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