# User:Jarle Pahr/EFM

### From OpenWetWare

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

*S**v* = 0

The (right) nullspace of S contains all possible vectors v which fulfill this equation. The rank-nullity theorem states that the dimensions of the nullspace equals the number of columns in S minus the rank of S, which is denoted r. If all reactions are linearly independent and the number of reactions *n* is greater than the number of metabolites *m*, then r = m. All possible flux vectors in the nullspace of S can then be constructed by a linear combination of *n* − *m* 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).

## Contents |

# Extreme pathways

# Links

http://www.cs.helsinki.fi/bioinformatiikka/mbi/courses/08-09/memo/slides/Lecture310309.pdf

# Software

EFMEvolver

# Bibliography

EFMEvolver: Computing elementary flux modes in genome-scale metabolic networks: http://subs.emis.de/LNI/Proceedings/Proceedings157/179.pdf

Computing the shortest elementary flux modes in genome-scale metabolic networks: http://bioinformatics.oxfordjournals.org/content/25/23/3158.short

Decomposing flux distributions into elementary flux modes in genome-scale metabolic networks: http://bioinformatics.oxfordjournals.org/content/27/16/2256.full

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