Hydrolysis of β-casein by the cell-envelope-located PI-type protease of Lactococcus lactis: A modelling approach

Lactic acid bacteria possess extracellular proteases that hydrolyze milk proteins. This work aimed to describe mathematically the hydrolysis of intact β-casein by the PI-type protease of Lactococcus lactis, using a mutant strain that lacks the oligopeptide transport system. Experiments were performed under a broad range of initial protein concentrations (17–196 μm), at constant enzyme concentration or at constant initial enzyme/substrate ratio. Hydrolysis of the intact β-casein was monitored and quantified. Four kinetic functions were evaluated to describe the hydrolysis: First-order, nth-order, Michaelis–Menten, and competitive inhibition kinetics. The hydrolysis rate was found to depend on the initial protein concentration, due to the micellisation behaviour of β-casein. This effect was accounted for by modifying the kinetic functions. The modified competitive inhibition model provided the lowest mean square error. This model has only three parameters and described the hydrolysis of intact β-casein effectively for a broad range of initial conditions.