A Quantitative Assessment of the Significance of Molecular Mobility as a Determinant for the Stability of Lyophilized Insulin Formulations

Purpose The purpose was to explore a method for quantitatively assessing the contribution of molecular mobility to the chemical reactivity of amorphous solids. Degradation of insulin in lyophilized formulations containing trehalose and poly(vinylpyrrolidone)(PVP) was chosen as a model system, and the temperature- and glass transition temperature (T_g)-dependence of the degradation rate was analyzed to obtain the relative contributions of molecular mobility and that of the chemical activational barrier reflected in the energy of activation.Methods Insulin degradation and dimerization in lyophilized trehalose and PVP formulations were monitored at various relative humidities (6–60% RH) and temperatures (10–60°C) by reverse-phase high-performance liquid chromatography (HPLC) and high-performance size-exclusion chromatography (HP-SEC), respectively. The T_g and fragility parameter of the lyophilized insulin formulations were determined by differential scanning calorimetry (DSC).Results Insulin degradation in the initial stage was describable with first-order kinetics for both of the trehalose and PVP formulations. The temperature- and T_g-dependence of the degradation rate indicated that the reactivity of insulin in the trehalose formulation is affected by molecular mobility at low humidity (12% RH), such that the ratio of the observed rate constant (k′) to the rate constant governed only by the activational barrier (k) was 0.051 at the T_g. At higher humidities, in contrast, the value of k′/k was much higher (0.914, 0.978, and 0.994 for 23% RH, 33% RH, and 43% RH, respectively), indicating that insulin degradation rate is determined predominantly by the activational barrier. For insulin degradation in the PVP formulation at temperatures below T_g, the contribution of molecular mobility to the degradation rate appeared to be negligible, as the extrapolated value of t₉₀ at the T_g exhibited a large difference between the formulations with differing T_g values (because of differing water contents).Conclusions The reactivity of insulin in the trehalose and PVP formulations can be described by an equation including factors reflecting the activational barrier (activation energy and frequency coefficient) and factors reflecting the molecular mobility (T_g, fragility parameter and a constant representing the relationship between the molecular mobility and the reaction rate). Thus, analysis of temperature dependence based on the proposed equation allows quantitative assessment of the significance of molecular mobility as a factor affecting chemical reactivity.