Inactivation and Aggregation of β-Galactosidase in Lyophilized Formulation Described by Kohlrausch-Williams-Watts Stretched Exponential Function

Abstract

Purpose. To examine whether the empirical Kohlrausch-Williams-Watts (KWW) equation is applicable not only to protein aggregation but also to protein denaturation in lyophilized formulations. Lyophilized β-galactosidase (β-GA) formulations containing polyvinylalcohol and methylcellulose were used as model formulations. The possibility of predicting storage stability based on the temperature dependence of the estimated parameters of inactivation/aggregation—time constant (τ) and its distribution (β) is discussed.

Methods. Protein aggregation in lyophilized β-GA formulations at 10-70°C and 6-43% relative humidity was determined as a function of time by size exclusion chromatography. Enzyme activity was also determined using 2-nitrophenyl-β-D-galactopyranoside as a substrate.

Results. Inactivation and aggregation of β-GA were describable with the empirical KWW equation, regardless of whether the temperature was above or below the NMR relaxation-based critical mobility temperature (T_mc) or whether protein molecules with different degrees of deformation resulting from stresses during lyophilization exist in the formulation. The estimated β parameter for protein aggregation decreased rapidly as temperature increased beyond T_mc because the mobility of polymer molecules increased in the initial stages of glass transition. The time required for 10% enzyme to aggregate (t₉₀) calculated from the τ and β parameters exhibited a change in temperature dependence gradient near T_mc. In contrast, t₉₀ for protein inactivation exhibited temperature dependence patterns varying with the excipients.

Conclusions. The t₉₀ calculated from the estimated τ and β parameters was found to be a useful parameter for evaluating the stability of lyophilized β-GA formulations. The prediction of t₉₀ by extrapolation was possible in the temperature range in which β did not rapidly vary with temperature.