Numerical Modelling of Insulin and Amyloglucosidase Release from Swelling Ca-Alginate Beads

The release of insulin hexamer (39 kD) and amyloglucosidase (AMG, 97 kD), entrapped in spherical Ca–alginate beads, was investigated. While the release of insulin could be described solely by diffusion this was not the case for the 1.6 (r _m /r _m) larger AMG protein, where r_m is the Stokes–Einstein effective molecular radius. Because the alginate bead size was not constant during the release experiments, it was hypothesised that in addition to the diffusional mass transfer, a non-negligible convective flow of liquid in or out of the beads was present due to swelling or shrinkage, respectively. Although it should be expected that the effective diffusion coefficient of AMG is only slightly lower than that of insulin, the results show that the effective diffusions coefficient of AMG was found to be much smaller. In the case of AMG, it was shown that including bead size changes and the resulting convective flow in the numerical model, release could be described more accurately. The numerical model was able to describe the release  characteristics from both shrinking, swelling, and non-swelling alginate beads. To evaluate the effect of bead swelling on the protein release rate, a swelling modulus and a release index was defined, describing the different effects on release of smaller and larger proteins.