All cellular functions are ultimately linked to the metabolism which constitutes a highly branched network of thousands of enzyme-catalyzed chemical reactions and carrier-mediated transport processes. Depending on the prevailing functions (e.g. detoxification of a toxin or accumulation of biomass) the distribution of fluxes in the metabolic network may vary considerably. To better reveal and quantify this flux-function relationship we propose a novel computational approach which identifies distinct contributions--so called minimal flux modes (short: MinModes)--to a stationary flux distribution in the network. Each of these contributions is characterized by a single metabolic output. A MinMode is a minimal (according to a defined cost function) steady state flux distribution that enables the production of a single metabolite. We apply this concept to a metabolic network of Methylobacterium extorquens AM1 comprising of 95 reactions and 74 metabolites, 17 of these metabolites entering the biomass of the bacterium and are thus considered as the metabolic output of the network. MinModes represent a manageable set of fundamental flux modes in the network having a clear physiological meaning and--although not representing a basis in strict mathematical sense - provide a satisfactory approximation of the overall flux distribution in cases tested so far.