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BIOMD0000000567 - Morris2008 - Fitting protein aggregation data via F-W 2-step mechanism


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Reference Publication
Publication ID: 18247636
Morris AM, Watzky MA, Agar JN, Finke RG.
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.
Biochemistry 2008 Feb; 47(8): 2413-2427
Department of Chemistry, Colorado State University, Fort Collins, Colorado 80523, USA.  [more]
Original Model: BIOMD0000000567.origin
Submitter: Audald Lloret i Villas
Submission ID: MODEL1501160000
Submission Date: 16 Jan 2015 15:31:13 UTC
Last Modification Date: 23 Jan 2015 16:57:13 UTC
Creation Date: 16 Jan 2015 16:30:06 UTC
Encoders:  Audald Lloret i Villas
set #1
bqbiol:hasProperty Human Disease Ontology Huntington's disease
Human Disease Ontology Parkinson's disease
Human Disease Ontology Alzheimer's disease
set #2
bqbiol:isVersionOf Gene Ontology amyloid fibril formation
set #3
bqbiol:hasTaxon Taxonomy Homo sapiens
set #4
bqmodel:isDerivedFrom PubMed 16981676
PubMed 16981683
PubMed 16981684
PubMed 12186976
PubMed 16081040
PubMed 16981679
PubMed 16301322
PubMed 16536526
PubMed 12785778
PubMed 15794636
PubMed 16117499
DOI 10.1021/ja9705102
Morris2008 - Fitting protein aggregation data via F-W 2-step mechanism

This model is described in the article:

Morris AM, Watzky MA, Agar JN, Finke RG.
Biochemistry 2008 Feb; 47(8): 2413-2427


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 >or=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.

To the extent possible under law, all copyright and related or neighbouring rights to this encoded model have been dedicated to the public domain worldwide. Please refer to CC0 Public Domain Dedication for more information.

Publication ID: 18247636 Submission Date: 16 Jan 2015 15:31:13 UTC Last Modification Date: 23 Jan 2015 16:57:13 UTC Creation Date: 16 Jan 2015 16:30:06 UTC
Mathematical expressions
Nucleation Growth    
Assignment Rule (variable: A0) Assignment Rule (variable: B)    
Physical entities
Compartments Species
Brain B A  
Global parameters
k1 k2 A0 k2A0
Reactions (2)
 Nucleation [A] → [B];   {A}
 Growth [A] + [B] → 2.0 × [B];   {A} , {B}
Rules (2)
 Assignment Rule (name: A0) A0 = k2A0/k2
 Assignment Rule (name: B) B = A0-(k1/k2+A0)/(1+k1/(k2*A0)*exp((k1+k2*A0)*time))
 Brain Spatial dimensions: 3.0  Compartment size: 1.0
Compartment: Brain
Initial concentration: 0.0
Compartment: Brain
Initial concentration: 1.0
Global Parameters (4)
Value: 4.0E-5
Value: 1.57E-6
Value: 184713.375796178
Value: 0.29
Representative curation result(s)
Representative curation result(s) of BIOMD0000000567

Curator's comment: (updated: 23 Jan 2015 16:30:12 GMT)

Figures 2, 7 and 9 of the reference publication have been reproduced here. Protein aggregation from the literature is fitted over time by the Finke-Watze 2-step model.
- Figure 2 (left). Amyloid β aggregation, hypothesized cause for pathology of Alzheimer's disease
- Figure 7 (center). α-Synuclein aggregation, hypothesized cause for pathology of Parkinson's disease
- Figure 9 (right). Polyglutamine aggregation, hypothesized cause for pathology of Hungington's disease

Note: Initial concentrations (A0) have been defined using Parameter Scan in order to match the simulation with the figures in the reference publication. Simulated values are 3.55 on Figure 2, 103 on Figure 7 and 98 on Figure 9.

The simulation was done using Copasi v4.14 (Build 89) and the plots were generated using Gnuplot. The Copasi file of the model with simulation settings can be downloaded from the below link:

Additional file(s)
  • Morris2008 - Fitting protein aggregation data via F-W 2-step mechanism:
    Copasi file of the model