The time course of hydrolysis of a beta-lactam antibiotic by intact gram-negative bacteria possessing a periplasmic beta-lactamase.

An equation is derived from first principles for describing the change in concentration with time of a beta-lactam antibiotic in the presence of intact Gram-negative bacteria possessing a beta-lactamase located in the periplasmic space. The equation predicts a first-order decline in beta-lactam concentration of the form [S] = [Si]e lambda t, where [S] is the exogenous concentration of beta-lactam, [Si] is the value of [S] at time zero, t is the time from mixing of cells and antibiotic and lambda (less than 0) is the decay constant. The value of lambda is exactly described by the theory in terms of experimentally measurable quantities. Quantitative data concerning cephaloridine hydrolysis by intact cells of Haemophilus influenzae agreed well with the theory, as did data concerning the uptake of 2-nitrophenyl galactoside by intact cells of Escherichia coli. Cephalosporin C hydrolysis by intact cells of Pseudomonas aeruginosa did not progress as predicted by the theory. The theory is applicable to any substrate which is acted on by an enzyme that is located solely in the periplasmic space and that obeys the Michaelis-Menten equation of enzyme kinetics.