Mathematical model for internal pH control in immobilized enzyme particles.

A mathematical model has been developed for the internal pH control in immobilized enzyme particles. This model describes the kinetics of a coupled system of two enzymes, immobilized in particles of either planar, cylindrical, or spherical shape. The enzyme kinetics are assumed to be of a mixed type, including Michaelis-Menten kinetics, uncompetitive substrate inhibition, and competitive and noncompetitive product inhibition. In a case study we have considered the enzyme combination urease and penicillin acylase, whose kinetics are coupled through the pH dependence of the kinetic parameters. The hydrolysis of urea by urease yields ammonia and carbon dioxide, whereas benzylpenicillin (Pen-G) is converted to 6-amino penicillanic acid and phenyl acetic acid by penicillin acylase. The production of acids by the latter enzyme will cause a decrease in pH. Because of the presence of the ammonia-carbon dioxide system, however, the pH may be kept under control. In order to obtain information about the optimum performance of this enzymatic pH controller, we have computed the effectiveness factor and the conversion in a CSTR at different enzyme loadings. The results of the computer simulations indicate that a high conversion of Pen-G may be achieved (80-90%) at bulk pH values of about 7.5-8.