An explicit model for bacterial resistance: application to beta-lactam antibiotics.

The effectiveness of beta-lactam antibiotics against Gram-negative bacteria that contain beta-lactamases is considered in terms of three factors. These are a rate constant for reaction of the beta-lactam antibiotic with a transpeptidase, the kinetic parameters for hydrolysis of the antibiotic by the beta-lactamase, and the permeability of the outer membrane. The concept of a dimensionless permeability number (Pn) is developed. When the permeability number is much less than one then permeability is important, and the MIC may be raised by a factor of up to 1/Pn. When the antibiotic is sufficiently reactive its effectiveness is given by the 'reactivity-permeability' product.