Resource constrained flux balance analysis predicts selective pressure on the global structure of metabolic networks - PubMed (original) (raw)
Resource constrained flux balance analysis predicts selective pressure on the global structure of metabolic networks
Nima Abedpour et al. BMC Syst Biol. 2015.
Abstract
Background: A universal feature of metabolic networks is their hourglass or bow-tie structure on cellular level. This architecture reflects the conversion of multiple input nutrients into multiple biomass components via a small set of precursor metabolites. However, it is yet unclear to what extent this structural feature is the result of natural selection.
Results: We extend flux balance analysis to account for limited cellular resources. Using this model, optimal structure of metabolic networks can be calculated for different environmental conditions. We observe a significant structural reshaping of metabolic networks for a toy-network and E. coli core metabolism if we increase the share of invested resources for switching between different nutrient conditions. Here, hub nodes emerge and the optimal network structure becomes bow-tie-like as a consequence of limited cellular resource constraint. We confirm this theoretical finding by comparing the reconstructed metabolic networks of bacterial species with respect to their lifestyle.
Conclusions: We show that bow-tie structure can give a system-level fitness advantage to organisms that live in highly competitive and fluctuating environments. Here, limitation of cellular resources can lead to an efficiency-flexibility tradeoff where it pays off for the organism to shorten catabolic pathways if they are frequently activated and deactivated. As a consequence, generalists that shuttle between diverse environmental conditions should have a more predominant bow-tie structure than specialists that visit just a few isomorphic habitats during their life cycle.
Figures
Fig. 1
Trade-off between traveling time and road maintenance costs in road network design. Left panel: road networks that minimize either traveling time (efficient road network) or maintenance cost (flexible road network). Right panel: comparison of traveling time and maintenance cost for both road networks
Fig. 2
Toy-model. The universe of metabolic reactions for a simple toy-model containing 12 metabolites including two extracellular substrates S1 and S2 and 14 reactions. A fluctuating environment is generated by shuttling between the two alternative substrates, S1 and S2. The objective function is to maximize the biomass production rate averaged over all environmental conditions
Fig. 3
Structural transitions and regulations of the toy-model. Blue and red arrows are regulated enzymatic reactions and black arrows are constantly active enzymatic reactions. Light-gray arrows shows the remaining reactions that belong to the universe of reactions of Fig. 2, but not selected within the optimal metabolic network. Bold-lines illustrate the active reactions in each environmental condition. a Low switching parameters, r<0.25, result in an efficient network design that connects the actual present substrate to the biomass reaction using the most direct metabolic route. **b** Intermediate switching parameters, 0.25<_r_<0.5, shows a strong reduction of enzymes that are regulated and the emergence of a common permanently upregulated metabolic route. **c** High switching parameters, _r_>0.5, result in permanent upregulation of all enzymes and a network design of minimal size
Fig. 4
Structural parameters for the toy-model. a Growth rate for different switching parameters, r. Two discontinuities exist in the slope of the curve at _r_=0.25 and _r_=0.5. b Pathway length vs. r. c Number of nodes vs. r. d Number of reactions vs. r. Structural parameters of the optimized network confirm that only _r_=0.25 is a structural transition
Fig. 5
Schematic graphical representation of the E. coli core metabolism. The network contains 72 metabolites and 95 reactions, including pseudo reactions [29]. Some important metabolites are named explicitly. Ex_ac, Ex_pyr, Ex_mal-L, Ex_glu-L and Ex_glc represent the extracellular concentrations of Acetate, Pyruvate, L-malate, L-glutamate and D-glucose, respectively, that are provided in random order to mimic fluctuations in nutrient availability
Fig. 6
Structural parameters for the E. coli core metabolic network. The average over 400 random realizations of α and β with 90 percent noise is taken. Here, 5 different environmental conditions that represent different carbon sources with 2 to 6 carbon atoms is used. a Average growth rate vs. r. b Average shortest path from an input metabolite to each of the biomass contents for the optimized network vs. r. c Number of selected input metabolites after optimization process vs. r. d Number of nodes of the optimized network vs. r. e Number of reactions of the optimized network vs. r. f Number of regulons vs. r
Fig. 7
Structural parameter distributions of Reconstructed networks. Distribution of different structural parameters of 143 different species classified in two groups of facultative and non-facultative organisms with size of 59 and 84 species, respectively. The distributions of a number of genes used in reconstructed metabolic model, b number of input metabolites (transporters), c average in- or out-degree of the networks considering directed links, d average of shortest path between an input metabolite and each of biomass ingredients, e the average of distances between input metabolites and f fraction of essential reactions. p-values are calculated by the Kruskal-Wallis test
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