Date Published: September 10, 2012
Publisher: Hindawi Publishing Corporation
Author(s): J. Paul Brooks, William P. Burns, Stephen S. Fong, Chris M. Gowen, Seth B. Roberts.
Constraint-based metabolic models are currently the most comprehensive system-wide models of cellular metabolism. Several challenges arise when building an in silico constraint-based model of an organism that need to be addressed before flux balance analysis (FBA) can be applied for simulations. An algorithm called FBA-Gap is presented here that aids the construction of a working model based on plausible modifications to a given list of reactions that are known to occur in the organism. When applied to a working model, the algorithm gives a hypothesis concerning a minimal medium for sustaining the cell in culture. The utility of the algorithm is demonstrated in creating a new model organism and is applied to four existing working models for generating hypotheses about culture media. In modifying a partial metabolic reconstruction so that biomass may be produced using FBA, the proposed method is more efficient than a previously proposed method in that fewer new reactions are added to complete the model. The proposed method is also more accurate than other approaches in that only biologically plausible reactions and exchange reactions are used.
Flux balance analysis (FBA) is the use of a linear program (LP) to model the flow of metabolites through the network of reactions in a cell . FBA simulations give insight into the relative rates at which reactions occur when the cell is optimized for a specific objective. A fundamental assumption of FBA is that organisms can function optimally (often as a result of adaptive evolution) in that they make optimal use of scarce resources to serve the needs of the organism. This characterization of cell behavior naturally leads to a math programming modeling paradigm. FBA has been used to predict growth rates, gene essentiality, and other features of multiple organisms [2–5].
FBA-Gap takes as input an FBA model and a lower bound for the flux through the artificial biomass reaction (to ensure growth). Whereas FBA can be considered a generalized maximum flow on a hypergraph, consider an analogy with maximum flows on graphs (Figure 1(a)). Intuitively, a gap corresponds to a missing arc. The main idea behind FBA-Gap is to find a minimum-cost set of artificial exchange reactions so that biomass may be produced. Note that for the graph in Figure 1(b), artificially adding flow to any of nodes C, D, or E will ensure positive flow along the artificial arc. Given that we would like to fill the gap, we would benefit the most by knowing the needed exchange reaction that is furthest from the biomass reaction. This desire leads us to define a notion of distance from the biomass reaction and a corresponding cost structure that will lead us to the gaps.
Application to a Partial Metabolic ReconstructionTo illustrate the ability of FBA-Gap to aid in the construction of new FBA models, we apply the methodology to a new multicompartment model for Cryptococcus neoformans. C. neoformans is a fungus that can cause meningitis in humans. Because no metabolic reconstruction of C. neoformans has been previously carried out, we assign a generic biomass reaction previously used for B. subtilis  using only central metabolites that occur in the cytosol:
(7)1.241 3 pg+2.097 AcCoa+1.236 Akg+35.115 ATP+0.397 e4p+0.428 g3p+0.712 g6p+0.542 Gly+14.405 NADPH+8.066 NH4+1.785 oaa+0.642 pep+1.640 Pi+2.994 Pyr+0.445 r5p+0.262 Ser-l+0.195 SO4→2.852 CO2+3.015 NADH.
This paper presents an optimization-based method for “debugging” metabolic reconstructions called FBA-Gap. We demonstrate the effectiveness of the procedure in helping to find gaps in a model for C. neoformans. FBA-Gap produces a more accurate reconstruction than an application of existing methods for filling gaps and requires less computation time. However, in contrast to other methods, FBA-Gap also involves manually selecting and approving which reactions to add to a model so that the overall time may be longer. As noted by Latendresse et al. , a fully automated gap-filling procedure likely leads to significant errors. The motivation behind FBA-Gap is to reduce the manual effort required by allowing the modeler to select from among a few suggested modifications to a model. The distance measure used in pricing artificial exchange reactions helps to indicate the location of gaps; these weights could also be incorporated into a procedure like MetaFlux , a more automated procedure that also has the capability of suggesting modifications to the biomass reaction. The FBA-Gap procedure provides hypotheses for defined culture media for organisms based on previously published models. One weakness of FBA-Gap is the computational complexity of solving (5). Finding optimal solutions to these integer programs is NP-Complete, but specialized solution methods may facilitate the computation of good solutions.