A mathematical model for toxin accumulation by killer yeasts based on the yeast population growth

The accumulation of toxin by killer yeast populations is modelled starting from a mechanistic approach that explains the toxin production in terms of yeast population growth, and takes into account the environmental inactivation of the toxin. A modified Richard's general equation for limited growth is used to define the function that describes the toxin produced in relation to the yeast biomass increase. The relationship between the rates of cell and toxin production is explicitly shown, and the implications of the resulting proportionality factor are discussed. The model parameters have been adjusted and the model has been validated using experimental data of growth and toxin accumulation from cultures of Pichia membranaefaciens in two different media. The differences between both types of cultures are analysed on the basis of parameter estimates and the predicted rate of toxin production per cell. The results support the hypothesis that biomass production and toxin synthesis are controlled in different ways; they also suggest that the composition of the medium could have a distinct effect on toxin synthesis. Model assumptions are discussed in comparison with a previous model for killer-sensitive interaction of Saccharomyces cerevisiae strains.