View source for Metabolic Control Analysis

;Analysis title
:[[File:Default-analysis-icon.png]] Metabolic Control Analysis
;Provider
:[[Institute of Systems Biology]]
;Class
:{{Class|biouml.plugins.modelreduction.MetabolicControlAnalysis}}
;Plugin
:[[Biouml.plugins.modelreduction (plugin)|biouml.plugins.modelreduction (Model reduction plug-in)]]

==== Description ====
The metabolic control analysis quantifies how variables, such as fluxes and species concentrations, depend on the systems parameters. If the systems consists of ''r'' reactions and ''m'' species, then the matrices of control coefficients includes ''m''-by-''r'' elasticity matrix ''E'', ''m''-by-''r'' concentration control matrix ''C <sup>S</sup>'' and ''r''-by-''r'' flux control matrix ''C <sup>J</sup>'' calculating by the formulas

:: [[File:DAE-models-Metabolic-Control-Analysis-mca.png]]

Here ''v'' is a vector of reaction rates, ''S'' is a vector of species concentrations, ''N = L × N<sub>R</sub>'' is the stiochiometric matrix decomposition generated by the mass conservation analysis, and ''Id'' is ''r''-by-''r'' identity matrix<sup>1</sup>. We also scaled all elements ''E<sub>i,j</sub>'', ''C<sup>S</sup><sub>i,j</sub>'' and ''C<sup>J</sup><sub>i,j</sub>'' of these matrices with the coefficients ''S<sub>j</sub>'' / ''v<sub>i</sub>'', ''v<sub>j</sub>'' / ''S<sub>i</sub>'' and ''v<sub>j</sub>'' / ''v<sub>i</sub>'' respectively.
==== References ====

# C Reder, "Metabolic control theory: a structural approach". J. Theor. Biol., 135:175-201, 1988.

[[Category:Analyses]]
[[Category:DAE models (analyses group)]]
[[Category:ISB analyses]]
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