The survival and proliferation of cells and organisms require a highly coordinated allocation of cellular resources to ensure the efficient synthesis of cellular components. In particular, the total enzymatic capacity for cellular metabolism is limited by finite resources that are shared between all enzymes, such as cytosolic space, energy expenditure for amino-acid synthesis, or micro-nutrients. While extensive work has been done to study constrained optimization problems based only on stoichiometric information, mathematical results that characterize the optimal flux in kinetic metabolic networks are still scarce. Here, we study constrained enzyme allocation problems with general kinetics, using the theory of oriented matroids. We give a rigorous proof for the fact that optimal solutions of the non-linear optimization problem are elementary flux modes. This finding has significant consequences for our understanding of optimality in metabolic networks as well as for the identification of metabolic switches and the computation of optimal flux distributions in kinetic metabolic networks.

Institute for Theoretical Biology Humboldt University Berlin Invalidenstraße 43 10115 Berlin Germany

Johann Radon Institute for Computational and Applied Mathematics Austrian Academy of Sciences Altenbergerstraße 69 4040 Linz Austria

Johann Radon Institute for Computational and Applied Mathematics Austrian Academy of Sciences Altenbergerstraße 69 4040 Linz Austria; CzechGlobe Global Change Research Center Academy of Sciences of the Czech Republic Belidla 986 4a 603 00 Brno Czech Republic

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