Modeling of Enzymatic Hydrolysis of Whey Proteins

The aim of this work was to emphasize the limitations of modeling complex phenomena under unrealistic model assumptions. As a case study, the whey protein hydrolysis mechanism was modeled. A stirred batch reactor was used to study the degree of hydrolysis of sweet whey protein concentrate by using the protease alcalase. A completely random two-factorial experimental design was used, three levels of initial enzyme concentrations (E0) (1.58, 3.18, 6.36 AU (Anson units)/L) times three levels of initial substrate concentrations (S0) (18.73, 38.45, 81.16 g/L). All treatments were carried out at optimal alcalase—activity conditions: pH 8 and 50 °C. Reactions were monitored for 180 min. The degree of hydrolysis (h) curves was finally adjusted for each treatment to the exponential model \( \frac{{{\text{d}}h}}{{{\text{d}}t}} = a \cdot \exp \left( { - b \cdot h} \right) \) using nonlinear regression techniques but not assuming a Michaelis–Menten relationship. From the estimation process, the coefficient b was constant (27.26 ± 1.37) and independent of E0 and S0, while coefficient a depended directly on the ratio E0/S0, ranging from 0.0017 to 0.0497. A noncritical strategy of forward modeling based on unrealistic assumptions was misleading in the face of complex phenomena; instead, a modeling strategy moving from data to the identification and estimation of parameters of practical interest must be considered.