Fig. 2: Dynamics of mixed good beta-lactamase production in a heterogeneous population.

A A simple dimensionless mathematical model captures the interactions of sensitive (\(S\)) and resistant (\(R\)) populations in the presence of antibiotic (\(A\)) and Bla inhibitor (\(I\)), in which resistant cells have both a slower growth rate (\({\mu }_{R}\, < \, {\mu }_{S}\)) and a slower antibiotic-mediated lysis rate (\({\gamma }_{R} \, < \, {\gamma }_{S}\)). Antibiotic degradation occurs via intact resistant bacteria (\(\varphi\)) and via free Bla (\(B\)) released from lysis of resistant cells. Inhibition affects both the private (red) and public (blue) components of Bla-mediated resistance. B Bla (teal) is localized to the cellular periplasm and offers private protection (red) to the producing cell (1). However, it also offers public protection (blue) to surrounding cells, which may be sensitive, through two mechanisms: overall reduction in antibiotic (gold) concentration (2) and Bla release upon cell death (3). C Simulated time courses of population densities (S, R), antibiotic (A), and extracellular Bla (B) after a dose of combined antibiotic and inhibitor treatment (\({a}_{0}=2.15\), \(i\) = 10). Antibiotic treatment results in the initial death of both resistant and sensitive populations. Over time, resistant cells and free Bla released by resistant cell lysis degrade antibiotic, eventually reducing lysis rates and allowing for the recovery of both populations to a steady state determined by total nutrient availability. Resistant cells may have an advantage while antibiotic levels remain high, but in the absence of antibiotic have a growth deficit relative to sensitive cells. Inset shows the corresponding time course of the fraction of resistant cells \({f}_{R}\) in the population. D Different doses of antibiotic and inhibitor correspond to different final cell densities (dimensionless, yellow to green color) and resistant fractions (blue to red color). Antibiotic and inhibitor have a synergistic effect, and higher concentrations of either lead to lower cell densities. Example time courses for doses that produce either majority-resistant or majority-sensitive populations are highlighted. E Clinical objectives for dose optimization include population suppression, which can be defined by an acceptable threshold, and using minimal drug concentrations within the acceptable range, to minimize cost, resistance, and side effects. Selection against resistance provides a third objective for dose optimization.