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A pseudo steady-state model for the kinetically controlled synthesis of galacto-oligosaccharides (GOS) with Aspergillus oryzae β-galactosidase is presented. The model accounts for the dynamics of lactose consumption and production of galactose, glucose, di, tri, tetra, and penta-oligosaccharides during the synthesis, being able to describe the total GOS content in the reaction medium at the experimental conditions evaluated. Experimental results show that the formation of GOS containing only galactose residues is significant at high conversions of substrate, which was taken into account in the model. The formation of enzyme transition complexes was considered and reasonable assumptions were made to reduce the number of parameters to be determined. The model developed has 8 parameters; 2 of them were experimentally determined and the other 6 were estimated by fitting to the experimental data using multiresponse regression. Temperature effect on kinetic and affinity constants was determined in the range from 40 to 55°C, and the data were fitted to Arrhenius type equation. Parameters of the proposed model are independent from the enzyme load in the reaction medium and, differently from previously reported models, they have a clear biochemical meaning. The magnitude of the kinetic and affinity constants of the enzyme suggests that the liberation of galactose from the galactosyl-enzyme complex is a very slow reaction and such complex is driven into GOS formation. It also suggests that the affinity for sugars of the galactosyl-enzyme complex is higher than that of the free enzyme.

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