ehrenstein2

The SBML for this model was obtained from the BioModels database (BioModels ID: BIOMD0000000553) Biomodels notes: Figure 1 has been reproduced here. Time course of the decline in acetylcholine is plotted ranging different values for k2 parameter. 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. JWS Online curation: This model was curated by reproducing the figures as described in the BioModels Notes. No additional changes were made.

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The choline-leakage hypothesis for the loss of acetylcholine in Alzheimer's disease.

  • G Ehrenstein
  • Z Galdzicki
  • GD Lange
Biophys. J. 1997; 73 (3): 1276-1280
Abstract
We present a hypothesis for the loss of acetylcholine in Alzheimer's disease that is based on two recent experimental results: that beta-amyloid causes leakage of choline across cell membranes and that decreased production of acetylcholine increases the production of beta-amyloid. According to the hypothesis, an increase in beta-amyloid concentration caused by proteolysis of the amyloid precursor protein results in an increase in the leakage of choline out of cells. This leads to a reduction in intracellular choline concentration and hence a reduction in acetylcholine production. The reduction in acetylcholine production, in turn, causes an increase in the concentration of beta-amyloid. The resultant positive feedback between decreased acetylcholine and increased beta-amyloid accelerates the loss of acetylcholine. We compare the predictions of the choline-leakage hypothesis with a number of experimental observations. We also approximate it with a pair of ordinary differential equations. The solutions of these equations indicate that the loss of acetylcholine is very sensitive to the initial rate of beta-amyloid production.

Unit definitions have no effect on the numerical analysis of the model. It remains the responsibility of the modeler to ensure the internal numerical consistency of the model. If units are provided, however, the consistency of the model units will be checked.

Name Definition
0.001 litre
86400.0 second
0.001 mole
Id Name Spatial dimensions Size
Brain Brain 3.0 1.0
Id Name Initial quantity Compartment Fixed
a a 50.0 Brain (Brain)
aRel aRel 1.0 Brain (Brain)
b b 0.0 Brain (Brain)

Initial assignments are expressions that are evaluated at time=0. It is not recommended to create initial assignments for all model entities. Restrict the use of initial assignments to cases where a value is expressed in terms of values or sizes of other model entities. Note that it is not permitted to have both an initial assignment and an assignment rule for a single model entity.

Definition
Id Name Objective coefficient Reaction Equation and Kinetic Law Flux bounds
Abeta_formation_from_APP Abeta formation from APP ∅ > b

Brain * Constant_flux__irreversible(k2)
Decrease_in_the_extracellular_concentration_of_beta_amyloid Decrease in the extracellular concentration of beta-amyloid b > ∅

Brain * Decrease_in_the_extracellular_concentration_of_beta_amyloid_0(k4, b)
Effect_of_extracellular_ACh Effect of extracellular ACh b > ∅

Brain * Effect_of_extracellular_ACh_0(k3, a)
Loss_of_intracellular_choline Loss of intracellular choline a > ∅

Brain * Loss_of_intracellular_choline_0(k1, a, b)

Global parameters

Id Value
k1 0.007
k2 0.33
k3 0.0042
k4 0.01

Local parameters

Id Value Reaction

Assignment rules

Definition
aRel = a / 50.0

Rate rules

Definition

Algebraic rules

Definition
Definition
Decrease_in_the_extracellular_concentration_of_beta_amyloid_0(k4, b) = k4 * b
Effect_of_extracellular_ACh_0(k3, a) = k3 * a
Loss_of_intracellular_choline_0(k1, a, b) = k1 * a * b
Constant_flux__irreversible(v) = v
Trigger Assignments