dupont1

The SBML for this model was obtained from the BioModels database (BioModels ID: BIOMD0000000117) Biomodels notes: Figure4B in the paper has been reproduced by RoadRunner and MathSBML. Damped Ca2+ oscillations elicited by a transient pulse of InsP3 applied intracellularly to a resting, non-oscillatory cell. 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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Signal-induced Ca2+ oscillations: properties of a model based on Ca(2+)-induced Ca2+ release.

  • G Dupont
  • MJ Berridge
  • Albert Goldbeter
Cell Calcium 1991; 12 : 73-85
Abstract
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. The discharge of the latter pool into the cytosol is activated by cytosolic Ca2+. Oscillations in cytosolic Ca2+ arise in this model either spontaneously or in an appropriate range of external stimulation; these oscillations do not require the concomitant, periodic variation of InsP3. The following properties of the model are reviewed and compared with experimental observations: (a) Control of the frequency of Ca2+ oscillations by the external stimulus or extracellular Ca2+; (b) correlation of latency with period of Ca2+ oscillations obtained at different levels of stimulation; (c) effect of a transient increase in InsP3; (d) phase shift and transient suppression of Ca2+ oscillations by Ca2+ pulses, and (e) propagation of Ca2+ waves. It is shown that on all these counts the model provides a simple, unified explanation for a number of experimental observations in a variety of cell types. The model based on Ca(2+)-induced Ca2+ release can be extended to incorporate variations in the level of InsP3 as well as desensitization of the InsP3 receptor; besides accounting for the phenomena described by the minimal model, the extended model might also account for the occurrence of complex Ca2+ oscillations.

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
1e-06 mole
Id Name Spatial dimensions Size
Cytosol 3.0 1.0
extracellular 3.0 1.0
intracellular_Ca_storepool 3.0 1.0
Id Name Initial quantity Compartment Fixed
y Ca in the InsP3-insensitive pool 1.4 intracellular_Ca_storepool
z Ca in the cytosol 0.1 Cytosol

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
reaction_0000001 InsP3 modulated release of Ca from the InsP3 sensitive store ∅ > z

v1 * beta * Cytosol
reaction_0000002 Constant input of Ca from the extracellular medium ∅ > z

v0 * Cytosol
reaction_0000003 Leak Ca from pool to cytosol y > z

kf * y * Cytosol
reaction_0000004 Pumping Ca into the InsP3-insensitive store z > y

intracellular_Ca_storepool * VM2 * pow(z, n) / (pow(K2, n) + pow(z, n))
reaction_0000005 Release of Ca from the pool into the cytosol y > z

Cytosol * VM3 * (pow(y, m) / (pow(KR, m) + pow(y, m))) * (pow(z, p) / (pow(KA, p) + pow(z, p)))
reaction_0000006 Transport of cytosolic ca into the extracellular medium z > ∅

k * z * extracellular

Global parameters

Id Value
K2 1.0
KA 0.9
KR 2.0
VM2 65.0
VM3 500.0
beta 0.0
flag 0.0
k 10.0
kf 1.0
m 2.0
n 2.0
p 4.0
tstim 4.0
v0 1.0
v1 7.3

Local parameters

Id Value Reaction

Assignment rules

Definition
beta = flag * 0.96 * exp(-0.2 * (time - tstim))

Rate rules

Definition

Algebraic rules

Definition
Trigger Assignments
gt(time, tstim) flag = 1