Systematic analysis of conservation relations in Escherichia coli genome-scale metabolic network reveals novel growth media

Abstract

A biochemical species is called producible in a constraints-based metabolic model if a feasible steady-state flux configuration exists that sustains its nonzero concentration during growth. Extreme semipositive conservation relations (ESCRs) are the simplest semipositive linear combinations of species concentrations that are invariant to all metabolic flux configurations. In this article, we outline a fundamental relationship between the ESCRs of a metabolic network and the producibility of a biochemical species under a nutrient media. We exploit this relationship in an algorithm that systematically enumerates all minimal nutrient sets that render an objective species weakly producible (i.e., producible in the absence of thermodynamic constraints) through a simple traversal of ESCRs. We apply our results to a recent genome scale model of Escherichia coli metabolism, in which we traverse the 51 anhydrous ESCRs of the metabolic network to determine all 928 minimal aqueous nutrient media that render biomass weakly producible. Applying irreversibility constraints, we find 287 of these 928 nutrient sets to be thermodynamically feasible. We also find that an additional 365 of these nutrient sets are thermodynamically feasible in the presence of oxygen. Since biomass producibility is commonly used as a surrogate for growth in genome scale metabolic models, our results represent testable hypotheses of alternate growth media derived from in silico analysis of the E. coli genome scale metabolic network.

FIGURE 1

The 17 biomass-containing anhydrous ESCRs associated with the iJR904 E. coli metabolic model induce 11 equivalence classes among the 143 extracellular species. Each species equivalence class corresponds to a row and each biomass, containing anhydrous ESCRs, to a column in the above plot. A square in position ij maps each species in equivalence class i to biomass-containing anhydrous ESCRs j. Equivalence classes with large numbers of species are represented by labels: Class 1 corresponds to 56 carbon sources (e.g., D-glucose, citrate, ethanol, lactose, L-tartrate), Class 2 corresponds to 54 nitrogen/carbon sources (e.g., most amino acids, nucleotides, and nucleotide precursors), and Class 3 represents 16 species that do not share anhydrous ESCRs with biomass (e.g., Fe²⁺, K⁺, D-methionine, trimethylamine, water, and proton). The full inventory of these species equivalence classes and legend of species abbreviations are given in Table 1.

FIGURE 2

There are 928 minimal weak aqueous nutrient sets for biomass in the E. coli iJR904 genome scale metabolic model. Two-hundred-and-eighty-seven of these nutrient sets permit growth when thermodynamic constraints are considered. Minimal weak aqueous nutrient sets are expressed in this figure as conjunctions of 11 equivalence classes of species that contribute to the same biomass-containing anhydrous ESCRs. Each conjunction represented by column j in this figure corresponds to a family of minimal weak aqueous nutrient sets, each formed by choosing one species from each equivalence class i that has a black box in entry ij. Each entry in the bottom row of the figure indicates how many total minimal weak aqueous nutrient sets are contributed by the conjunction in column j. Class 1 and Class 2 correspond to central carbon sources and nitrogen/carbon sources, respectively. Class 3 contains species that do not share anhydrous ESCRs with biomass. Please refer to Table 1 for full inventory of the species in equivalence Classes 1–3 and a legend of species abbreviations.

FIGURE 3

(a) All cobalamin-containing minimal weak aqueous nutrient sets are thermodynamically infeasible due to the inability of E. coli iJR904 to break down the cobalamin moiety. This results from the irreversibility of reaction ADOCBLS, which mediates the biosynthesis of adenosylcobalamin (adocbl) from N1-(α-D-ribosyl)-5,6-dimethylbenzimidazole (rdmbzi) and adenosine-GDP-cobinamide (agdpcbi). Additional metabolite abbreviations: ppi, pyrophosphate; gmp, guanosine monophosphate. (b) Taurine-containing, minimal weak aqueous-nutrient sets fail to render biomass producible in the presence of irreversibility constraints. Taurine acts as a sulfur donor by undergoing oxygen-dependent degradation to sulfite (so3) via reaction TAUDO. In the absence of thermodynamic constraints, oxygen is producible by E. coli iJR904 and this reaction is active. Oxygen fails to be producible in all minimal weak aqueous nutrient sets when thermodynamic constraints are considered, rendering the utilization of taurine as a sulfur source infeasible. Addition of oxygen renders 323 of 457 taurine-containing nutrient sets thermodynamically feasible. Networks visualized using Pajek (http://vlado.fmf.uni-lj.si/pub/networks/pajek/).