Batch cultures of supplemented whey permeate using Lactobacillus helveticus: unstructured model for biomass formation, substrate consumption and lactic acid production.

The Luedeking and Piret expression can not account for the cessation of production observed at the end of batch; so an empiric term has been previously added to this equation which accounted in a global way for possible substrate limitations. In the model developed in this work, a carbon substrate limitation appeared explicitly in the production expression. Assuming a sigmoidal variation with time of specific growth rate previously validated, the new production model matched well the entire experimental production kinetics. It has been successfully tested for a wide range of nitrogen supplementations, i.e. from an almost total coupling between growth and production for largely supplemented media, to a high decoupling in case of few available nitrogen. Since all the parameters of this model have an obvious biologic meaning, it may be an unvaluable tool for the comprehension of the phenomenon. The model accounted also well for the variation of the specific production rate versus specific growth rate, avoiding the noise due to the direct differentiation of experimental data.