Validity and sensitivity analysis of the kinetic coefficients of a mechanistical mathematical model proposed to predict lactose hydrolysis by b-galactosidase in permeabilized cell mass of kluyveromyces lactis

Abstract

The mechanistical mathematical model was developed to describe the lactose hydrolysis, taking into consideration the inhibition effect for galactose. It was used a dynamic system of ordinary differential equations of the lactose variation, glucose and galactose with the time. Those equations were resolved in the Fortran 90 program that generated a table of simulated data of lactose, glucose and galactose along the time. The analysis of sensibility of the coefficients of the model was accomplished varying in + 20% the values of the kinetic coefficients. The glucose concentrations and galactose were not influenced by the variations in the coefficients K_m and K_i, and an increase in the value of V_max in 20% a better adjustment of the model was observed with the experimental data. For the validation of the model, hydrolysis tests were accomplished in solution phosphate buffer containing 5% of lactose and in skimmed milk with of 4.8% lactose. The model represented the hydrolysis process satisfactorily in solution phosphate buffer with 5% of lactose. For this solution the variation among the measured value and predicted of glucose was of 4%, when 75% of hydrolysis were reached, altering the value of V_max in 30%. In the case of the lactose hydrolysis of the milk, a variation was verified among the concentrations of measured glucose and predicted of 13% when 85% of lactose hydrolysis was reached. The simulated data for the model presented good correlation with the originated experimental data of the lactose hydrolysis in half synthetic containing 5% of lactose and in skimmed milk.