Sensitivity of Escherichia coli to various β‐lactams is determined by the interplay of outer membrane permeability and degradation by periplasmic β‐lactamases: a quantitative predictive treatment

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Abstract
In Gram‐negative bacteria, β‐lactam antibiotics must overcome two barriers, the outer membrane and the periplasmic β‐lactamase, before they reach the targets of their action, penicillin‐binding proteins. Although the barrier property of the outer membrane and catalytic property of the β‐lactamases have been studied and their significance in creating β‐lactam resistance emphasized, the interaction between these two barriers has not been treated quantitatively. Such treatment shows that the sensitivity, to a variety of β‐lactams, of the Escherichia coli K‐12 cells containing very different levels of chromosomally coded AmpC β‐lactamase, or a plasmid‐coded TEM‐type β‐lactamase, can be predicted rather accurately from the penetration rate through the outer membrane and the hydrolysis rate in the periplasm. We further propose a new parameter,‘target access Index', which is a quantitative expression of the result of interaction between the two barriers, and reflects the probability of success for the antibiotic to reach the targets.