Modeling the kinetics of the permeation of antibacterial agents into growing bacteria and its interplay with efflux [PublishAheadOfPrint]

A mathematical model of the passive permeation of a novel solute into bacteria is developed that explicitly accounts for intracellular dilution through growth. A bacterial cell envelope permeability coefficient of >10^-8 cm².s^-1 approx., is predicted to ensure passive permeation into rapidly replicating bacterial cells. The relative importance of the permeability coefficients of the cytoplasmic and outer membranes of Gram-negative bacteria in determining the overall envelope permeability coefficient is analyzed quantitatively. A mathematical description of the balance between passive influx and active efflux is also developed that shows that bacterial expansion through growth can usually be neglected for compounds likely to be prepared in antibacterial drug discovery programs, and the balance between passive inward permeation and active outwardly-directed efflux predominates. A new parameter, efflux efficiency = k/P (where k is the rate coefficient for the efflux pump and P is the permeability coefficient for the membrane across which the pump acts), is introduced and the consequences explored for the efficiency of efflux pumping by a single pump, two pumps in parallel across either the cytoplasmic or outer membrane, and two pumps in series, one across the cytoplasmic membrane and one across the outer membrane of Gram-negative bacteria. The results, showing additive efficiency for two pumps acting across a single membrane, and multiplicative efficiency for two pumps acting in series across the cytoplasmic and outer membranes, can be quantitatively related to the ratios between minimum inhibitory concentrations measured against pump-sufficient and -deletion strains, and agree with previous experimental and theoretical studies.

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