JWS Online

Model

Name

lavrentovich1

Notes

The SBML for this model was obtained from the BioModels database (BioModels ID: BIOMD0000000184) Biomodels notes: The plot corresponds to Fig 3 of the paper. Result obtained using MathSBML. JWS Online curation: This model was curated by reproducing the figures as described in the BioModels Notes. No additional changes were made.

Substance units

None

Time units

None

Volume units

None

Area units

None

Length units

None

Reaction extent units

None

Manuscript information

A mathematical model of spontaneous calcium(II) oscillations in astrocytes.

Maxim Lavrentovich
Sheryl Hemkin

J. Theor. Biol. 2008; 251 (4): 553-560

PubMed: 18275973
DOI: 10.1016/j.jtbi.2007.12.011
ISSN: 1095-8541
URL: https://ncbi.nlm.nih.gov/pubmed/18275973

Abstract

Astrocytes exhibit oscillations and waves of Ca2+ ions within their cytosol and it appears that this behavior helps facilitate the astrocyte's interaction with its environment, including its neighboring neurons. Often changes in the oscillatory behavior are initiated by an external stimulus such as glutamate, recently however, it has been observed that oscillations are also initiated spontaneously. We propose here a mathematical model of how spontaneous Ca2+ oscillations arise in astrocytes. This model uses the calcium-induced calcium release and inositol cross-coupling mechanisms coupled with a receptor-independent method for producing inositol (1,4,5)-trisphosphate as the heart of the model. By computationally mimicking experimental constraints we have found that this model provides results that are qualitatively similar to experiment.

Simulations using this model 1

Simulation
lavrentovich2008_Fig3	SED-ML COMBINE Archive

Unit definitions 5

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
—	1e-06 mole litre^(-1.0)
—	1e-06 mole litre^(-1.0) second^(-1.0)
—	1.0 second^(-1.0)
—	1.0 dimensionless

Compartments 2

Id	Name	Spatial dimensions	Size
ER	Endoplasmic Reticulum	3.0	1.0
compartment	Cytoplasm	3.0	1.0

Species 3

Id	Name	Initial quantity	Compartment	Fixed
X	Cytoplasmic Calcium	0.1	compartment (Cytoplasm)	✘
Y	Calcium in ER	1.5	ER (Endoplasmic Reticulum)	✘
Z	IP3	0.1	compartment (Cytoplasm)	✘

Initial assignments 0

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

Reactions 7

Id	Name	Reaction Equation and Kinetic Law
R1	vin	∅ > X compartment * vin
R2	Calcium export from cell	X > ∅ compartment * kout * X
R3	CICR	Y > X ER * 4 * vM3 * pow(k_CaA, n) * (pow(X, n) / ((pow(X, n) + pow(k_CaA, n)) * (pow(X, n) + pow(k_CaI, n)))) * (pow(Z, m) / (pow(Z, m) + pow(kip3, m))) * (Y - X)
R4	serca	X > Y compartment * vM2 * pow(X, 2) / (pow(X, 2) + pow(k2, 2))
R5	Leak flux	Y > X ER * kf * (Y - X)
R6	PLC	∅ > Z compartment * vp * pow(X, 2) / (pow(X, 2) + pow(kp, 2))
R7	IP3 degradation	Z > ∅ compartment * kdeg * Z

Parameters 0 14

Global parameters

Id	Value
k2	0.1 uM
k_CaA	0.15 uM
k_CaI	0.15 uM
kdeg	0.08 sec_1
kf	0.5 sec_1
kip3	0.1 uM
kout	0.5 sec_1
kp	0.3 uM
m	2.2 dimensionless
n	2.02 dimensionless
vM2	15.0 uM_sec_1
vM3	40.0 sec_1
vin	0.05 uM_sec_1
vp	0.05 uM_sec_1

Local parameters

Id	Value	Reaction

Rules 0 0 0

Assignment rules

Definition

Rate rules

Definition

Algebraic rules

Definition

Function definitions 0

Definition

Events 0

Trigger	Assignments