Antibiotic tolerance due to filamentation shapes β-lactam pharmacodynamics in Escherichia coli

Pharmacodynamic curves describe how changes in drug concentration affect pathogen growth. They are essential for designing treatments that promote pathogen eradication and minimize the evolution of antibiotic resistance. The classical function for modelling pharmacodynamics is a phenomenological, S-shaped curve with stable growth and death rates separated by a single drop. In this study, we characterized the pharmacodynamic curve of the {beta}-lactam antibiotic cefotaxime (CTX) acting against Escherichia coli. We found that the relationship between CTX concentration and net growth rate diverged from classical model predictions, instead yielding a two-step curve defined by distinct phases of growth, population maintenance, and killing. We hypothesized that the intermediate phase arose from antibiotic tolerance conferred by bacterial filaments. Microscopic assessment of treated cells indeed showed a difference in degree of filamentation with concentration. We further sought to explain this with a semi-mechanistic pharmacodynamic function, modelling the binding of CTX to its cellular targets, penicillin binding proteins (PBP) 1 and 3. By incorporating the preferential concentration-dependent binding of CTX to PBP3 and then PBP1, yielding filaments or lysed cells respectively, we replicated the two-step curve in silico. We also assessed the pharmacodynamics of CTX against mutants conferring resistance; these displayed further altered curves, in line with their fitness costs. Altogether, our results show that CTX has a two-step pharmacodynamic curve against E. coli arising from multiple targets separated in their affinity for the antibiotic. We present a model offering a mechanistically grounded framework for capturing such dynamics. These pharmacodynamic curves deserve careful consideration when defining optimal dosing.