Abstract
The development of new antibiotics against Gram-negative bacteria is hampered by the powerful protective properties of their cell envelope. This envelope consists of two membranes augmented by efflux transporters, which act in synergy to restrict cellular access to a broad range of chemical compounds. Recently, a kinetic model of this system has been constructed. The model revealed a complex, nonlinear behavior of the system, complete with a bifurcation, and matched very well to experimental uptake data. Here, we expand the model to include multiple transporters and apply it to an experimental analysis of antibiotic accumulation in wild-type and efflux-deficient Escherichia coli. We show that transporters acting across the inner and outer membranes have synergistic effects with each other. In contrast, transporters acting across the same membrane are additive as a rule but can be synergistic under special circumstances owing to a bifurcation controlled by the barrier constant. With respect to ethidium bromide, the inner membrane transporter MdfA was synergistic to the TolC-dependent efflux across the outer membrane. The agreement between the model and drug accumulation was very good across a range of tested drug concentrations and strains. However, antibiotic susceptibilities related only qualitatively to the accumulation of the drugs or predictions of the model and could be fit to the model only if additional assumptions were made about the physiological consequences of prolonged cell exposure to the drugs. Thus, the constructed model correctly predicts transmembrane permeation of various compounds and potentially their intracellular activity.