smallbone22

The SBML for this model was obtained from the BioModels database (BioModels ID: BIOMD0000000456) Biomodels notes: As there are no plots to reproduce as curation figure, Table 2 that provides the steady-state concentrations of variables and fluxes, are reproduced here - using Copasi v4.8 (Build 35). 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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Metabolic Control Analysis: Rereading Reder

  • Kieran Smallbone
Quantitative Methods 2013; :
Abstract
Metabolic control analysis is a biochemical formalism defined by Kacser and Burns in 1973, and given firm mathematical basis by Reder in 1988. The algorithm defined by Reder for calculating the control matrices is still used by software programs today, but is only valid for some biochemical models. We show that, with slight modification, the algorithm may be applied to all models.

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
1.0 dimensionless
1.0 dimensionless
1.0 dimensionless
1.0 dimensionless
Id Name Spatial dimensions Size
cell cell 3.0 1.0
Id Name Initial quantity Compartment Fixed
x1 x1 0.05625738310526 cell (cell)
x2 x2 0.76876151899652 cell (cell)
x3 x3 4.23123848100348 cell (cell)
x4 x4 1.0 cell (cell)
y1 y1 10.0 cell (cell)
y2 y2 0.0 cell (cell)
y3 y3 0.0 cell (cell)
y4 y4 1.0 cell (cell)
y5 y5 1.0 cell (cell)
y7 y7 1.0 cell (cell)
y8 y8 0.0 cell (cell)

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
v1 v1 y1 + x2 = x1 + x3

e1 * (p1 * y1 * x2 - x1 * x3) / (1 + y1 + x2 + x1 + x3 + y1 * x2 + x1 * x3)
v2 v2 y4 + x3 = y5 + x2

e2 * (p2 * y4 * x3 - y5 * x2) / (1 + x3 + x2 + y4 + y5 + x3 * y4 + x2 * y5)
v3 v3 x1 = y2

e3 * (p3 * x1 - y2) / (1 + x1 + y2)
v4 v4 x1 = y3

e4 * (p4 * x1 - y3) / (1 + x1 + y3)
v6 v6 y7 = x4

e6 * p6 * y7
v7 v7 x4 = y8

e7 * p7

Global parameters

Id Value

Local parameters

Id Value Reaction
e1 1.0 dimensionless v1 (v1)
p1 10.0 dimensionless v1 (v1)
e2 1.0 dimensionless v2 (v2)
p2 10.0 dimensionless v2 (v2)
e3 1.0 dimensionless v3 (v3)
p3 50.0 dimensionless v3 (v3)
e4 1.0 dimensionless v4 (v4)
p4 10.0 dimensionless v4 (v4)
e6 1.0 dimensionless v6 (v6)
p6 1.0 dimensionless v6 (v6)
e7 1.0 dimensionless v7 (v7)
p7 1.0 dimensionless v7 (v7)

Assignment rules

Definition

Rate rules

Definition

Algebraic rules

Definition
Trigger Assignments