Robust, linear correlations between growth rates and β-lactam-mediated lysis rates

Abstract

It is widely acknowledged that faster-growing bacteria are killed faster by β-lactam antibiotics. This notion serves as the foundation for the concept of bacterial persistence: dormant bacterial cells that do not grow are phenotypically tolerant against β-lactam treatment. Such correlation has often been invoked in the mathematical modeling of bacterial responses to antibiotics. Due to the lack of thorough quantification, however, it is unclear whether and to what extent the bacterial growth rate can predict the lysis rate upon β-lactam treatment under diverse conditions. Enabled by experimental automation, here we measured >1,000 growth/killing curves for eight combinations of antibiotics and bacterial species and strains, including clinical isolates of bacterial pathogens. We found that the lysis rate of a bacterial population linearly depends on the instantaneous growth rate of the population, regardless of how the latter is modulated. We further demonstrate that this predictive power at the population level can be explained by accounting for bacterial responses to the antibiotic treatment by single cells. This linear dependence of the lysis rate on the growth rate represents a dynamic signature associated with each bacterium-antibiotic pair and serves as the quantitative foundation for designing combination antibiotic therapy and predicting the population-structure change in a population with mixed phenotypes.

Keywords: antibiotic resistance; beta-lactams; quantitative biology; systems biology.

Fig. 1.

The growth rate predicted the β-lactam–mediated lysis rate, regardless of how the overall growth rate was modulated. (A, Top) Time courses of bacterial growth and lysis dynamics over time. t_A indicates the time when the antibiotic was added. Four replicates are shown. (A, Bottom) The rate of change calculated from the growth curves. Before antibiotic treatment, G is defined as the instantaneous growth rate. The lowest point of the curve corresponds to the sum of preantibiotic growth rate and maximum lysis rate (L). (B) Growth modulation with various parameters, including nutrient concentration (N), temperature (T), and second antibiotic concentration (A). A robust, linear correlation emerges between growth and lysis rates collected from various modes of growth-rate modulation. The linear fit has a slope of 1.62, a y-intercept of 0.48, and an R² value of 0.7903. CM, chloramphenicol; Kan, kanamycin.

Fig. 2.

Antibiotic dose-dependent correlations between growth and lysis rates in E. coli MG1655. (A–C) E. coli MG1655 strain was treated with 10, 20, or 50 μg/mL carbenicillin at various time points. The growth condition was kept the same otherwise. The linear correlations shift according to specific antibiotic concentrations. At 10 μg/mL carbenicillin, there is a threshold for growth rate for lysis to occur. At 20 and 50 μg/mL carbenicillin, there is a basal-level lysis rate (by extrapolation), even when the growth rate is 0, which increased with the antibiotic concentration. (D–F) Simulation results capture the qualitative trends in the experimental data. The average growth rate varies from 0.5 to 1.5 per hour. Parameter a increases with increasing growth rates: ${\mathit{a}}^{\text{'}}=\mathit{a}$, $\mathit{b}=2.5$, ${\mathit{b}}^{\text{'}}=5\mathit{b}$, $\mathit{\lambda }=0.2$, ${\mathit{\sigma }}_1=0.548$, ${\mathit{\sigma }}_1^{\text{'}}=5.0$, ${\mathit{\sigma }}_2=0.0344$, ${\mathit{\sigma }}_3=0.2$, ${\mathit{P}}_{\mathit{high}}=0.1$, ${\mathit{P}}_{\mathit{b}1}=0.1$. (D) ${\mathit{P}}_{\mathit{b}2}=0$. (E) ${\mathit{P}}_{\mathit{b}2}=0.02$. (F) ${\mathit{P}}_{\mathit{b}2}=0.03$. See SI Appendix, Model Development for a detailed description of the stochastic model.

Fig. 3.

Generality of the linear correlation between the growth rate and the lysis rate. (A–H) We examined the correlations between growth and lysis rates in different drug–bacterial species pairs. The degree of correlation was different for each pair. The numbers in the panels indicate the concentrations (in micrograms per milliliter) of the drug used for each condition. In general, increasing concentrations of antibiotic increased the basal lysis level (y-intercept) and decreased the slope of the correlation, except for E. coli ESBL 008 and cefotaxime pairs. For ESBL strains, either 10 or 20 μg/mL clavulanic acid was supplemented in the media to inhibit ESBLs, making these strains sensitive to cefotaxime.

Fig. 4.

Predicting the change in the population structure in a Bla-producing population consisting of subpopulations with varying growth rates. Bacterial subpopulations exhibit a wide range of growth rates due to genetic and phenotypic variations. The change in the population structure has a particular importance when populations exhibit collective tolerance against β-lactams (8, 25). (A) Schematic of the growth-rate (G) distribution of the bacterial population. (B) Growth/death dynamics of sample subpopulations, each with a different maximum growth rate. A, antibiotic. (C–E) Enrichment of each bacterial subpopulation when assuming different correlations between growth and lysis rates. This simulation result indicates that the quantitative property of the correlation can drastically influence the effects of antibiotic treatment on the population structure of an infecting population.