# Density-dependent feedback limits the spread of beta-lactamase mutants: experimental observations and population dynamic model

## TL;DR

This study shows how cell density and antibiotic levels influence the spread of antibiotic-resistant bacteria through eco-evolutionary feedback.

## Contribution

The study experimentally validates a population dynamic model showing how cell density mediates eco-evolutionary feedback in β-lactamase mutant spread.

## Key findings

- Cell density determines whether resistant TEM-52 outcompetes or coexists with susceptible TEM-19.
- A population model accurately predicts equilibrium frequencies based on growth and antibiotic degradation rates.
- Ecological feedback significantly affects the evolutionary dynamics of antibiotic resistance.

## Abstract

β-Lactamases play an important role in antibiotic-resistant bacterial infections. Understanding the spread of these enzymes may inform the development of better drug therapies. However, this is complicated by the fact that β-lactamases reduce the antibiotic concentration in their environment, thereby altering their own selective advantage via eco-evolutionary feedback. We investigated the effect of such feedback on the spread of bacterial strains expressing β-lactamase enzymes that confer different levels of resistance to the cephalosporin cefotaxime. Specifically, we conducted head-to-head competitions between two clinically observed β-lactamase mutants, TEM-19 and TEM-52, with low and high activity against cefotaxime, respectively. By experimentally varying nutrient levels, we altered cell density—and hence the strength of ecological feedback—and examined its impact on competitive fitness and strain coexistence across a range of cefotaxime concentrations. A population dynamic model, parameterized solely with independently measured traits, revealed cell density as the key mediator of this feedback. Our results show that cell density dictates whether the resistant strain (TEM-52) outcompetes or coexists stably with the susceptible strain (TEM-19). By validating our model with experimental data, we showed that it can reasonably predict the equilibrium frequencies based on dose-dependent growth rates and antibiotic degradation rates of both strains. Our study emphasizes the importance of considering ecological feedback in understanding the fate of antibiotic-degrading mutants, including in clinical environments.

Since the discovery of penicillin, β-lactam antibiotics have become the most widely used antibiotics to treat bacterial infections. Their applicability is decreasing because bacteria evolve resistance via expression of antibiotic-degrading β-lactamase enzymes. Because the spread of resistance is a large health problem, the prediction of resistance evolution is a big target. Several mutations increasing resistance have been studied, but as enzymes with increased activity spread, cells deactivate the β-lactam antibiotics, thereby opening a niche for susceptible variants. This eco-evolutionary feedback complicates the prediction of resistance evolution and makes it context-dependent. Here, we show that both the cell density and the antibiotic concentration affect the success of a new β-lactamase variant and whether it can invade, replace, or coexist with an ancestor variant. With a mathematical model, we can predict the success of new variants and therefore predict evolutionary paths depending on the environmental variables.