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BIOMD0000000551 - Das2010 - Effect of a gamma-secretase inhibitor on Amyloid-beta dynamics

 

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Reference Publication
Publication ID: 20411345
Das R, Nachbar RB, Edelstein-Keshet L, Saltzman JS, Wiener MC, Bagchi A, Bailey J, Coombs D, Simon AJ, Hargreaves RJ, Cook JJ.
Modeling effect of a γ-secretase inhibitor on amyloid-β dynamics reveals significant role of an amyloid clearance mechanism.
Bull. Math. Biol. 2011 Jan; 73(1): 230-247
Department of Mathematics, University of British Columbia, 1984 Mathematics Road, Vancouver, BC V6T 1Z2, Canada. dodo@math.ubc.ca  [more]
Model
Original Model: BIOMD0000000551.origin
Submitter: Audald Lloret i Villas
Submission ID: MODEL1409230000
Submission Date: 23 Sep 2014 13:18:51 UTC
Last Modification Date: 08 Apr 2016 18:42:21 UTC
Creation Date: 23 Sep 2014 12:29:00 UTC
Encoders:  Audald Lloret i Villas
set #1
bqbiol:hasTaxon Taxonomy Macaca mulatta
set #2
bqbiol:hasProperty Human Disease Ontology Alzheimer's disease
set #3
bqbiol:isVersionOf Gene Ontology beta-amyloid clearance
Notes
Das2010 - Effect of a gamma-secretase inhibitor on Amyloid-beta dynamics

This model is described in the article:

Das R, Nachbar RB, Edelstein-Keshet L, Saltzman JS, Wiener MC, Bagchi A, Bailey J, Coombs D, Simon AJ, Hargreaves RJ, Cook JJ.
Bull. Math. Biol. 2011 Jan; 73(1): 230-247

Abstract:

Aggregation of the small peptide amyloid beta (A?) into oligomers and fibrils in the brain is believed to be a precursor to Alzheimer's disease. A? is produced via multiple proteolytic cleavages of amyloid precursor protein (APP), mediated by the enzymes ?- and ?-secretase. In this study, we examine the temporal dynamics of soluble (unaggregated) A? in the plasma and cerebral-spinal fluid (CSF) of rhesus monkeys treated with different oral doses of a ?-secretase inhibitor. A dose-dependent reduction of A? concentration was observed within hours of drug ingestion, for all doses tested. A? concentration in the CSF returned to its predrug level over the monitoring period. In contrast, A? concentration in the plasma exhibited an unexpected overshoot to as high as 200% of the predrug concentration, and this overshoot persisted as late as 72 hours post-drug ingestion. To account for these observations, we proposed and analyzed a minimal physiological model for A? dynamics that could fit the data. Our analysis suggests that the overshoot arises from the attenuation of an A? clearance mechanism, possibly due to the inhibitor. Our model predicts that the efficacy of A? clearance recovers to its basal (pretreatment) value with a characteristic time of >48 hours, matching the time-scale of the overshoot. These results point to the need for a more detailed investigation of soluble A? clearance mechanisms and their interaction with A?-reducing drugs.

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: 20411345 Submission Date: 23 Sep 2014 13:18:51 UTC Last Modification Date: 08 Apr 2016 18:42:21 UTC Creation Date: 23 Sep 2014 12:29:00 UTC
Mathematical expressions
Rules
Assignment Rule (variable: g(t)) Assignment Rule (variable: f(t)) Rate Rule (variable: C) Rate Rule (variable: P)
Rate Rule (variable: l)      
Physical entities
Compartments Species
CSF C    
Plasma P    
Global parameters
l Sc g(t) Ki
k1 J r deltap
epsilon alpha f(t) aplasma
bplasma tauplasma aCSF bCSF
tauCSF      
Reactions (0)
Rules (5)
 
 Assignment Rule (name: g_t) g(t) = piecewise(time/tauCSF*aCSF*exp((-bCSF)*tauCSF), (time < tauCSF), aCSF*exp((-bCSF)*time))
 
 Assignment Rule (name: f_t) f(t) = piecewise(time/tauplasma*aplasma*exp((-bplasma)*tauplasma), (time < tauplasma), aplasma*exp((-bplasma)*time))
 
 Rate Rule (name: C) d [ C] / d t= Sc/(1+g_t/Ki)-k1*C+J
 
 Rate Rule (name: P) d [ P] / d t= k1*r*C-J*r-deltap*P*l
 
 Rate Rule (name: l) d [ l] / d t= epsilon*(1/(1+alpha*f_t)-l)
 
 CSF Spatial dimensions: 3.0  Compartment size: 1.0
 
 C
Compartment: CSF
Initial concentration: 1.0
 
 Plasma Spatial dimensions: 3.0  Compartment size: 1.0
 
 P
Compartment: Plasma
Initial concentration: 1.0
 
Global Parameters (17)
 
 l
Value: 1.0
 
 Sc
Value: 1.16
Constant
 
  g(t)  
 
 Ki
Value: 0.0232
Constant
 
 k1
Value: 1.13
Constant
 
 J
Constant
 
 r
Value: 0.43
Constant
 
 deltap
Value: 0.55
Constant
 
 epsilon
Value: 0.0206
Constant
 
 alpha
Value: 0.522
Constant
 
  f(t)  
 
 aplasma
Value: 187.0
Constant
 
 bplasma
Value: 0.089
Constant
 
 tauplasma
Value: 1.66
Constant
 
 aCSF
Value: 4.92
Constant
 
 bCSF
Value: 0.259
Constant
 
 tauCSF
Value: 2.06
Constant
 
Representative curation result(s)
Representative curation result(s) of BIOMD0000000551

Curator's comment: (updated: 30 Sep 2014 15:55:58 GMT)

Notes:

Figure 4 of the reference publication has been reproduced here In this model some parameters are missing. Optimization is done in order to fit the figure. See values:

- Deltap = 0.55
- K1 = 1.13
- r = 0.43

Dynamics of A? in CSF and plasma with a dose of 120 mpk of gamma-secretase inhibitor are plotted during 72 hours.

The simulation was done using Copasi v4.12 (Build 81) and the plos were generated using Gnuplot. The Copasi file of the model wih simulation setings can be downloaded from the below link:

Additional file(s)
  • Das2010 - Effect of a gamma-secretase inhibitor on Amyloid-beta dynamics:
    Copasi file of the model
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