BioModels Database logo

BioModels Database

spacer

BIOMD0000000533 - Steckmann2012 - Amyloid beta-protein fibrillogenesis (kinetics of secondary structure conversion)

 

 |   |   |  Send feedback
Reference Publication
Publication ID: 22586726
Steckmann T, Awan Z, Gerstman BS, Chapagain PP.
Kinetics of peptide secondary structure conversion during amyloid β-protein fibrillogenesis.
J. Theor. Biol. 2012 May; 301: 95-102
Theoretical and Computational Biophysics Group, Department of Physics, Florida International University, Miami, FL 33199, USA.  [more]
Model
Original Model: BIOMD0000000533.origin
Submitter: Audald Lloret i Villas
Submission ID: MODEL1407300001
Submission Date: 30 Jul 2014 13:33:07 UTC
Last Modification Date: 24 Sep 2014 14:16:24 UTC
Creation Date: 30 Jul 2014 15:14:54 UTC
Encoders:  Audald Lloret i Villas
set #1
bqbiol:hasProperty Human Disease Ontology Alzheimer's disease
set #2
bqbiol:isVersionOf Gene Ontology beta-amyloid formation
Gene Ontology inclusion body assembly
set #3
bqbiol:hasTaxon Taxonomy Homo sapiens
Notes
Steckmann2012 - Amyloid beta-protein fibrillogenesis (kinetics of secondary structure conversion)

This model is described in the article:

Steckmann T, Awan Z, Gerstman BS, Chapagain PP.
J. Theor. Biol. 2012 May; 301: 95-102

Abstract:

Amyloid fibrils are a common component in many debilitating human neurological diseases such as Alzheimer's (AD), Parkinson's, and Creutzfeldt-Jakob, and in animal diseases such as BSE. The role of fibrillar ?? proteins in AD has stimulated interest in the kinetics of ?? fibril formation. Kinetic models that include reaction pathways and rate parameters for the various stages of the process can be helpful towards understanding the dynamics on a molecular level. Based upon experimental data, we have developed a mathematical model for the reaction pathways and determined rate parameters for peptide secondary structural conversion and aggregation during the entire fibrillogenesis process from random coil to mature fibrils, including the molecular species that accelerate the conversions. The model and the rate parameters include different molecular structural stages in the nucleation and polymerization processes and the numerical solutions yield graphs of concentrations of different molecular species versus time that are in close agreement with experimental results. The model also allows for the calculation of the time-dependent increase in aggregate size. The calculated results agree well with experimental results, and allow differences in experimental conditions to be included in the calculations. The specific steps of the model and the rate constants that are determined by fitting to experimental data provide insight on the molecular species involved in the fibril formation process.

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: 22586726 Submission Date: 30 Jul 2014 13:33:07 UTC Last Modification Date: 24 Sep 2014 14:16:24 UTC Creation Date: 30 Jul 2014 15:14:54 UTC
Mathematical expressions
Rules
Assignment Rule (variable: RC) Assignment Rule (variable: beta) Rate Rule (variable: RCT0) Rate Rule (variable: alpha)
Rate Rule (variable: BN1) Rate Rule (variable: BN2) Rate Rule (variable: BN3) Rate Rule (variable: BN4)
Rate Rule (variable: BTX) Rate Rule (variable: BM) Rate Rule (variable: RCT1)  
Physical entities
Compartments Species
cell RCT0 alpha BN1
BN2 BN3 BN4
BTX BM RCT1
RC beta  
Global parameters
k0 k1 k2 k3
k4 q epsilon  
Reactions (0)
Rules (11)
 
 Assignment Rule (name: RC) RC = RCT0+RCT1
 
 Assignment Rule (name: beta) beta = BM+BN1+BN2+BN3+BN4+BTX
 
 Rate Rule (name: RCT0) d [ RCT0] / d t= (-k0)*(epsilon+BM)*RCT0-k1*BTX*RCT0
 
 Rate Rule (name: alpha) d [ alpha] / d t= k1*BTX*RCT0-k2*BTX^q*alpha
 
 Rate Rule (name: BN1) d [ BN1] / d t= k2*BTX^q*alpha-4*k3*BN1
 
 Rate Rule (name: BN2) d [ BN2] / d t= 4*k3*BN1-4*k3*BN2
 
 Rate Rule (name: BN3) d [ BN3] / d t= 4*k3*BN2-4*k3*BN3
 
 Rate Rule (name: BN4) d [ BN4] / d t= 4*k3*BN3-4*k3*BN4
 
 Rate Rule (name: BTX) d [ BTX] / d t= 4*k3*BN4-k4*BTX
 
 Rate Rule (name: BM) d [ BM] / d t= k4*BTX
 
 Rate Rule (name: RCT1) d [ RCT1] / d t= k0*(epsilon+BM)*RCT0
 
 cell Spatial dimensions: 3.0  Compartment size: 1.0
 
 RCT0
Compartment: cell
Initial concentration: 88.1
 
 alpha
Compartment: cell
Initial concentration: 0.0
 
 BN1
Compartment: cell
Initial concentration: 11.9
 
 BN2
Compartment: cell
Initial concentration: 0.0
 
 BN3
Compartment: cell
Initial concentration: 0.0
 
 BN4
Compartment: cell
Initial concentration: 0.0
 
 BTX
Compartment: cell
Initial concentration: 0.0
 
 BM
Compartment: cell
Initial concentration: 0.0
 
 RCT1
Compartment: cell
Initial concentration: 0.0
 
  RC
Compartment: cell
Initial concentration: 88.1
 
  beta
Compartment: cell
Initial concentration: 11.9
 
Global Parameters (7)
 
   k0
Value: 0.59
Constant
 
 k1
Value: 0.672
Constant
 
 k2
Value: 0.678
Constant
 
   k3
Value: 0.0392
Constant
 
   k4
Value: 0.554
Constant
 
 q
Value: 2.0
Constant
 
   epsilon
Constant
 
Representative curation result(s)
Representative curation result(s) of BIOMD0000000533

Curator's comment: (updated: 31 Jul 2014 11:22:28 GMT)

Figure 3 of the reference publication has been reproduced here. The mathematical model proposed by the authors fits with experimental data from "Kirkitadze et al., (2001) - Identification and characterization of key kinetic intermediates in amyloid beta-protein fibrillogenesis".

The simulation was done using Copasi v4.12 (Build 81) 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)
  • Steckmann2012 - Amyloid beta-protein fibrillogenesis (kinetics of secondary structure conversion):
    Copasi file for simulation of Figure 4 of the model
  • Steckmann2012 - Amyloid beta-protein fibrillogenesis (kinetics of secondary structure conversion):
    SBML file of the model reproducing Figure 4. The mathematical model proposed by the authors fits with experimental data from "Walsh et al. (1990 - Amyloid beta-protein fibrillogenesis. Structure and biological activity of protofibrillar intermediates".

    The simulation was done using Copasi v4.12 (Build 81). The Copasi file of the model with simulation settings can be downloaded from the below link.
  • Steckmann2012 - Amyloid beta-protein fibrillogenesis (kinetics of secondary structure conversion):
    Copasi file of the model
spacer
spacer