A mathematical model for microbial growth under limitation by conservative substrates.

A mathematical model is suggested for growth of microorganisms under limitation by "conservative" substrates such as inorganic ions or vitamins that are not broken down after uptake into the cells, but that wholely or partly remain available for production of biomass. The specific growth rate is expressed here as a function of the intracellular "concentration" of the limiting substrate, defined as the amount of substrate within the cells per unit of cell dry weight. In the model, the intracellular substrate is divided into two parts. One part is a "structural" substrate not available for further growth. The other part is an "excess" or "functional" substrate that is used for biomass production and is assumed to be converted into structural substrate proportionally to growth. The rate of growth is believed to be controlled by the intracellular concentration of excess substrate.