The response surface methodology and canonical analysis were employed to find the most suitable conditions forLactobacillus helveticusto produce lactic acid from cheese whey in batch fermentation. The analyzed variables were temperature, pH, and the concentrations of lactose and yeast extract. The experiments were carried out according to a central composite design with three center points. An empiric equation that correlated the concentration of lactic acid with the independent variables was proposed. The optimal conditions determined by the canonical analysis of the fitted model were 40°C, pH 6.8, 82 g/L of lactose, and 23.36 g/L of yeast extract. At this point, the lactic acid concentration reached 59.38 g/L. A subsequent fermentation, carried out under optimal conditions, confirmed the product concentration predicted by the adjusted model. This concentration of lactic acid is the highest ever reported forLactobacillus helveticusATCC 15009 in batch process using cheese whey as substrate.
Processes producing sigmoid curves are common in many areas such as biology, agrarian sciences, demography and engineering. Several mathematical functions have been proposed for modeling sigmoid curves. Some models such as the logistic, Gompertz, Richards and Weibull are widely used. This work introduces the Gudermannian function as an option for modeling sigmoid growth curves. The original function was transformed and the resulting equation was called the "Gudermannian growth model." This model was applied to four sets of experimental growth data to illustrate its practical application. The results were compared with those obtained by the logistic and Gompertz models. Since all these models are nonlinear in the parameters, the statistical properties of the least squares estimators were evaluated using measures of nonlinearity. For each experimental data set, the Akaike's corrected information criterion was utilized to discriminate among the models. In general, the Gudermannian model fitted better to the experimental data than the logistic and Gompertz models. The results showed that the Gudermannian model can be a good alternative to the classical sigmoid models.
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