BIOPHYSICAL THEORY AND MODELING |
The Geometry of the Flux Cone of a Metabolic Network
Clemens Wagner 1* and Robert Urbanczik 1
1 University of Bern
* To whom correspondence should be addressed. E-mail: clemens.wagner{at}pki.unibe.ch.
Submitted on October 27, 2004
Revised on January 3, 2005
Accepted on 7 September 2005
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Abstract |
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The analysis of metabolic networks has become a major topic in biotechnology in recent years. Applications range from the enhanced production of selected outputs to the prediction of genotype-phenotype relationships. The concepts used are based on the assumption of a pseudo steady state of the network, so that for each metabolite inputs and outputs are balanced. The stoichiometric network analysis expands the steady state into a combination of non-redundant sub-networks with positive coefficients called extremal currents. Based on the unidirectional representation of the system these sub-networks form a convex cone in the flux-space. A modification of this approach allowing for reversible reactions led to the definition of elementary modes. Extreme pathways are obtained with the same method but splitting up internal reactions into forward and backward rates. In this study we explore the relationship between these concepts. Due to the combinatorial explosion of the number of elementary modes in large networks, we promote a further set of metabolic routes, which we call the minimal generating set. It is the smallest subset of elementary modes required to describe all steady states of the system. For large-scale networks the size of this set is of several magnitudes smaller than that of elementary modes and of extreme pathways.
Key Words:
Convex Analysis, Elementary Modes, Extreme Pathways, Flux Balance Analysis, Optimization
