Flux balance analysis: A geometric perspective

Abstract

a b s t r a c tAdvances in the field of bioinformatics have led to reconstruction of genome-scale networks for a number of key organisms. The application of physicochemical constraints to these stoichiometric networks allows researchers, through methods such as flux balance analysis, to highlight key sets of reactions necessary to achieve particular objectives. The key benefits of constraint-based analysis lie in the minimal knowledge required to infer systemic properties. However, network degeneracy leads to a large number of flux distributions that satisfy any objective; moreover, these distributions may be dominated by biologically irrelevant internal cycles. By examining the geometry underlying the problem, we define two methods for finding a unique solution within the space of all possible flux distributions; such a solution contains no internal cycles, and is representative of the space as a whole. The first method draws on typical geometric knowledge, but cannot be applied to large networks because of the high computational complexity of the problem. Thus a second method, an iteration of linear programs which scales easily to the genome scale, is defined. The algorithm is run on four recent genome-scale models, and unique flux solutions are found. The algorithm set out here will allow researchers in flux balance analysis to exchange typical solutions to their models in a reproducible format. Moreover, having found a single solution, statistical analyses such as correlations may be performed.

A Method of Accounting for Enzyme Costs in Flux Balance Analysis Reveals Alternative Pathways and Metabolite Stores in an Illuminated Arabidopsis Leaf

“…Applying FVA reveals the equivalence of R1, R2, and R3, with each taking a flux value of between 0 and 1, emphasizing both the inability of the constraints to produce a unique solution and the potential existence of alternative flux distributions to the one picked by conventional FBA. Geometric FBA (Smallbone and Simeonidis, 2009), which identifies a unique flux solution that corresponds to the center of the optimal flux solution space, predicts an equal division of flux between R1, R2, and R3 and a flux of 1 unit through R4. As an alternative to these established methods, using 1,000 sets of randomly chosen weighting factors and averaging the flux solutions gave predicted fluxes of approximately onethird through R1, R2, and R3, five-sixths through R4, and one-sixth through R5 and R6 (Table I).…”

“…FVA and geometric FBA were performed in ScrumPy following the algorithms described by Mahadevan and Schilling (2003) and Smallbone and Simeonidis (2009), respectively.…”

“…This is an improvement on random sampling of the flux solution space (Price et al, 2004) because the combination of random weighting with flux minimization increases the biological relevance of the flux predictions. Costweighted FBA is also superior to geometric FBA (Smallbone and Simeonidis, 2009), which only identifies alternative pathways with an equal number of reactions (Table I). Moreover, the use of flux-weighting factors allows a more nuanced exploration of alternative pathways than FVA, which only generates a permissible range for each flux satisfying the objective function and constraints.…”

Flux Measurement Selection in Metabolic Networks

“…More recent methods for determining metabolic fluxes often optimize a biological objective function such a growth or ATP production. A well-known method that uses this strategy is flux balance analysis [9,12,23]. However for eukaryotic cells a biological objective function is often not easy to determine.…”

Kinetic modelling of large-scale metabolic networks

“…provide metrics about the connectedness of the network; elementary flux mode analysis provides a unique decomposition of the network in minimal subsets that are capable of operating independently. By joining extra quantivative information about input and output fluxes, the network can also be studied using flux balance analysis [3]. These methods require little amount of molecular information, however they are only able to provide a restricted number of steady state properties of the system.…”