Network analysis of intermediary metabolism using linear optimization. I. Development of mathematical formalism.

Analysis of metabolic networks using linear optimization theory allows one to quantify and understand the limitations imposed on the cell by its metabolic stoichiometry, and to understand how the flux through each pathway influences the overall behavior of metabolism. A stoichiometric matrix accounting for the major pathways involved in energy and mass transformations in the cell was used in our analysis. The auxiliary parameters of linear optimization, the so-called shadow prices, identify the intermediates and cofactors that cause the growth to be limited on each nutrient. This formalism was used to examine how well the cell balances its needs for carbon, nitrogen, and energy during growth on different substrates. The relative values of glucose and glutamine as nutrients were compared by varying the ratio of rates of glucose to glutamine uptakes, and calculating the maximum growth rate. The optimum value of this ratio is between 2-7, similar to experimentally observed ratios. The theoretical maximum growth rate was calculated for growth on each amino acid, and the amino acids catabolized directly to glutamate were found to be the optimal nutrients. The importance of each reaction in the network can be examined both by selectively limiting the flux through the reaction, and by the value of the reduced cost for that reaction. Some reactions, such as malic enzyme and glutamate dehydrogenase, may be inhibited or deleted with little or no adverse effect on the calculated cell growth rate.