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Fitting Neurological Protein Aggregation Kinetic Data via a 2-Step, Minimal/“Ockham's Razor” Model:  The Finke−Watzky Mechanism of Nucleation Followed by Autocatalytic Surface Growth

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    Fitting Neurological Protein Aggregation Kinetic Data via a 2-Step, Minimal/“Ockham's Razor” Model:  The Finke−Watzky Mechanism of Nucleation Followed by Autocatalytic Surface Growth†
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    Department of Chemistry, Colorado State University, Fort Collins, Colorado 80523, and Department of Chemistry and Volen Center, Brandeis University, 415 South Street, Waltham, Massachusetts 02454
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    Biochemistry

    Cite this: Biochemistry 2008, 47, 8, 2413–2427
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    https://doi.org/10.1021/bi701899y
    Published February 5, 2008
    Copyright © 2008 American Chemical Society
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    Abstract

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    The aggregation of proteins has been hypothesized to be an underlying cause of many neurological disorders including Alzheimer's, Parkinson's, and Huntington's diseases; protein aggregation is also important to normal life function in cases such as G to F-actin, glutamate dehydrogenase, and tubulin and flagella formation. For this reason, the underlying mechanism of protein aggregation, and accompanying kinetic models for protein nucleation and growth (growth also being called elongation, polymerization, or fibrillation in the literature), have been investigated for more than 50 years. As a way to concisely present the key prior literature in the protein aggregation area, Table 1 in the main text summarizes 23 papers by 10 groups of authors that provide 5 basic classes of mechanisms for protein aggregation over the period from 1959 to 2007. However, and despite this major prior effort, still lacking are both (i) anything approaching a consensus mechanism (or mechanisms), and (ii) a generally useful, and thus widely used, simplest/“Ockham's razor” kinetic model and associated equations that can be routinely employed to analyze a broader range of protein aggregation kinetic data. Herein we demonstrate that the 1997 Finke−Watzky (F−W) 2-step mechanism of slow continuous nucleation, A → B (rate constant k1), followed by typically fast, autocatalytic surface growth, A + B → 2B (rate constant k2), is able to quantitatively account for the kinetic curves from all 14 representative data sets of neurological protein aggregation found by a literature search (the prion literature was largely excluded for the purposes of this study in order provide some limit to the resultant literature that was covered). The F−W model is able to deconvolute the desired nucleation, k1, and growth, k2, rate constants from those 14 data sets obtained by four different physical methods, for three different proteins, and in nine different labs. The fits are generally good, and in many cases excellent, with R2 values ≥0.98 in all cases. As such, this contribution is the current record of the widest set of protein aggregation data best fit by what is also the simplest model offered to date. Also provided is the mathematical connection between the 1997 F−W 2-step mechanism and the 2000 3-step mechanism proposed by Saitô and co-workers. In particular, the kinetic equation for Saitô's 3-step mechanism is shown to be mathematically identical to the earlier, 1997 2-step F−W mechanism under the 3 simplifying assumptions Saitô and co-workers used to derive their kinetic equation. A list of the 3 main caveats/limitations of the F−W kinetic model is provided, followed by the main conclusions from this study as well as some needed future experiments.

    Copyright © 2008 American Chemical Society

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    †

     The F−W mechanism grew out of long-term support by DOE Grant SE-FG02-03ER15453; without that long-term support its discovery would not have been possible. Partial support by NSF Grant 0611588 is also gratefully acknowledged as is Grant ALSA 1392 to J.N.A.'s laboratories.

    ‡

     Colorado State University.

    §

     Brandeis University.

    *

     Corresponding author. E-mail:  [email protected]. Tel:  (970) 491-2541. Fax:  (970) 491-1801.

    Supporting Information Available

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    Derivation of the analytic equation of the F−W 2-step mechanism; derivation of Saitô and co-workers' 2-step mechanism for the aggregation of calcitonin and its equivalence to the F−W 2-step mechanism; comparison of the original and generalized form of the F−W 2-step mechanism; examination of the scaling factors for the rate constants, k1 and k2; additional references for nanocluster formation data accounted for with the F−W mechanism; additional references for fibril intermediate species; numerical integration of kinetic data using MacKinetics; effect of added [Zn2+] on the rate constants of amyloid β aggregation; alternative mechanisms considered:  the 3- and 4-step mechanisms; fits of amyloid β aggregation data to the 3- and 4-step mechanisms; comparison of rate constants obtained from the 2-, 3-, and 4-step mechanisms, derivation of analytic equations for autocatalysis alone and the 2-step mechanism when [B]0 ≠ 0; fits of polyglutamine seeded data for autocatalysis alone, the 2-step mechanism, and the 2-step mechanism with [B]0 ≠ 0, along with a table of resultant rate constants; fits of α-synuclein seeded data for the 2-step and 2-step with [B]0 ≠ 0 mechanisms with a table of resultant rate constants; correlations of the k1 and k2 rate constants with the [B]0. This material is available free of charge via the Internet at http://pubs.acs.org.

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    Cite this: Biochemistry 2008, 47, 8, 2413–2427
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    Published February 5, 2008
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