The topological analysis of metabolic networks has attracted increasing interest in recent years. Dynamic mathematical modelling of large-scale metabolic and regulatory networks meets difficulties as the necessary mechanistic detail is rarely available. In contrast, structure-oriented methods such as metabolic pathway analysis only require network topology. In my talk, several concepts central to this analysis are explained: basis vectors of the null-space, enzyme subsets, and elementary flux modes [1,2]. In mathematical terms, elementary modes can be considered as uniquely determined, simple basis vectors of the null-space to the stoichiometry matrix, which comply with the non-negativity restriction for irreversible reactions. These vectors span a convex polyhedral cone.
It is shown that the concept of elementary modes is well-suited for determining routes enabling maximum yields of bioconversions and properly describes knockouts. Thus, it is well-suited for analysing redundancy and robustness properties of living cells . Another application is the assessment of the impact of enzyme deficiencies in medicine. The advantages of elementary modes in comparison to basis vectors of the null-space are outlined. An algorithm for computing elementary modes is presented. The analysis is illustrated by several biochemical examples, such as lysine synthesis in Escherichia coli.
Metabolic pathway analysis for large, complex metabolic networks often meets the problem of combinatorial explosion. One method for coping with this problem is to set all intermediates that participate in more than a threshold number of reactions to external status . Thus, networks can be decomposed into tractable subnetworks.
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