Ca(2+) oscillations based on Ca-induced Ca-release (Dupont et al 1991)

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We consider a simple, minimal model for signal-induced Ca2+ oscillations based on Ca(2+)-induced Ca2+ release. The model takes into account the existence of two pools of intracellular Ca2+, namely, one sensitive to inositol 1,4,5 trisphosphate (InsP3) whose synthesis is elicited by the stimulus, and one insensitive to InsP3. See paper for more and details.
1 . Dupont G, Berridge MJ, Goldbeter A (1991) Signal-induced Ca2+ oscillations: properties of a model based on Ca(2+)-induced Ca2+ release. Cell Calcium 12:73-85 [PubMed]
Model Information (Click on a link to find other models with that property)
Model Type: Molecular Network;
Brain Region(s)/Organism:
Cell Type(s):
Channel(s): I Calcium;
Gap Junctions:
Transmitter(s): Ions;
Simulation Environment: XPP;
Model Concept(s): Oscillations; Simplified Models; Signaling pathways; Calcium dynamics; Calcium waves;
Implementer(s): Wu, Sheng-Nan [snwu at]; Chang, Han-Dong; Wu, Jiun-Shian [coolneon at];
Search NeuronDB for information about:  I Calcium; Ions;
% Signal-induced Ca(2+) oscillations
% Dupont G, Berridge MJ, Goldbeter A. Signal-induced Ca(2+) oscillations: properties of a model based 
% on Ca(2+)-induced Ca(2+) release. Cell calcium 1991;12:73-85
% The result was shown on Figure 4A in the paper.

init z=0.1, y=1.4

par v0=1.0, v1=7.3, VM2=65, VM3=500, KR=2, KA=0.9, K2=1, kf=1, k=10, n=2, m=2, p=4
par tstim=4.0

v2 = VM2 * z^n / (K2^n + z^n)
v3 = VM3 * (y^m/(KR^m + y^m)) *(z^p/(KA^p + z^p))

z' = v0 + v1*beta -v2 + v3 + kf*y - k*z
y' =  v2 -v3 - kf*y

aux b=beta

% Numerical and plotting parameters for xpp
@ meth=Euler, dt=.005, total=20
@ yp=z, yhi=1.6, ylo=-0.0, xlo=0, xhi=20, bound=100

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