Usefulness of the Kohlrausclh-Williams-Watts stretched exponential function to describe protein aggregation in lyophilized formulations and the temperature dependence near the glass transition temperature

Purpose. We studied the feasibilily of using the Kohlrausch-Williams-Watts stretched exponential function (KWW equation) to describe protein aggregation in lyophilized formulations during storage. Parameters representing "mean aggregation time" (tau (a)) and stretched exponential constant (beta (a)) were calculated according to the KWW equation by assuming that the time required for protein molecules to aggregate (tau) varies because of the fact that protein aggregation occurs at a rate that depends on the degree of protein defor mation resulting from stresses created during freeze-drying. The temperature dependence of the parameters near the glass transition temperature was examined to discuss the possibility of predicting protein aggregation bp accelerated testing. Methods. Protein aggregation in lyophilized bovine serum gamma -globulin (BGG) formulations containing dextran or methylcellulose, at temperatures ranging from 10 to 80 degreesC, was followed by size-exclusion chromatography. Results. Non-exponential EGG aggregation in lyophilized formulations could be described by the KWW equation. The tau (a) and beta (a) parameters changed abruptly around the NMR relaxation-based critical mobility temperature for formulations containing: dextran and methylcellulose. In the glassy state, in contrast, the tau (a) parameter of these formulations exhibited continuous temperature dependence. The parameter tau (Gamma), as calculated from tau (a) and beta (a), reflected differences in tau values between the two excipients. Conclusions. The results indicate that the parameter beta (a) is reflective of physical changes wihtin lyophilized formulations. Within the temperature range, during which no abrupt changes in beta (a) were observed, knowledge regarding the tau (a) and beta (a) parameters allows the rate of protein aggregation to be predicted. The parameter tau (Gamma) was found to be useful in comparing the protein aggregation behavior of formulations ha different and P values.