Unstructured models for growth and lactic acid production during two-stage continuous cultures of Lactobacillus helveticus

During lactic acid fermentation, seed culture is usually carried out without pH control, while culture is carried out at pH controlled at the optimal value to overcome inhibitory effects. The Luedeking–Piret expression was therefore previously modified by introducing additional terms involving the undissociated form of the lactic acid, the main inhibitory species, in case of batch cultures without pH control or involving the residual lactose concentration to account for the carbon substrate limitation, responsible for cessation of production during batch cultures of Lactobacillus helveticus at controlled pH. Both expressions were also merged to deduce a generalized model. Both models, as well as the Luedeking–Piret model, were developed to describe continuous two-stage culture of L. helveticus. By considering the parameter values obtained from the fitting of batch culture data, both modified Luedeking–Piret models showed interesting predictive potential. Indeed, some rather reliable predictive calculated values were recorded in both stages; the residual standard deviations were 0.5 and less than 8.8 for the biomass and the product concentrations at steady-state in the culture stage (second stage). The optimization of the parameters for growth- and non-growth-associated parameters improved the fitting in the culture stage, leading to residual standard deviations below 2.6 for lactic acid concentrations at steady-state.