Abstract
A common strategy used by bacteria to resist antibiotics is enzymatic degradation or modification. This reduces the antibiotic threat in the environment and is therefore potentially a collective mechanism that also enhances the survival of nearby cells. Collective resistance is of clinical significance, yet a quantitative understanding at the population level is still incomplete. Here, we develop a general theoretical framework of collective resistance by antibiotic degradation. Our modeling study reveals that population survival crucially depends on the ratio of timescales of two processes: the rates of population death and antibiotic removal. However, it is insensitive to molecular, biological, and kinetic details of the underlying processes that give rise to these timescales. Another important aspect of antibiotic degradation is the degree of cooperativity, related to the permeability of the cell wall to antibiotics and enzymes. These observations motivate a coarse-grained, phenomenological model, with two compound parameters representing the population's race to survival and single-cell effective resistance. We propose a simple experimental assay to measure the dose-dependent minimal surviving inoculum and apply it to Escherichia coli expressing several types of β-lactamase. Experimental data analyzed within the theoretical framework corroborate it with good agreement. Our simple model may serve as a reference for more complex situations, such as heterogeneous bacterial communities. IMPORTANCE Collective resistance occurs when bacteria work together to decrease the concentration of antibiotics in their environment, for example, by actively breaking down or modifying them. This can help bacteria survive by reducing the effective antibiotic concentration below their threshold for growth. In this study, we used mathematical modeling to examine the factors that influence collective resistance and to develop a framework to understand the minimum population size needed to survive a given initial antibiotic concentration. Our work helps to identify generic mechanism-independent parameters that can be derived from population data and identifies combinations of parameters that play a role in collective resistance. Specifically, it highlights the relative timescales involved in the survival of populations that inactivate antibiotics, as well as the levels of cooperation versus privatization. The results of this study contribute to our understanding of population-level effects on antibiotic resistance and may inform the design of antibiotic therapies.