A model of enzyme adsorption and hydrolysis of microcrystalline cellulose with slow deactivation of the adsorbed enzyme

Reduction in the activity and the concentration of the adsorbed enzyme are noted in the experimental data. Two alternative mechanisms, inactivation of the adsorbed enzyme and mass transfer of the enzyme from the bulk solution to the solution within the cellulose fibril where the cellulase is assumed to be inactive, are used to represent the decline in activity. The decline in concentration of the adsorbed enzyme is represented by a modest product inhibition and, more importantly, the assumption that the concentration of the adsorption sites is proportional to the square of the remaining substrate concentration. Measurements of both adsorbed enzyme and product concentration over time are used in determining parameter values. The model is applied to a series of experiments having a 10-fold range of substrate concentration and to an experiment in which the product is removed continuously. For both deactivation mechanisms, a very good representation of product concentration (standard deviation 3.6%) is obtained over the full period (168 h) of hydrolysis; the representation of adsorbed enzyme is, however, less accurate (standard deviation 6.7-6.8%).