁷ organisms. The area in which the growth rate of the RC genotype is smaller than the death rate (i.e., where extinction is inevitable) is shaded in gray. The dashed lines represent fitness isoclines for the RC genotype. Other parameters take the following values: a = 1, c_C = 0.1, c_R = 0.2, e_R = 0.9, e_C,drug = 0.6, and μ_→ = 10⁻⁸.

FIG. 6.

Mutation rate, population size, and extinction during treatment. These graphs show the minimal c_R for which a bacterial population goes extinct for a given e_R. Extinction is defined to occur when the total population size drops below 1 during antimicrobial therapy. The area in which the growth rate of the RC genotype is smaller than the death rate (i.e., where extinction is inevitable) is shaded in gray. The dashed lines correspond to an initially homogeneous wild-type population, while the solid lines correspond to a population that expanded from 10³ cells to the population size at which treatment commenced. (A) Various initial population sizes (N₀). (B) Various mutation rates (μ_→). Unless varied, parameters take the following values: a = 1, c_C = 0.1, c_R = 0.2, e_R = 0.9, e_C,drug = 0.6, μ_→ = 10⁻⁸, and N₀ = 10⁷.

FIG. 7.

Probability of generating RC bacteria before R+ extinction. This graph shows for which maximal e_R the probability that the R+ population becomes extinct before creating an RC genotype is larger than 95%. It was created by solving for e_R, yielding for a = 1. The values of μ_→ are given next to the corresponding curves. For mutation rates of ≥10^−4.25, the RC genotype could always emerge. N₀ = 10⁷, ν_→ = 10μ_→.

FIG. 8.

Reversion to susceptibility after cessation of treatment and relative to kill rate. In this figure, we show how the fitness of the RC genotype and the bacterial kill rate relative to the growth rate influence reversion to susceptibility. The initial population consisted of 10⁹ bacteria of the R+ (A) or the RC (B) genotype. The x axis (horizontal) shows the relative kill rate, i.e., the kill rate divided by the growth rate, and the y axis shows the efficiency of compensation, and thus RC fitness relative to that of the wild type. On the z axis are the numbers of days until >95% of the population consisted of the wild-type genotype. Other parameters take the following values: a = 1, e_R = 1, c_R = 0.5, c_C = 0.5, e_R = 1, μ_→ = 10⁻⁸, and N₀ = 10⁹.