Population Density Modulates Drug Inhibition and Gives Rise to Potential Bistability of Treatment Outcomes for Bacterial Infections
A. Time for population to grow from OD = 0.2 to OD = 0.8 (“threshold”) in the presence of tigecycline, relative to time with no drug. Curves represent theoretical predictions with (ε = 0.9, black, solid) and without (ε = 0, red, dashed) density dependence. Points represent experimental measurements in regular media (black) and highly buffered media (red). Inset: comparison of theory (smooth lines) and experimental time series of optical density in regular media (blue) and buffer (red) for [tigecycline] = 1.2 (units of IC50). B. Decrease in final population size when naïve dosing (upper right inset, dashed red line) at initial concentration D0 is replaced by optimal step-like dosing (upper right inset, dashed blue line). Dashed white line: ε = 0.9, as for tigecycline. Small inset: Fraction decrease in the population as a function of <D> for tigecycline (ε = 0.9). The step-like therapy introduces drug at initial concentration D0/τ and then sets drug concentration to zero at time t = τT. The parameter τ is chosen to minimize the cell density n(T) at time T, the end of the treatment (0≤τ≤1). In the absence of density dependence, both therapies result in a time-averaged drug concentration . Upper right inset: drug concentration over time with (“actual”; solid lines) and without (“expected”; dashed lines) density dependence for naïve (red) and step-like (blue) dosing. Lower right inset: final population size (relative to the case with no density dependence) for the naïve treatment (red) and the optimal step-like treatment (blue) as a function of ε. At a given value of ε, density-dependence can significantly increase n(T) (magenta arrow), but the optimal step dosing can often reduce the effects by 50% or more (green arrow).