Kinetic kill curves

The potential interaction between two antimicrobials can be demonstrated using a variety of laboratory procedures, e.g. checkerboard MIC assays where the microorganism is exposed to varying dilutions of each drug alone and in combination, disc diffusion tests (see Fig. 11.4) and kinetic kill curve assays. With the former, results can be plotted in the form of a figure called an isobologram (see Fig. 11.7). 

The more usual pattern found experimentally is that shown by B, which is called a sigmoid curve. Here the graph is indicative of a slow initial rate of kill, followed by a faster, approximately linear rate of kill where there is some adherence to first-order reaction kinetics this is followed again by a slower rate of kill. This behaviour is compatible with the idea of a population of bacteria which contains a portion of susceptible members which die quite rapidly, an aliquot of average resistance, and a residue of more resistant members which die at a slower rate. When high concentrations of disinfectant are used, i.e. when the rate of death is rapid, a curve ofthe type shown by C is obtained here the bacteria are dying more quickly than predicted by first-order kinetics and the rate constant diminishes in value continuously during the disinfection process. 

A, obtained if the disinfection process obeyed the first-order kinetic law. B, sigmoid curve. This shows a slow initial rate of kill, a steady rate and finally a slower rate of kill. This is the form of curve most usually encountered. C, obtained if bacteria are dying more quickly than first-order kinetics would predict. The constant, K, diminishes in value continuously during the process. 

Onkelinx et al. (1973) analyzed the kinetics of Ni(II) in rats and rabbits by use of a two-compartment mathematical model. These authors generated computer-fitted curves to depict the distribution of Ni(II) in extracellular and tissue spaces, as well as the excretory clearances of " Ni in urine and feces. This model was consistent with the observed distribution of nickel in tissues of nickel-treated rats and rabbits in various experiments, as summarized by Sunderman (1986b). In rabbits killed 2 h after an intravenous injection of " Ni(II), the relative uptake of " Ni in various tissues was ranked as follows kidney > pituitary > skin > lung... 

Mutation yields, and in particular the position and magnitude of maximum yields, should be measured as carefully as possible as a means of verifying the apparent pattern of mutation-induction kinetics revealed in mutation-frequency curves. For purely linear mutation induction and exponential survival, the maximum mutant yield occurs at the LD37 dose for other nonlinear kinetic patterns, the position and magnitude of the maximum yield shift in mathematically predictable ways. For any given kinetic pattern of killing and mutation, the ratio of the maximum mutant yields plotted over lethal... 

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