A Lumry−Eyring Nucleated Polymerization Model of Protein Aggregation Kinetics:  1. Aggregation with Pre-Equilibrated Unfolding

Abstract

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.

Aggregation Kinetics for Monoclonal Antibody Products

“…1) Lumry-Eyring model, according to which a native protein unfolds in a reversible way into an unfolded state which then aggregates irreversibly [6], [7] 2) Native polymerization models, in which nucleation and polymer growth are treated in detail, but conformational changes prior to or during assembly are not included [5], [8] 3) Extended Lumry-Eyring models, in which aggregation kinetics observed experimentally, are described as a combination of reversible conformational transitions and the intrinsic kinetics via non native states. However, in contrast to classical Lumry Eyring model, these models include a detailed description of the intrinsic aggregation kinetics [9] 4) Aggregate condensation and polymerization models, which specifically take care of the higher order assembly of aggregates that are formed during the initial steps of nucleation and polymerization [5], [10] The modified Lumry Eyring kinetic model has been successfully used by researchers to describe the monoclonal antibody aggregation process at low pH (3-4) [6].…”

“…However, in contrast to classical Lumry Eyring model, these models include a detailed description of the intrinsic aggregation kinetics [9] 4) Aggregate condensation and polymerization models, which specifically take care of the higher order assembly of aggregates that are formed during the initial steps of nucleation and polymerization [5], [10] The modified Lumry Eyring kinetic model has been successfully used by researchers to describe the monoclonal antibody aggregation process at low pH (3-4) [6]. A mathematical model of non-native protein aggregation has also been presented which combines the Lumry Eyring and Nucleated Polymerization (LENP) descriptions that is useful under conditions where detailed kinetics of folding or unfolding can be neglected [5]. However, a detailed study of aggregation behavior of monoclonal antibodies at several different conditions of pH, temperature and salt molarity pertaining to different types of chromatography could not be found in the literature and this work is an attempt to address the same by analyzing the stability of monoclonal antibodies under the different experimental conditions employed for Protein A chromatography, Cation Exchange Chromatography and Anion Exchange Chromatography.…”

“…Kinetic studies and data curve fitting are keys to rigorous mechanistic studies [4]. When combined with experimental kinetic and thermodynamic data, models of aggregation kinetics can provide a unique and noninvasive way to gain qualitative and quantitative details about the aggregation mechanism and also help in the design of experiments and additives to more accurately predict or control aggregation rates [5]. The hold time of the monoclonal antibody in the buffer can be appropriately chosen depending on its aggregation behavior in order to minimize the formation of aggregates.…”

The effect of charge mutations on the stability and aggregation of a human single chain Fv fragment

“…The long term loss of monomer is generally predicted through quantitative monitoring of aggregation under accelerated and stress conditions over weeks to months. Recent progress has been made in: (i) the development of detailed kinetic models [2,4,5,34,42,49,60,96]; (ii) correlating aggregation kinetics with protein structure and folding [11,15,16,32,35,52,53,54,67,88]; (iii) and with native-state protein-protein interaction measurements [36,46,57,74,75,79,82].…”

A Comprehensive Evaluation of Nanoparticle Tracking Analysis (NanoSight) for Characterization of Proteinaceous Submicron Particles

“…32,33 Equilibrium may also exist between smaller and larger aggregates on static storage of stressed samples. It has also been reported that visible and subvisible particles generated by shake stress could be reversible and may dissociate into smaller aggregates over time.…”