cloutier1

The SBML for this model was obtained from the BioModels database (BioModels ID: BIOMD0000000558) Biomodels notes: Figure 1C of the reference publication has been reproduced here. Concentration dynamics of misfolded ?-synuclein (?SN) and Reactive Oxygen Spices (ROS) are plotted over 200 days. Stress of 2.6 obtained by optimization (parameter S1) was imposed between days 10 and 150 in order to reproduce the Figure. Reactions, parameters, rate equations and differential equations are found in Figure 1 and Table 1. 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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Feedback motif for the pathogenesis of Parkinson's disease.

  • M Cloutier
  • R Middleton
  • P Wellstead
IET Syst Biol 2012; 6 (3): 86
Abstract
Previous article on the integrative modelling of Parkinson's disease (PD) described a mathematical model with properties suggesting that PD pathogenesis is associated with a feedback-induced biochemical bistability. In this article, the authors show that the dynamics of the mathematical model can be extracted and distilled into an equivalent two-state feedback motif whose stability properties are controlled by multi-factorial combinations of risk factors and genetic mutations associated with PD. Based on this finding, the authors propose a principle for PD pathogenesis in the form of the switch-like transition of a bistable feedback process from 'healthy' homeostatic levels of reactive oxygen species and the protein α-synuclein, to an alternative 'disease' state in which concentrations of both molecules are stable at the damagingly high-levels associated with PD. The bistability is analysed using the rate curves and steady-state response characteristics of the feedback motif. In particular, the authors show how a bifurcation in the feedback motif marks the pathogenic moment at which the 'healthy' state is lost and the 'disease' state is initiated. Further analysis shows how known risks (such as: age, toxins and genetic predisposition) modify the stability characteristics of the feedback motif in a way that is compatible with known features of PD, and which explain properties such as: multi-factorial causality, variability in susceptibility and severity, multi-timescale progression and the special cases of familial Parkinson's and Parkinsonian symptoms induced purely by toxic stress.

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
1e-06 mole
Id Name Spatial dimensions Size
Neuron Neuron 3.0 1.0
Id Name Initial quantity Compartment Fixed
ROS ROS 1.0 Neuron (Neuron)
alpha_syn alpha-syn 1.0 Neuron (Neuron)

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
ROS_1 ROS 1 ∅ > ROS

Neuron * V1(k1, S1, dalphasyn, alpha_syn, kalphasyn)
ROS_2 ROS 2 ROS > ∅

Neuron * V2_4(k2, ROS, S2_4)
aSyn_1 aSyn 1 ∅ > alpha_syn

Neuron * V3(k3, ROS, S2_4)
aSyn_2 aSyn 2 alpha_syn > ∅

Neuron * V2_4(k4, alpha_syn, S2_4)

Global parameters

Id Value
S1 0.0
S2_4 1.0
dalphasyn 15.0
k1 17280.0
k2 17280.0
k3 0.168
k4 0.168
kalphasyn 8.5

Local parameters

Id Value Reaction

Assignment rules

Definition
S1 = piecewise(2.6, and(gt(time, 10.0), lt(time, 150.0)), 0.0)

Rate rules

Definition

Algebraic rules

Definition
Definition
V1(k1, Sx, d, S, k2) = k1 * (1 + Sx + d * (pow(S / k2, 4) / (1 + pow(S / k2, 4))))
V3(k, S, Sx) = k * S * Sx
V2_4(k, S, Sx) = k * S * Sx
Trigger Assignments