A mechanistical mathematical model to predict lactose hydrolysis by β-galactosidase in a permeabilized cell mass of Kluyveromyces lactis:: validity and sensitivity analysis

The kinetics of lactose hydrolysis by intracellular beta -galactosidase in a preparation of Kluyveromyces lactis cells permeabilized with ethanol was assessed in the presence of lactose and its hydrolysis reaction products galactose and glucose. Enzyme inhibition by the reaction products was tested using different concentrations of galactose (1, 5, 10, 20, 30 and 40 mM) and glucose (10, 30 and 50 mM) and a combination of both. Galactose was a competitive inhibitor. The competitive or non-competitive nature of the inhibition was defined by the smallest value presented by the residual sum of squares of regression as determined using the Marquardt iterative method of the non-linear regression (NLIN) program of the statistical analysis system (SAS). The kinetic constants V-max K-m and K-i, with values corresponding to 0.291 +/-0.01 mM min(-1); 2.536 +/-0.412 mM and 10.88 +/-8.86 mM, respectively, were also estimated by the same program. Enzyme activity was not affected by glucose at the concentrations tested. Glucose affected enzyme activity only when galactose was present. A mechanistic mathematical model was developed to describe lactose hydrolysis, taking into consideration the inhibitory effect of galactose. Sensitivity analysis of the coefficients of the model proposed was performed. Varying estimated K-m and K-i values by +/- 20% had no effect on lactose hydrolysis kinetics. However, with a 20% increase in the estimated V-max value, the model more closely approximated the experimental data for initial concentrations of 30 mM glucose and 10 mM galactose. Model simulation closely approximated experimental data from lactose hydrolysis in a 5% phosphate-buffered lactose solution as well as in skim milk. (C) 2001 Elsevier Science Ltd. All rights reserved.