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” (τa) and stretched exponential constant (βa) were calculated according to the KWW equation by assuming that the time required for protein molecules to aggregate (τ) 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.