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β‐Lactam ring stability and antibacterial potency: A novel eigenvalue problem
Author(s) -
Davies R. H.,
Morris T. R.
Publication year - 1983
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560230423
Subject(s) - lactam , unitary transformation , potency , ring (chemistry) , chemistry , eigenvalues and eigenvectors , combinatorial chemistry , stereochemistry , mathematics , in vitro , physics , biochemistry , organic chemistry , quantum mechanics , quantum
Low inoculum potency data in vitro for 16 clinical β‐lactam antibiotics have been analyzed, and a physical model for interpreting the results of a number of bacterial strains has been derived. An analytic criterion for performing a unitary transformation on the potency data is developed following the identification of a physical vector present within the data which is attributable to an activation energy required for the transport of the β‐lactam into a biological membrane. This vector has inverse slope relations in Gram positive and Gram negative bacteria and provides the basis for the analytic criterion for the unitary transformation. Compounds with similar potency spectra which differ only in the absolute magnitude of their effect will possess similar transport properties. It is shown that a slow rate of membrane entry for the β‐lactam has overriding consequences on differences in fast rates of binding to the target enzymes and to β‐lactamases, and a second primary vector is established directly from the biological data related to the ease of β‐lactam ring opening. This vector offers precise evidence for testing the solvational and theoretical requirements for predicting the biological stability of novel β‐lactam ring compounds.