Metabolism of living cells converts substrates into metabolic energy, redox potential and metabolic end products that are essential to maintain cellular function. The flux distribution among the various biochemical pathways is determined by the kinetic properties of enzymes which are subject to strict regulatory control. Simulation of metabolic behavior therefore requires the complete knowledge of biochemical pathways, enzyme kinetics as well as their regulation. Unfortunately, complete kinetic and regulatory information is not available for microbial cells, thus preventing accurate dynamic simulation of their metabolic behavior. However, it is possible to define wider limits on metabolic behavior based solely on flux balances of biochemical pathways. We present here comprehensive information about the catabolic pathways of the bacterium Escherichia coli. Using this biochemical database, we formulate a stoichiometric model of the bacterial network of fueling reactions. After logical structural reduction, the network consists of 53 metabolic fluxes and 30 metabolites. The solution space of this under-determined system of equations presents the bounds of metabolic flux distribution that the bacterial cell can achieve. We use specific objective functions and linear optimization to investigate the capability of E. coli catabolism to maximally produce the 12 biosynthetic precursors and three key cofactors within this solution space. For the three cofactors, the maximum yields are calculated to be 18.67 ATP, (11.6 \mathrm{NADH}) and 11 NADPH per glucose molecule, respectively. The yields of NADH and NADPH are less than 12 owing to the energy costs of importing glucose. These constraints are made explicit by the interpretation of shadow prices. The optimal yields of the 12 biosynthetic precursors are computed. Four of the 12 precursors (3-phosphoglycerate, phosphoenolpyruvate, pyruvate and oxaloacetate) can be made by E. coli with complete carbon conversion. Conversely, none of the sugar monophosphates can be made with (100 %) carbon conversion and analysis of the shadow prices reveals that this conversion is constrained by the energy cost of importing glucose. Three of the 12 precursors (acetyl-coA, (\alpha)-ketoglutarate, and succinyl-coA) cannot be made with full carbon conversion owing to stoichiometric constraints; there is no route to these compounds without carrying out a decarboxylation reaction. Metabolite flux balances and linear optimization have thus been used to determine the catabolic capabilities of (E). coli.