Reaction routes in biochemical reaction systems: algebraic properties,validated calculation procedure and example from nucleotide metabolism |
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Authors: | Schuster S Hilgetag C Woods J H Fell D A |
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Institution: | (1) Department of Bioinformatics, Max Delbrück Centre for Molecular Medicine, D-13092 Berlin-Buch, Germany. e-mail: stschust@mdc-berlin.de, DE;(2) International University Bremen, Campus Ring 1, Rm. 212, D-28759 Bremen, Germany., DE;(3) School of Biological and Molecular Sciences, Oxford Brookes University, Headington, Oxford OX3 0BP, UK, GB |
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Abstract: | Elementary flux modes (direct reaction routes) are minimal sets of enzymes that can operate at steady state, with all irreversible
reactions used in the appropriate direction. They can be interpreted as component pathways of a (bio)chemical reaction network.
Here, two different definitions of elementary modes are given and their equivalence is proved. Several algebraic properties
of elementary modes are then presented and proved. This concerns, amongst other features, the minimal number of enzymes of
the network not used in an elementary mode and the situations where irreversible reactions are replaced by reversible ones.
Based on these properties, a refined algorithm is presented, and it is formally proved that this algorithm will exclusively
generate all the elementary flux modes of an arbitrary network containing reversible or irreversible reactions or both. The
algorithm is illustrated by a biochemical example relevant in nucleotide metabolism. The computer implementation in two different
programming languages is discussed.
Received: 1 January 2001 / Revised version: 17 December 2001 / Published online: 17 July 2002 |
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