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 aggregati on in lyophilized formulations during storage. Parameters representing "mea n aggregation time" (tau (a)) and stretched exponential constant (beta (a)) were calculated according to the KWW equation by assuming that the time re quired for protein molecules to aggregate (tau) varies because of the fact that protein aggregation occurs at a rate that depends on the degree of pro tein defor mation resulting from stresses created during freeze-drying. The temperature dependence of the parameters near the glass transition tempera ture was examined to discuss the possibility of predicting protein aggregat ion bp accelerated testing. Methods. Protein aggregation in lyophilized bovine serum gamma -globulin (B GG) formulations containing dextran or methylcellulose, at temperatures ran ging 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 chang ed abruptly around the NMR relaxation-based critical mobility temperature f or formulations containing: dextran and methylcellulose. In the glassy stat e, in contrast, the tau (a) parameter of these formulations exhibited conti nuous 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 temperatur e range, during which no abrupt changes in beta (a) were observed, knowledg e 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 usef ul in comparing the protein aggregation behavior of formulations ha differe nt and P values.