Model discrimination for the propionic acid diffusion into hydrogel beads using lifetime confocal laser scanning microscopy

Hydrogels are increasingly used for the entrapment of biocatalysts, especially for the use of enzymes in organic solvent systems. Hence, it is necessary to understand the influence of the hydrogel matrix on the transport kinetics (diffusion and phase transfer) and on the reaction kinetics (activity and stability of the enzymes). Here, the diffusion of propionic acid into Ca-alginate hydrogel beads is studied using a structured methodology, model-based experimental analysis (MEXA).The basis for all further investigations is a rigorous model of all processes occurring during the diffusion of the propionic acid into the Ca-alginate hydrogel bead. As competing model assumptions the Fickian and Nernst–Planck diffusion laws are integrated. Then, an optimal experimental design is performed to determine those experiments that allow an efficient discrimination of the rival model candidates. The change in pH-value over time resulting from the diffusion of propionic acid into the hydrogel bead is observed in the centre of the hydrogel bead. The fluorescent pH-indicator resorufin shows pH-dependent lifetimes that are measured by time-correlated single photon counting using a confocal laser scanning microscope at high temporal resolution (every 1 s). To our knowledge lifetime confocal laser scanning microscopy is used for the first time in this study for the quantification of dynamic pH-changes in macroscopically large particles. The model parameters for each candidate model are estimated based on 16 independent experimental data sets. Finally, the likelihood function is used to evaluate and discriminate the competing diffusion laws.For the diffusion of propionic acid into spherical Ca-alginate hydrogel beads, it could be shown that Fickian diffusion is not able to describe the process accurately in contrast to Nernst–Planck diffusion. The influence of the Ca-alginate hydrogel density was found to be insignificant for the estimated diffusion coefficient.