Usefulness of the Kohlrausch-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 feasibility 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" (taua) and stretched exponential constant (betaa) 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 deformation 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 by accelerated testing.
METHODS: Protein aggregation in lyophilized bovine serum gamma-globulin (BGG) formulations containing dextran or methylcellulose, at temperatures ranging from 10 to 80 degrees C, was followed by size-exclusion chromatography.
RESULTS: Non-exponential BGG aggregation in lyophilized formulations could be described by the KWW equation. The taua and betaa, parameters changed abruptly around the NMR relaxation-based critical mobility temperature for formulations containing dextran and methylcellulose. In the glassy state, in contrast, the taua parameter of these formulations exhibited continuous temperature dependence. The parameter taur, as calculated from taua, and betaa, reflected differences in tau values between the two excipients.
CONCLUSIONS: The results indicate that the parameter betaa is reflective of physical changes wihtin lyophilized formulations. Within the temperature range, during which no abrupt changes in betaa were observed, knowledge regarding the taua and betaa parameters allows the rate of protein aggregation to be predicted. The parameter taur was found to be useful in comparing the protein aggregation behavior of formulations having different taua and betaa values.