[A mathematical study of the mortality curve of Escherichia coli exposed to aminoglycosides].

The time killing curves of three strains of E. coli (CIP54117, ATCC25922 and ATCC29194) exposed to kanamycin, amikacin, netilmicin and dibekacin are decreasing exponentials. The absolute value of the killing rate m is related to the antibiotic concentration through a Michaelis-Henry equation. A maximum killing rate m max and an affinity constant Kc between bacteria and antibiotic can thus be estimated. m max is mainly strain dependent. On the contrary, Kc is related to the antibiotic. Kc is much higher (i.e. the affinity is much lower) for kanamycin and amikacin than for netilmicin or dibekacin. The dose-effect curve is a saturation curve. Increasing doses of antibiotic do not increase the mortality proportionally.