## Abstract |
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In metabolic pathway analysis, it should be considered that many enzymes operate with low specificity (e.g. nucleoside diphosphokinase, uridine kinase, transketolase, aldolase), so that various substrates and products can be converted. Here, we analyze the effect of enzymes with low substrate specificity on the elementary flux modes (pathways). We also study the benefits of two different approaches to describing multifunctional enzymes. The usual description is in terms of (overall) enzymatic reactions. At a more detailed level, the reaction steps (half-reactions, hemi-reactions) of the formation and conversion of enzyme-substrate complexes are considered. Multifunctional enzymes operate according to various mechanisms. This is illustrated here by the reaction schemes for the different enzyme mechanisms of bifunctional enzymes. For enzymes with two or more functions, it is important to consider only linearly independent functions, because otherwise cyclic elementary modes would occur which do not perform any net transformation. However, the choice of linearly independent functions is not a priori unique. We give a method for making this choice unique by considering the extreme pathways of the hemi-reactions system. A formal application of the algorithm for computing elementary flux modes (pathways) yields the result that the number of such modes sometimes depend on the level of description if some reactions are reversible and the products of the multifunctional enzymes are external metabolites or some multifunctional enzymes partly share the same metabolites. However, this problem can be solved by appropriate interpretation of the definition of elementary modes and the correct choice of independent functions of multifunctional enzymes. The analysis is illustrated by a biochemical example taken from nucleotide metabolism, comparing the two ways of description for nucleoside diphosphokinase and adenylate kinase, and by several smaller examples.