Correlation of biological activity in β-lactam antibiotics with Woodward and Cohen structural parameters—a Cambridge database study

Abstract

Biological activity in β-lactam antibiotics has been correlated previously with one of two geometrical parameters, the Woodward height-of-pyramid, h, or the Cohen lactam O-atom to carboxylate C-atom distance, c. Here we describe a joint correlation of the two empirical parameters, h and c, with biological activity and the implications of such a correlation to enzyme–drug interactions in the β-lactam class of antibiotics. The Cambridge Structural Database (CSD) was the natural method of analysis and a substantial number of β-lactam structures (114) has been examined. It has been found that molecules with either high h and high c values or low h and low c values correspond to active skeletons. In contrast, molecules with high h and low c or low h and high c values are largely devoid of activity. The behaviour of outliers in both sets of populations has been explained on the basis of chemical and stereochemical factors. This correlation is far superior to the correlation of biological activity based either on h or c alone. Such an observation, namely that activity is a multivariate phenomenon, hints that a third parameter, which could be a torsional parameter about a non-bonded vector, is probably a better indicator of activity. Using crystal structure information on the binding of β-lactam antibiotics to their target enzymes, transpeptidases and β-lactamases, this parameter is shown to be an overall shape factor. The joint correlation of h and c parameters with biological activity provides a better understanding of structure–activity relationships and should find application in the rational discovery of new β-lactam antibiotics.