Difference between revisions of "Metabolic Control Analysis"

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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
 
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:Metabolic-Control-Analysis-mca.png]]
+
:: [[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.
 
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.

Revision as of 12:36, 16 May 2013

Analysis title
File:Metabolic-Control-Analysis-icon.png Metabolic Control Analysis
Provider
Institute of Systems Biology
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 S and r-by-r flux control matrix C J calculating by the formulas

DAE-models-Metabolic-Control-Analysis-mca.png

Here v is a vector of reaction rates, S is a vector of species concentrations, N = L × NR is the stiochiometric matrix decomposition generated by the mass conservation analysis, and Id is r-by-r identity matrix1. We also scaled all elements Ei,j, CSi,j and CJi,j of these matrices with the coefficients Sj / vi, vj / Si and vj / vi respectively.

References

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