The innate growth bistability and fitness landscapes of antibiotic-resistant bacteria

Abstract

To predict the emergence of antibiotic resistance, quantitative relations must be established between the fitness of drug-resistant organisms and the molecular mechanisms conferring resistance. These relations are often unknown and may depend on the state of bacterial growth. To bridge this gap, we have investigated Escherichia coli strains expressing resistance to translation-inhibiting antibiotics. We show that resistance expression and drug inhibition are linked in a positive feedback loop arising from an innate, global effect of drug-inhibited growth on gene expression. A quantitative model of bacterial growth based on this innate feedback accurately predicts the rich phenomena observed: a plateau-shaped fitness landscape, with an abrupt drop in the growth rates of cultures at a threshold drug concentration, and the coexistence of growing and nongrowing populations, that is, growth bistability, below the threshold.

Figure 1. Heterogeneous response of Cm-resistant cells

E. coli cells were diluted from log phase batch cultures lacking Cm, and were spread onto LB agar at densities of several hundred cells per plate before overnight incubation at 37°C. (A) Typical plate images of Cm-resistant Cat1 (top row) and Cm-sensitive wild type (bottom row) cells, with Cm concentration indicated below each plate and also given above as approximate fraction of the empirically determined MIC_plate for each strain (figs. S2A and S3A). (B) Percentage of viable cells grown on Cm-LB plates; CAT-expressing cells (Cat1, green) and wild type cells (EQ4, blue). Error bars estimate SD of CFU, assuming Poisson-distributed colony appearance.

Figure 2. Drug-induced growth bistability

(A) Upon increasing Cm concentration from 0 to 0.9 mM in microfluidic chambers (fig. S4), genetically identical Cat1m cells growing exponentially in glucose minimal medium either continued growing (circled in green) or were growth-arrested (circled in white); see Movie S1. None of the Cat1m cells grew after adding Cm to 1.0 mM. (B) A typical example of the cells that remained dormant throughout the 24 hours during which microfluidic chambers contained 0.9 mM Cm; growth resumed ~8 hours after Cm was reduced to 0.1 mM, which is still well above the MIC of wild type cells (see Movie S2). (C) Height of colored bars gives the percentage of Cat1m cells to continue exponential growth in microfluidic chambers upon adding indicated concentration of Cm; error bars give 95% CI assuming a binomial distribution. Bar color indicates growth rates of growing cells, with the relative growth rate given by the scale bar on the right. (D) Growth curves at different Cm concentrations, given by the size of growing colonies (y-axis) in the microfluidic device. The deduced growth rates dropped abruptly from 0.35 hr⁻¹ (green squares) at 0.9 mM Cm to zero at 1.0 mM Cm (black triangles). (E) As in panel C, but for immotile wild type cells (EQ4m) that showed no significant correlation between growth rate and fraction of growing cells (ρ_s~0.1). (F) Fraction of Cat1 cells remaining after the batch culture Amp-Cm enrichment assay (fig. S5). The results (fig. S7) reveal significant fractions of non-growing cells well above the basal level of natural persisters (~10⁻³), for [Cm] ≥ 0.4 mM until the MIC of 1.0 mM above which no cells grew. Error bars estimate SD of CFU, assuming Poisson-distributed colony appearance.

Figure 3. Growth-mediated feedback

(A) Components of interactions defining the feedback model. Each link describes a relation substantiated in panels (B)–(D) (clockwise). (B) The relationship between the internal and external Cm concentration ([Cm]_int and [Cm]_ext respectively), described by the red line, is obtained by balancing the passive influx of Cm into the cell (J_influx, Eq. [1]) with the rate of Cm modification by CAT (J_CAT, Eq. [2]). This nonlinear relation is characterized by an approximate threshold-linear form, with a “threshold” Cm concentration, ${[\text{Cm}]}_{\text{ext}}^{\text{threshold}}$ (red arrow), below which [Cm]_int is kept low as the capacity for clearance by CAT well exceeds the Cm influx; Eq. [S12]. For ${[\text{Cm}]}_{\text{ext}}\gg {[\text{Cm}]}_{\text{ext}}^{\text{threshold}}$, CAT is saturated and J_influx ≈ V_max (dashed grey line). (C) The expression levels of constitutively expressed CAT (green) and LacZ (black) reporters (reported here in units of activity per OD (42)) are proportional to the growth rate for growth with sub-inhibitory doses of Tc and Cm respectively. (D) The doubling time (blue circles) of wild type (EQ4) cells grown in minimal medium with various concentrations of Cm increases linearly with [Cm] (Eq. [4] and Box 1). I₅₀ (dashed vertical line) gives the Cm concentration at which cell growth is reduced by 50%. Here, [Cm]_int ≈ [Cm]_ext due to the absence of endogenous Cm efflux for wild type cells in minimal media (41) (see also Eq. [S9]). Each point represents a single experiment; error bars of the doubling times are standard error of inverse slope in linear regression of log(OD₆₀₀) versus time.

Figure 4. Growth rate predictions and phase diagram

(A) Growth rate of Cat1 strain in minimal medium batch culture with varying Cm (filled circles) agrees quantitatively with the prediction of the growth feedback model (line) based on the measured MIC (dashed red line). Error bars SD; n ≥ 3. Dashed blue line is the theoretical MCC. Diamonds indicate drug levels at which enrichment experiments identified significant numbers of non-growing cells (fig. S7). (B) The MCC (blue line) and MIC (red line) predicted by the growth feedback model for strains with different degrees of basal CAT expression (V₀) define a phase diagram, with the coexistence of growing and non-growing populations between the MCC and MIC (beige). MIC (circles, fig. S14) and MCC (diamonds, fig. S15) are measured for strains differing only in their levels of constitutive CAT expression (quantified by the relative CAT activity in the absence of Cm, given by the bar graph below). Error bars SD; n ≥ 2. (C) and (D) Measured and predicted growth rate (circles and lines of like colors), in minimal medium with varying Cm for strains of known relative CAT activities; the wild type is shown in blue for reference. Predictions were obtained by solving Eq. [S28] for V₀/κ, using the measured MIC for strain Cat1 and the measured relative CAT activity between the different strains (bottom of panel B), without any parameter fitting.

Figure 5. Fitness landscapes of drug resistance

(A) Predicted growth rates (height of surface) for arbitrary CAT activity and Cm levels (V₀ and [Cm]_ext respectively): High (purple surface) and low growth rates (grey surface) overlap in the region of coexistence (growth bistability) that terminates at the bifurcation point (filled white circle). Predictions from Fig. 4C–D are reproduced here (colored lines). The orthogonal white line illustrates the expected effect of changing CAT activity at a fixed Cm concentration; it can be viewed as a plateau-shaped fitness landscape. (B) The survival resistance threshold required for growth, V_SRT, is predicted to vary linearly with the drug concentration (diagonal black dashed line). For a population initially at point A (black circle) in the phase diagram, i.e., with resistance activity $V_0^A$ and surviving in niches with [Cm]_ext < MIC^A, a mutation (μ₁, white arrow) that increases the resistance activity level to $V_0^B$ can “expand its range” (45) and proliferate into all niches with MIC^A ≤ [Cm]_ext ≤ MIC^B without competition (solid black arrow). Additional mutations, e.g. upstream of the gene at the ribosomal binding sequence (see table S3), or gene amplification events (69) provide a simple pathway for sequential expansions into increasingly harsh environments (45, 70).