Race to survival during antibiotic breakdown determines the minimal surviving population size

A common strategy used by bacteria to resist antibiotics is enzymatic degradation or modification. Such a collective mechanism also enhances the survival of nearby cells, an effect that increases with the number of bacteria that are present. Collective resistance is of clinical significance, yet a quantitative understanding at the population level is lacking. Here we develop a general theoretical framework of collective resistance under antibiotic degradation. Our modeling 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 for this race to survival is the degree of cooperativity, which is related to the permeability of the cell wall for antibiotics and enzymes. These observations motivate a coarse-grained, phenomenological model and simple experimental assay to measure the dose-dependent minimal surviving population size. From this model, two dimensionless parameters can be estimated, representing the populations race to survival and single-cell resistance. Our simple model may serve as reference for more complex situations, such as heterogeneous bacterial communities.