Real-time measurement and modeling of intraparticle pH gradient formation in immobilized cephalosporin C amidase

Abstract

A new and generic approach of dynamic reaction–diffusion modeling was applied to analyze the catalytic performance of an industrially used cephalosporin C amidase immobilized on a series of insoluble carriers (epoxy-activated Sepabeads) that differed in particle or pore diameter. Enzymatic conversion of cephalosporin C into 7-amino cephalosporanic acid and d-α-amino adipic acid (DAAA) results in net proton release, and this was shown previously to bring about significant internal acidification of the enzyme immobilizates during reaction. In this study, we demonstrate first time model parameter estimation to in situ measured real-time pH data, recorded both inside the enzyme carrier as well as externally in the liquid bulk of a stirred tank reactor. An essential and novel feature of the model was applicability to intraparticle pH data derived from space-averaged opto-chemical measurements. Using model-based estimation, we determined the maximal intrinsic reaction rate of the immobilized amidase completely unmasked from diffusional and carrier acidification effects (vmax,specific) as well as the effective proton diffusion coefficient (Deff, H+). Neither parameter is accessible directly from the experiment. The resulting vmax,specific estimates showed that carrier-bound amidase had lost between 14% and 55% of the free enzyme's activity due to immobilization, depending on the carrier type used. The Deff, H+ estimate (≈1×10−10m2/s) was about one order of magnitude lower than expected for proton diffusion in such porous structures, suggesting a role for co-diffusion of the proton and the corresponding DAAA anion in decreasing the proton diffusivity. The model was validated against independent time-course data sets, and it was shown to give useful prediction of immobilized enzyme effectiveness factors for the applied range of carrier characteristics and enzyme loadings. Simulation was used to characterize the influence of geometrical features of the carrier on distribution of substrate and products in the carrier pore, and it is demonstrated how these intraparticle concentration gradients affect enzyme reactor performance under different process conditions.