Bifurcation kinetics of drug uptake by Gram-negative bacteria

Cell envelopes of many bacteria consist of two membranes studded with efflux transporters. Such organization protects bacteria from the environment and gives rise to multidrug resistance. We report a kinetic model that accurately describes the permeation properties of this system. The model predicts complex non-linear patterns of drug uptake complete with a bifurcation, which recapitulate the known experimental anomalies. We introduce two kinetic parameters, the efflux and barrier constants, which replace those of Michaelis and Menten for trans-envelope transport. Both compound permeation and efflux display transitions, which delineate regimes of efficient and inefficient efflux. The first transition is related to saturation of the transporter by the compound and the second one behaves as a bifurcation and involves saturation of the outer membrane barrier. The bifurcation was experimentally observed in live bacteria. We further found that active efflux of a drug can be orders of magnitude faster than its diffusion into a cell and that the efficacy of a drug depends both on its transport properties and therapeutic potency. This analysis reveals novel physical principles in the behavior of the cellular envelope, creates a framework for quantification of small molecule permeation into bacteria, and should invigorate structure-activity studies of novel antibiotics.