Review
Protein aggregation kinetics, mechanism, and curve-fitting: A review of the literature

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Abstract

Protein aggregation is an important phenomenon that alternatively is part of the normal functioning of nature or, central to this review, has negative consequences via its hypothesized central role in neurodegenerative diseases. A key to controlling protein aggregation is understanding the mechanism(s) of protein aggregation. Kinetic studies, data curve-fitting, and analysis are, in turn, keys to rigorous mechanistic studies. The main goal of this review is to analyze and report on the primary literature contributions to protein aggregation kinetics, mechanism, and curve-fitting. Following a brief introduction, the multiple different physical methods that have been employed to follow protein aggregation are presented and briefly discussed. Next, key information on the starting proteins and especially the products, and any detectable intermediates, involved in protein aggregation are presented. This is followed by tabulation (in the Supporting information) and discussion (in the main text), of the many approaches in the literature striving to determine the kinetics and mechanism of protein aggregation. It is found that these approaches can be broadly divided into three categories: (i) kinetic and thermodynamic, (ii) empirical, and (iii) other approaches. The first two approaches are the main focus of the present contribution, their goal being curve-fitting the available kinetic data and obtaining quantitative rate constants characterizing the nucleation, growth, and any other parts of the overall aggregation process. The large literature of protein aggregation is distilled down to five classes of postulated mechanisms: i) the subsequent monomer addition mechanism, ii) the reversible association mechanism, iii) prion aggregation mechanisms, iv) an “Ockham's razor”/minimalistic model first presented in 1997 and known as the Finke–Watzky 2-step model, and v) quantitative structure activity relationship models. These five classes of mechanisms are reviewed in detail in historical order; where possible corresponding kinetic equations, and fits to aggregation data via the proposed mechanisms, are analyzed and discussed. The five classes of mechanisms are then analyzed and discussed in terms of their similarities and differences to one another. Also included is a brief discussion of selected empirical approaches used to investigate protein aggregation. Three problem areas in the protein aggregation kinetic and mechanistic studies area are identified, and a Summary and Conclusions section is provided en route to moving the field forward towards the still unachieved goal of unequivocal elucidation of the mechanism(s) of protein aggregation.

Introduction

The aggregation1 of proteins such as amyloid-β, polyglutamine, α-synuclein, and prions has been suggested to be intimately associated with neurodegenerative disorders such as Alzheimer's [1], Huntington's [2], Parkinson's [3], and prion [4] diseases, respectively. Aggregation is also a nuisance in industrial applications where it can interfere with the production and characterization of therapeutic polypeptides [5]. Naturally occurring, productive protein aggregation is also important in nature in cases such as the protein fibrillation reaction of n(G-actin)  (F-actin)n, where G-actin is the globular, and F-actin the fibrillar form, of the protein actin.

For the purposes of this review, we will categorize protein aggregation into three classes: (i) naturally occurring, productive aggregation as in the n(G-actin)  (F-actin)n example mentioned. This reaction occurs throughout the human body, as well as in other organisms, and is necessary in controlling the mobility and shape of the cells [6]. Another example of naturally occurring protein aggregation includes the enzyme glutamate dehydrogenase [7], [8], [9], [10]. Both actin and glutamate dehydrogenase function with aggregation of a protein in its native state. A second class of aggregation phenomenon can be classified as (ii) unwanted aggregation in biology. This class includes α-synuclein, amyloid β, polyglutamine, and prions as common examples of proteins that aggregate and are suspected to play a key role in the neurodegenerative diseases Parkinson's [3], Alzheimer's [1], Huntington's [2], and prion [4] diseases, respectively. This type of aggregation is generally believed to involve aggregation of the protein in a non-native state (vide infra). The final class of aggregation phenomenon is (iii) unwanted aggregation in an industrial setting. This class of aggregation usually produces amorphous aggregates and its control and understanding is important to the biotechnology industry for keeping proteins in a non-aggregated, bottleable, long-shelf-life form [11].

Because of its importance, the kinetics and mechanism of protein aggregation have been of interest for approximately fifty years [12]. Protein aggregation is, therefore, a topic that has been the subject of numerous other recent reviews, although from perspectives different than herein [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26]. Of particular interest is the excellent and critical review on the detailed steps of protein aggregation recently published by C. J. Roberts [14], as well as a review on entropy-driven polymerization of proteins by M. A. Lauffer [26]. However, still missing in our opinion among the available reviews of the expansive protein aggregation literature is an analysis and review focusing on models that can fit kinetic data, give useful, quantitative rate constants, and ideally provide mechanistic insight. Key questions to be answered herein include: (i) How many distinct mechanisms actually exist in the literature for protein aggregation? (ii) What is the essence of each mechanism? (iii) Which mechanisms or models have been used to curve-fit kinetic data? (iv) Do any of these mechanisms have similarities to each other? Also, (v) which of the terms used in the sometimes confusing nomenclature2 in the protein aggregation literature have the same meaning? These are some of the key questions we hope to answer herein. In short, a main goal of the present contribution is to analyze and report the primary (in our opinion) literature contributions to protein aggregation kinetics, mechanism, and curve-fitting.

In what follows we have tried to identify key papers in terms of the 5 main classes (vide infra) of mechanistic models in the literature, and to trace each (class of) mechanism back to its earliest origins. Our goal is to distill the literature to its essential components, again in our view. We apologize in advance to the authors of literature we were not able to cover in the space available or have somehow inadvertently missed.

We begin with a brief survey of the physical methods used to measure protein aggregation noting whether the methods are direct or indirect, in-situ or ex-situ, and whether the method is able to measure kinetics. Next, we discuss what is known about the starting proteins, products, and intermediates of protein aggregation—since knowing one's products and intermediates is key to rigorous mechanistic science. Third, we tabulate and discuss the main thermodynamic and kinetic based studies we have found that support what turns out to be the 5 main classes of suggested mechanisms of protein aggregation, all in a somewhat historical order. We also briefly discuss empirical approaches that have been used to fit protein aggregation kinetic data. We end with a discussion of what seems to be some of the common pitfalls in attacking the highly complex problem of the mechanism(s) of protein aggregation. We also list some of the important unsolved problems and hence needed future research directions, and then conclude with a Summary and Conclusions section of the highlights of this review.

Section snippets

Advantages and disadvantages of the physical methods used to monitor protein aggregation

The kinetics and products of protein aggregation have been measured using at least 18 different analytical techniques, each having its own intrinsic advantages and disadvantages. Each technique is summarized in Table 1 and discussed in more detail in the Supporting information. The interested reader is also referred to the recent, excellent review by S. E. Bondos that compares the various methods used to detect protein aggregation, with an emphasis on the concentration and volume ranges for

Starting proteins, products, and detectable intermediates of protein aggregation

It has long been known that “know your product(s)” is the first rule of rigorous mechanistic science, since the steps in any proposed mechanism must add up to those observed products. We review, therefore, what is generally known vs. not known about the starting proteins, products, and any detectable intermediates of protein aggregation when fibrils are formed, as this category involves many important studies of (native and non-native) protein aggregation. While a main goal of this review is to

Thermochemistry of protein aggregation

The aggregation of many biologically important proteins including, but not limited to, tobacco mosaic virus, tubulin, sickle cell hemoglobin, collagen, actin, myosin, flagellin, glutamate dehydrogenase, and α-chymotrypsin have been shown to exhibit a positive enthalpy and entropy [26], [74]. We refer the readers to the scholarly work contained in references [26] and [74] for the quantitative ΔH° and ΔS° values. The positive enthalpy (i.e., endothermic nature) has been verified by calorimetry

Approaches to determine the kinetics and mechanism of protein aggregation

As Scheme 2 illustrates, many approaches exist in the literature for determining the kinetics and mechanism of protein aggregation. Kinetic, thermodynamic, empirical, or other approaches can provide useful information depending upon what one is trying to obtain from the analysis. Herein, we are most interested in being able to curve-fit kinetic data and extract useful information from that data—kinetics being a required part of reliable mechanistic studies. Therefore, the majority of what

Three problem areas in the protein aggregation kinetic and mechanistic literature

One must ask, why has such an important question, as ‘what are the mechanism(s) of protein aggregation?’, yet to be unequivocally answered despite the numerous contributions cited herein? The simple answer is that protein aggregation is a highly complex problem with complicated molecular level and kinetic details, along with associated complex mathematics. In hopes of moving this area forward, we list a few possible problem areas of importance, in our opinion, for future studies in protein

Summary and conclusions

Despite the importance of the problem and the nearly 50 years of research aimed at determining the mechanism(s) and rate constant(s) for protein aggregation, many questions still remain. Frieden concisely summarizes the state of affairs in his recent review: “In spite of the extensive literature, however, the mechanism of [protein] aggregation is poorly understood” [16]. The focus of the present review has been to examine the protein aggregation literature from the perspective of trying to fit

Acknowledgements

We thank Mr. Steve Hays for his graphic design of the schematic fibril pictured in Scheme 1. We also thank Professors Eric D. Ross and Jeffrey N. Agar for providing their insightful comments on the manuscript. Finally, we gratefully acknowledge NSF grant #0611588 for partial support of this project.

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