A model-based approach to characterize enzyme-mediated response to antibiotic treatments: going beyond the SIR classification

Commensal and pathogenic E. coli strains are increasingly found to be resistant to {beta}-lactams, one of the most widely prescribed classes of antibiotics. Understanding escape to such treatments is complex since {beta}-lactams have several cellular targets and since several mechanisms might be involved in treatment escape in a combined manner. Surprisingly, the accumulated knowledge has not yet proven effective enough to predict the bacterial response to antibiotic treatments at both cellular and population levels with quantitative accuracy for -producing bacteria. Here, we propose a mathematical model that captures in a comprehensive way key phenomena happening at the molecular, cellular, and population levels, as well as their interactions. Our growth-fragmentation model gives a central role to cellular heterogeneity and filamentation as a way for cells to gain time until the degradation of the antibiotic by the {beta}-lactamases released by the dead cell population. Importantly, the model can account for the observed temporal evolution of the total (live and dead) biomass and of the live cell numbers for various antibiotic concentrations. To our knowledge, this is the first model able to quantitatively reconciliate these two classical views on cell death (OD and CFUs) for clinical isolates expressing extended-spectrum beta-lactamases (ESBL). Moreover, our model has a strong predictive power. When calibrated using a slight extension of OD-based data that we propose here, it can predict the CFU profiles in initial and delayed treatments despite inoculum effects, and suggest non-trivial optimal treatments. Generating quality data in quantity has been essential for model development and validation on non-model E. coli strains. We developed protocols to increase the reproducibility of growth kinetics assays and to increase the throughput of CFU assays.