Mathematical modelling of antifungal action

In this paper a simplified modelling approach indicated that yeast growth was inhibited by an antifungal drug according to an exponential function. In addition, the corresponding inhibition rate followed a hyperbolic function the parameters of which permit us to determine the percentage of maximum inhibition and the minimum inhibitory concentration for 80%. From the equation of a hyperbola it was also possible to calculate an affinity constant Kaff corresponding to the inverse of the concentration of antifungal drugs giving half the maximal inhibition. The affinity constant was demonstrated to be characteristic of the yeast strain and of the antifungal drug employed. Simulation of the mathematical modelling enabled determination of a theoretical inhibition level corresponding to strong concentrations of antifungal drugs which cannot be carried out for technical reasons (precipitates, opacity etc.). The interest of this mathematical modelling of growth and inhibition to predict the doses of antifungals which can act synergistically is discussed.