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

TL;DR: 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.

Abstract: 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.

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### Cites background from "Network analysis of intermediary me..."

...A metabolic steady state is assumed, in which the metabolic pathway flux leading to the formation of a metabolite and that leading to the degradation of a metabolite must balance, which generates the flux balance equation (3, 13):...

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### Cites methods from "Network analysis of intermediary me..."

...A few groups, notably that of Heinrich, have indeed applied analytical optimization methods (e.g. Heinrich et al., 1987, 1997; Schuster and Heinrich, 1987, 1991; Savinell and Palsson, 1992; Klipp and Heinrich, 1994) to several pathway schemes to investigate the conditions for maximal flux, minimal concentrations, and a series of other criteria....

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...…notably that of Heinrich, have indeed applied analytical optimization methods (e.g. Heinrich et al., 1987, 1997; Schuster and Heinrich, 1987, 1991; Savinell and Palsson, 1992; Klipp and Heinrich, 1994) to several pathway schemes to investigate the conditions for maximal flux, minimal…...

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### Cites background or methods from "Network analysis of intermediary me..."

...DOI 10.1016/j.mib.2010.03.003 Introduction Flux balance analysis (FBA) [1] is a widely used approach for studying biochemical networks, in particular the genome-scale metabolic network reconstructions that have been built in the past decade [2,3]....

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...With metabolic models becoming available for a growing number of organisms [5] and high-throughput technologies enabling the construction of many more each year [6], FBA is an important tool for harnessing the knowledge encoded in these models....

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...Available online at www.sciencedirect.com The biomass objective function Adam M Feist1 and Bernhard O Palsson2 Flux balance analysis (FBA) is a mathematical approach for analyzing the flow of metabolites through a metabolic network....

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...of ATP production, (3) minimizing total nutrient uptake, and (4) minimize redox metabolism through minimizing NADH production Linear programming Hybridoma cell line central metabolism (83 reactions, 42 metabolites) [11] (1) Aerobic batch bioreactor with growth, uptake, secretion, and protein production rates [20] Optimization of biomass production can be used to examine growth characteristics and explain observed phenomena [13] 1997 Max....

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...This issue was recognized in the very first paper on large-scale network analysis using FBA [11,12] where a series of selected objective functions were used to find which one fit the data the best....

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