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Notes on Elementary Flux Modes: | Notes on Elementary Flux Modes: | ||
Given a metabolic reaction network with stoichiometric matrix S, the steady state condition (no change in metabolite concentrations) is given by the equation | |||
<math>Sv = 0</math> | |||
The (right) nullspace of S contains all possible vectors v which fulfill this equation. The dimensions of the nullspace equals the rank of S, denoted r. If all reactions are linearly independent and the number of reactions <math>n</math> is greater than the number of metabolites <math>m</math>, then r = n - m. All possible flux vectors in the nullspace of S can then be constructed by a linear combination of <math>r</math> vectors spanning the nullspace. However, vectors spanning the nullspace may not be biologically meaningful and contain non-integer values, making it hard to interpret the nullspace. Elementary flux modes provide a basis for the nullspace which is easier to interpret. | |||
Elementary flux modes decompose a metabolic network into components such that | Elementary flux modes decompose a metabolic network into components such that |
Revision as of 10:18, 15 February 2014
Notes on Elementary Flux Modes:
Given a metabolic reaction network with stoichiometric matrix S, the steady state condition (no change in metabolite concentrations) is given by the equation
[math]\displaystyle{ Sv = 0 }[/math]
The (right) nullspace of S contains all possible vectors v which fulfill this equation. The dimensions of the nullspace equals the rank of S, denoted r. If all reactions are linearly independent and the number of reactions [math]\displaystyle{ n }[/math] is greater than the number of metabolites [math]\displaystyle{ m }[/math], then r = n - m. All possible flux vectors in the nullspace of S can then be constructed by a linear combination of [math]\displaystyle{ r }[/math] vectors spanning the nullspace. However, vectors spanning the nullspace may not be biologically meaningful and contain non-integer values, making it hard to interpret the nullspace. Elementary flux modes provide a basis for the nullspace which is easier to interpret.
Elementary flux modes decompose a metabolic network into components such that
- Each component can operate in a steady state independently from the rest of metabolism
- Any steady state can be described as a combination of such components
Any steady state flux vector can be described as a non-negative combination of the elementary flux modes, but the mapping need not be unique (several combinations might describe one flux vector).
Links
http://www.cs.helsinki.fi/bioinformatiikka/mbi/courses/08-09/memo/slides/Lecture310309.pdf
Bibliography
Detection of elementary flux modes in biochemical networks: a promising tool for pathway analysis and metabolic engineering.: http://www.ncbi.nlm.nih.gov/pubmed/10087604
Elementary flux modes in a nutshell: properties, calculation and applications.: http://www.ncbi.nlm.nih.gov/pubmed/23788432
Analysis of Metabolic Subnetworks by Flux Cone Projection: http://www.almob.org/content/7/1/17