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. 2013 May 31;8(5):e64567.
doi: 10.1371/journal.pone.0064567. Print 2013.

Community Flux Balance Analysis for Microbial Consortia at Balanced Growth

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Free PMC article

Community Flux Balance Analysis for Microbial Consortia at Balanced Growth

Ruchir A Khandelwal et al. PLoS One. .
Free PMC article

Abstract

A central focus in studies of microbial communities is the elucidation of the relationships between genotype, phenotype, and dynamic community structure. Here, we present a new computational method called community flux balance analysis (cFBA) to study the metabolic behavior of microbial communities. cFBA integrates the comprehensive metabolic capacities of individual microorganisms in terms of (genome-scale) stoichiometric models of metabolism, and the metabolic interactions between species in the community and abiotic processes. In addition, cFBA considers constraints deriving from reaction stoichiometry, reaction thermodynamics, and the ecosystem. cFBA predicts for communities at balanced growth the maximal community growth rate, the required rates of metabolic reactions within and between microbes and the relative species abundances. In order to predict species abundances and metabolic activities at the optimal community growth rate, a nonlinear optimization problem needs to be solved. We outline the methodology of cFBA and illustrate the approach with two examples of microbial communities. These examples illustrate two useful applications of cFBA. Firstly, cFBA can be used to study how specific biochemical limitations in reaction capacities cause different types of metabolic limitations that microbial consortia can encounter. In silico variations of those maximal capacities allow for a global view of the consortium responses to various metabolic and environmental constraints. Secondly, cFBA is very useful for comparing the performance of different metabolic cross-feeding strategies to either find one that agrees with experimental data or one that is most efficient for the community of microorganisms.

Conflict of interest statement

Competing Interests: The authors have declared that no competing interests exist.

Figures

Figure 1
Figure 1. Metabolic network overview of a microbial community of two microorganisms engaging in metabolic cross feeding.
Species i and j exchange ammonium (NH3) and succinate (Succ). These metabolites are allowed to overflow into the environment. Species i and j respectively take up glucose (Glu) and dinitrogen gas (N2) supplied by the environment. Each organism operates at an intracellular metabolic steady state and contains four coarse-grained metabolic processes: catabolism, anabolism, product formation and respiration. Detailed information about the stoichiometric description of this community can be found in information S1. Three types of reaction rates occur: specific fluxes (q’s; in mol•(gram biomass) −1•h 1), environment fluxes (J’s; in mol•h 1), and specific growth rates (μ; h 1). Xi and Xj denote the biomass abundances of the two microorganisms in gram biomass.
Figure 2
Figure 2. Illustration of environmental and metabolic limitations at the consortium level, for the consortium depicted in Figure 1E.
A: Optimal consortium growth rate (formula image), in h−1, as a function of fractional biomass abundance of species formula image (formula image) at different cross-feeding (CF) reaction capacities, with all formula image’s in mol•h 1 and all formula image’s in mol•g−1•h 1. We consider a limited glucose (flux: formula image and excess nitrogen (flux: formula image and vary the flux bounds for CF fluxes (i.e. succinate (formula image) and ammonia (formula image) production fluxes) to distinguish different limitation regimes and optimality states: i. infinite CF when, ii. critical CF (formula image), iii. two cases for above critical CF: curve I (for:formula image and curve II (for: formula image, and iv. below critical CF (for: formula image. This figure indicates that the CF reactions determine the optimal value of the community growth rate and the optimal fractional biomass abundance. B: A contour plot is generated for the optimal community growth rate formula image as function of the upper bound of the succinate production flux by species formula image and the ammonia production flux of species formula image. The environmental conditions are the same as in Figure 2A. The different points depict the various cross-feeding regimes distinguished in Figure 2A (• Above Critical CF – I, ★ Above Critical CF – II, ♦Below Critical CF). This figure indicates that the CF fluxes between the organisms determine the optimal community state at a fixed environment. C: Contour plot of the maximum community growth rateformula image, as a function of the environment while cross-feeding capacities are kept unconstrained. This figure indicates that the optimal state of the ecosystem can be determined by specific environmental fluxes.
Figure 3
Figure 3. Illustration of cFBA applied to a genome-scale stoichiometric model of a microbial consortium evolved in a chemostat.
A: Consortium of two E. coli strains; one is a glucose consumer ‘formula image’ and other is a specialist acetate consumer ‘formula image’. They both take up glucose with specific glucose consumption fluxes formula imageand formula image in mmol•g−1•h 1 but ‘formula image’ does this with lower activity than ‘formula image’. Strain ‘formula image’ produces acetate with flux formula image and strain ‘formula image’ consumes it via flux formula image. In the chemostat, glucose is provided at a constant rate formula image. Andformula imageis the acetate production rate (mol•h 1). Various metabolites could be cross-fed between both organisms besides acetate, which leads to the question whether those alternative metabolites can be predicted by cFBA. B: A biomass ratio scan was performed and the community growth rate formula imageis plotted as a function of the steady-state biomass ratio. The following parameter were determined from the experimental data of Rosenzweig et al. (1994):formula image; formula image; dilution rate (D) = formula image = 0.2; and steady state biomass ratio formula image. To plot the ‘Below Critical Cross-feeding’ curve, cross-feeding fluxes were constrained as indicated in the plot, while for the ‘Infinite Cross-feeding” curve, unconstrained acetate cross-feeding capacities were assumed. C: Percentage change in minimum glucose uptake rate formula imageneeded to achieve the growth rate formula image of 0.2 h 1 for alternative cross-feeding metabolites (one-at-a-time).
Figure 4
Figure 4. General structure of the stoichiometric matrix of a microbial consortium.
The community stoichiometry matrix formula image has formula image rows (metabolites) and formula image columns (reactions) and is created by merging individual stoichiometric matrices (formula image ,formula image) of community microorganisms and the environmental fluxes. The species-specific stoichiometric matrices have a consistent organization of metabolites (intracellular (formula image), cross-feeding (formula image) and extracellular (formula image)) and reactions (intracellular (formula image), cross-feeding (formula image), unique transport (formula image) and environmental exchange (formula image)). Any sub-matrix notation has species name (formula image or formula image) as subscript and type of metabolites and reactions as superscript. The community stoichiometry matrix multiplied by the fractional biomass matrix formula image and flux vector formula image then gives the steady state mass balances of the community (equation (3)).

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Grant support

Funded by NWO Computational Life Science MEMESA Project (635.100.021) url: http://www.nwo.nl/en/research-and-results/research-projects/31/2300150131.html, ZonMW Genomics-Zenith Program, project number 93511039, and Netherlands Institute for Systems Biology (NISB). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
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