Kinetics of Irreversible Protein Aggregation:  Analysis of Extended Lumry−Eyring Models and Implications for Predicting Protein Shelf Life

A general phenomenological kinetic model of irreversible protein aggregation in aqueous solution proceeding via non-native conformations is examined with a view toward the development of techniques to predict in vitro protein shelf life quantitatively. Approximate analytical solutions are derived for interpreting experimental data and agree with explicit numerical simulations over a broad range of physically relevant conditions. Results are presented in terms of the observed kinetics of monomer loss to provide a basis for direct comparison with typical experimental measures of aggregation as well as to provide a basis for quantitative prediction of protein shelf life. Similar to classic Lumry−Eyring models, experimentally observed aggregation kinetics are described as a combination of reversible conformational transitions and the intrinsic kinetics of aggregation via non-native states. However, in contrast to classic models, the extended Lumry−Eyring model developed here includes a detailed description of the intrinsic aggregation kinetics. The results indicate that apparent or observed aggregation kinetics can be grouped into one of four qualitatively distinct classes on the basis of their apparent reaction orders with respect to monomer concentration, each of which may be realized in practice depending on the experimental conditions and the relative rates of the intrinsic aggregation steps for the protein in question. The results also provide a basis for predicting shelf life by extrapolating high-temperature (“accelerated”) aggregation kinetics to lower-temperature, long-term storage conditions. Illustrations are given within the context of a model pharmaceutical protein for which sufficient data are available. Generalizations to systems with more complex conformational transitions are discussed briefly.