Theoretical and experimental studies of glucose sensitive membranes

Abstract

A mathematical model has been developed to describe the steady-state behavior of two types of glucose sensitive membranes. Both membranes are synthetic hydrogels containing immobilized glucose oxidase enzyme (GluOx). The formation of gluconic acid from glucose and oxygen, catalyzed by GluOx, is the key to the functioning of either type of membrane since it causes a pH decrease within the membrane. In amine group-containing membranes, the pH decrease enhances the swelling (and permeability) of the gels, allowing control of insulin delivery in response to glucose concentrations. In membranes containing immobilized pH indicator dyes the pH decrease causes a color change, thus providing the basis for a glucose sensor. The model's predictions of the response of amine-containing membranes to glucose show that the pH decrease is often limited by O 2 depletion and that the occurrence of O 2 depletion is strongly influenced by enzyme loading and membrane thickness. At a given thickness, an optimal enzyme loading exists which results in the maximum response to glucose over a given range of glucose concentrations. The influence of buffer and amine concentrations, amine pK, solute diffusivities, and flowrate past the membrane also have been examined. For polyacrylamide membranes containing phenol red (but no amines), substrate turnover rates, oxygen depletion, and the pH decrease within the membrane have been calculated using the model and found to agree qualitatively with experimentally determined values of these parameters. Quantitative agreement is lacking, however. In particular, the model predicts that as GluOx loading is increased (all other parameters, including glucose concentration, held constant) the pH decrease should asymptotically approach a maximum value. However, it is found experimentally that as GluOx loading is increased, the measured pH decrease increases progressively over the full range of GluOx concentrations that we have studied. Possible reasons for the quantitative disagreements between simulated and observed results will be discussed. Implications of the model with respect to optimizing membrane designs will be presented. One finding of particular interest is that a glucose sensor using immobilized GluOx will achieve a maximum response at sub-physiological concentrations of glucose, and not respond to higher glucose concentrations, unless the enzyme loading is made sufficiently low.