A Lumry-Eyring nucleated polymerization model of protein aggregation kinetics: 1. Aggregation with pre-equilibrated unfolding.

A mathematical model is presented of the kinetics of non-native protein aggregation that combines Lumry-Eyring and nucleated polymerization (LENP) descriptions. The LENP model is solved for cases in which aggregation rates are slow compared to folding-unfolding equilibration and is shown to be a generalization of a number of previously proposed nucleation-and-growth models for non-native and native protein aggregation. The model solutions exhibit a number of qualitative kinetic regimes. Each regime has a characteristic set of experimental signatures that are related to the relative rates of growth and nucleation as well as to the threshold size at which aggregates condense to form higher-order structures or other phases. Approximate model solutions provide practical rate equations that can be regressed against typical experimental kinetic data to obtain mechanistic parameters characterizing the aggregation pathway. In all kinetic regimes, it is found that observed rate coefficients (kobs) or half-lives (t50) obtained from extent-of-reaction measurements are convolutions of more than one stage in the pathway unless purely seeded growth occurs. Despite this convolution, the combination of apparent reaction order (time domain) and the scaling of kobs or t50 with initial protein concentration provides a means to determine a value for the dominant nucleus size in each case. Additional information, such as equilibrium unfolding thermodynamics and the limiting aggregate size distribution, are required to further deconvolute kobs into intrinsic contributions from nucleation, growth, and conformational changes. The model and analysis are expected to be generally applicable to a wide range of proteins and polypeptides that form non-native aggregates.