Difference between revisions of "Metabolic Control Analysis"
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| − | :[[File: | + | :[[File:Differential-algebraic-equations-Metabolic-Control-Analysis-icon.png]] Metabolic Control Analysis |
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:[[Institute of Systems Biology]] | :[[Institute of Systems Biology]] | ||
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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: | + | :: [[File:Differential-algebraic-equations-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. | ||
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[[Category:Analyses]] | [[Category:Analyses]] | ||
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[[Category:ISB analyses]] | [[Category:ISB analyses]] | ||
[[Category:Autogenerated pages]] | [[Category:Autogenerated pages]] | ||
Latest revision as of 18:14, 9 December 2020
- Analysis title
Metabolic Control Analysis
- Provider
- Institute of Systems Biology
- Class
MetabolicControlAnalysis- Plugin
- biouml.plugins.modelreduction (Model reduction plug-in)
[edit] 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.
[edit] References
- C Reder, "Metabolic control theory: a structural approach". J. Theor. Biol., 135:175-201, 1988.
