[Mathematical study of the sensitivity curves of Escherichia coli exposed to polymyxins].

The time killing curves of five strains of Escherichia coli (ATCC 25922, ATCC 29194, CIP 54125, CIP 54127, CIP 54117 (K 12)) exposed to five concentrations of polymyxin B are similar: latency phasis, two decreasing phasis and for the low polymyxin B concentrations growth phasis. In our experimental conditions, the Mg(+)+ and Ca(+)+ concentrations of the medium (Mueller-Hinton; medium A: Ca(+)+ = 9 mg/l, Mg(+)+ = 0.5 mg/l; medium B: Ca(+)+ = 35 mg/l, Mg(+)+ = 15.5 mg/l; medium C: Ca(+)+ = 60 mg/l, Mg(+)+ = 20 mg/l) have no time effect upon the killing curves. A decreasing biexponential model can be fitted to the data. Such a model is compatible with interaction between antibiotic and bacterium and can be formalized accorrding to the equation: T + ATB K1 in equilibrium of K2 T* - ATB K3----ATB + dead with ATB: Polymyxine B in excess, T: target bacterium and T*: modification target bacterium.