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kummer1

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Model

kummer1

The SBML for this model was obtained from the BioModels database (BioModels ID: BIOMD0000000329) Biomodels notes: This model correspond to the core model (3 variable model defined by equations 6 to 8) of the reference publication. Figure 7 of the paper has been reproduced here. The simulation was done using Copasi v4.14 (Build 89) and the plot was generated using Gnuplot. 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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Manuscript information

Switching from simple to complex oscillations in calcium signaling.

  • Ursula Kummer
  • Lars F Olsen
  • CJ Dixon
  • AK Green
  • E Bornberg-Bauer
  • G Baier
Biophys. J. 2000; 79 (3): 1188-1195
Abstract
We present a new model for calcium oscillations based on experiments in hepatocytes. The model considers feedback inhibition on the initial agonist receptor complex by calcium and activated phospholipase C, as well as receptor type-dependent self-enhanced behavior of the activated G(alpha) subunit. It is able to show simple periodic oscillations and periodic bursting, and it is the first model to display chaotic bursting in response to agonist stimulations. Moreover, our model offers a possible explanation for the differences in dynamic behavior observed in response to different agonists in hepatocytes.

Unit definitions 1

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-09 mole

Compartments 1

Id Name Spatial dimensions Size
compartment compartment 3.0 0.0000000000001

Species 3

Id Name Initial quantity Compartment Fixed
a G-alpha 0.01 compartment (compartment) ✘
b activePLC 0.01 compartment (compartment) ✘
c Calcium 0.01 compartment (compartment) ✘

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 8
Id Name Objective coefficient Reaction Equation and Kinetic Law Flux bounds
R1 R1 ∅ > a

compartment * Constant_flux__irreversible(v)
R2 R2 ∅ > a

compartment * linear_activation(constant, a)
R3 R3 a > ∅

compartment * Irr_Michaelis_Menten__enzyme__userdefined(V, b, a, Km)
R4 R4 a > ∅

compartment * Irr_Michaelis_Menten__enzyme__userdefined(V, c, a, Km)
R5 R5 ∅ > b

compartment * linear_activation(constant, a)
R6 R6 b > ∅

compartment * Henri_Michaelis_Menten__irreversible(b, Km, V)
R7 R7 ∅ > c

compartment * linear_activation(constant, a)
R8 R8 c > ∅

compartment * Henri_Michaelis_Menten__irreversible(c, Km, V)

Parameters 12   0

Global parameters

Id Value

Local parameters

Id Value Reaction
v 0.212 R1 (R1)
constant 2.9 R2 (R2)
V 1.52 R3 (R3)
Km 0.19 R3 (R3)
V 4.88 R4 (R4)
Km 1.18 R4 (R4)
constant 1.24 R5 (R5)
Km 29.09 R6 (R6)
V 32.24 R6 (R6)
constant 13.58 R7 (R7)
Km 0.16 R8 (R8)
V 153.0 R8 (R8)

Rules 0   0   0

Assignment rules

Definition

Rate rules

Definition

Algebraic rules

Definition

Function definitions 4

Definition
Constant_flux__irreversible(v) = v
Henri_Michaelis_Menten__irreversible(substrate, Km, V) = V * substrate / (Km + substrate)
linear_activation(constant, Activator) = constant * Activator
Irr_Michaelis_Menten__enzyme__userdefined(V, E, S, Km) = V * E * S / (Km + S)

Events 0

Trigger Assignments