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BIOMD0000000555 - Auer2010 - Correlation between lag time and aggregation rate in protein aggregation

 

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Reference Publication
Publication ID: 20602358
Auer S, Kashchiev D.
Insight into the correlation between lag time and aggregation rate in the kinetics of protein aggregation.
Proteins 2010 Aug; 78(11): 2412-2416
Centre for Molecular Nanoscience, University of Leeds, Leeds, LS2 9JT, United Kingdom. s.auer@leeds.ac.uk  [more]
Model
Original Model: BIOMD0000000555.origin
Submitter: Audald Lloret i Villas
Submission ID: MODEL1411100000
Submission Date: 10 Nov 2014 13:33:38 UTC
Last Modification Date: 08 Apr 2016 18:42:51 UTC
Creation Date: 10 Nov 2014 14:26:52 UTC
Encoders:  Audald Lloret i Villas
set #1
bqbiol:hasProperty Human Disease Ontology DOID:14330
Human Disease Ontology Alzheimer's disease
set #2
bqbiol:isVersionOf Gene Ontology amyloid fibril formation
set #3
bqbiol:hasTaxon Taxonomy Homo sapiens
Notes
Auer2010 - Correlation between lag time and aggregation rate in protein aggregation

This model is described in the article:

Auer S, Kashchiev D.
Proteins 2010 Aug; 78(11): 2412-2416

Abstract:

Under favorable conditions, many proteins can assemble into macroscopically large aggregates such as the amyloid fibrils that are associated with Alzheimer's, Parkinson's, and other neurological and systemic diseases. The overall process of protein aggregation is characterized by initial lag time during which no detectable aggregation occurs in the solution and by maximal aggregation rate at which the dissolved protein converts into aggregates. In this study, the correlation between the lag time and the maximal rate of protein aggregation is analyzed. It is found that the product of these two quantities depends on a single numerical parameter, the kinetic index of the curve quantifying the time evolution of the fraction of protein aggregated. As this index depends relatively little on the conditions and/or system studied, our finding provides insight into why for many experiments the values of the product of the lag time and the maximal aggregation rate are often equal or quite close to each other. It is shown how the kinetic index is related to a basic kinetic parameter of a recently proposed theory of protein aggregation.

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.

Model
Publication ID: 20602358 Submission Date: 10 Nov 2014 13:33:38 UTC Last Modification Date: 08 Apr 2016 18:42:51 UTC Creation Date: 10 Nov 2014 14:26:52 UTC
Mathematical expressions
Rules
Assignment Rule (variable: Amyloid) Assignment Rule (variable: a) Assignment Rule (variable: ka) Assignment Rule (variable: t1)
Physical entities
Compartments Species
Brain Amyloid    
Global parameters
omega n a e
k ka C+ t1
Reactions (0)
Rules (4)
 
 Assignment Rule (name: Amyloid) Amyloid = 1-exp(-(time/omega)^n)
 
 Assignment Rule (name: a) a = n*exp((-(n-1))/n)-1
 
 Assignment Rule (name: ka) ka = k/e
 
 Assignment Rule (name: t1) t1 = (log(1/C)-e+1)*1/k
 
 Brain Spatial dimensions: 3.0  Compartment size: 1.0
 
  Amyloid
Compartment: Brain
Initial concentration: 0.0
 
Global Parameters (8)
 
 omega
Value: 35.3
Constant
 
 n
Value: 7.2
Constant
 
  a
Value: 2.04338357605325
 
   e
Value: 2.718
Constant
 
 k
Value: 0.205
Constant
 
  ka
Value: 0.0754231052244297
 
 C+
Value: 6.9E-4
Constant
 
  t1
Value: 27.1259461481608
 
Representative curation result(s)
Representative curation result(s) of BIOMD0000000555

Curator's comment: (updated: 10 Nov 2014 15:15:48 GMT)

Figure 1 (upper panel) and Figure 2 (lower panel) have been reproduced here.

Figure 1. Analysis of kinetic amyloid fibrils data for 80 hours protein aggregation.
Figure 2. Dependence of the parameter a on the kinetic index n in overall aggregation.

The simulation was done using Copasi v4.12 (Build 81) and the plots were generated using Gnuplot. The models with simulation settings can be downloaded from the below link:

Additional file(s)
  • Auer2010 - Correlation between lag time and aggregation rate in protein aggregation:
    Copasi file of the model
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