Abstract
BackgroundFlux balance analysis is traditionally implemented to identify the maximum theoretical flux for some specified reaction and a single distribution of flux values for all the reactions present which achieve this maximum value. However it is well known that the uncertainty in reaction networks due to branches, cycles and experimental errors results in a large number of combinations of internal reaction fluxes which can achieve the same optimal flux value.ResultsIn this work, we have modified the applied linear objective of flux balance analysis to include a poling penalty function, which pushes each new set of reaction fluxes away from previous solutions generated. Repeated poling-based flux balance analysis generates a sample of different solutions (a characteristic set), which represents all the possible functionality of the reaction network. Compared to existing sampling methods, for the purpose of generating a relatively “small” characteristic set, our new method is shown to obtain a higher coverage than competing methods under most conditions.The influence of the linear objective function on the sampling (the linear bias) constrains optimisation results to a subspace of optimal solutions all producing the same maximal fluxes. Visualisation of reaction fluxes plotted against each other in 2 dimensions with and without the linear bias indicates the existence of correlations between fluxes. This method of sampling is applied to the organism Actinobacillus succinogenes for the production of succinic acid from glycerol.ConclusionsA new method of sampling for the generation of different flux distributions (sets of individual fluxes satisfying constraints on the steady-state mass balances of intermediates) has been developed using a relatively simple modification of flux balance analysis to include a poling penalty function inside the resulting optimisation objective function. This new methodology can achieve a high coverage of the possible flux space and can be used with and without linear bias to show optimal versus sub-optimal solution spaces. Basic analysis of the Actinobacillus succinogenes system using sampling shows that in order to achieve the maximal succinic acid production CO2 must be taken into the system. Solutions involving release of CO2 all give sub-optimal succinic acid production.Electronic supplementary materialThe online version of this article (doi:10.1186/s12859-015-0476-5) contains supplementary material, which is available to authorized users.
Highlights
Flux balance analysis is traditionally implemented to identify the maximum theoretical flux for some specified reaction and a single distribution of flux values for all the reactions present which achieve this maximum value
Case study: central metabolism of Actinobacillus succinogenes Actinobacillus succinogenes is an organism which is known for producing succinic acid either from glucose [24,25,26,27,28,29] or glycerol [30]
A new methodology has been introduced to sample the possible flux space of biochemical systems. This is an extension of flux balance analysis, which involves the addition of a poling penalty function forcing new solutions away from any of the existing solutions generated
Summary
Flux balance analysis is traditionally implemented to identify the maximum theoretical flux for some specified reaction and a single distribution of flux values for all the reactions present which achieve this maximum value. It is well known that the uncertainty in reaction networks due to branches, cycles and experimental errors results in a large number of combinations of internal reaction fluxes which can achieve the same optimal flux value. Using experimental measurements where available for the significant reaction fluxes going in and out of the system (external fluxes) flux balance analysis can be applied to compute the remaining internal and external fluxes using linear programming with steady-state constraints. For genome-scale models Mahadevan and Schilling [6] and Soh et al [7] suggest that the existence of alternative solutions for flux balance analysis (FBA) resulting from this uncertainty is a key challenge and Soh et al suggest this could be resolved with the identification of characteristic flux distributions explaining the observed steady-state behaviour of the phenotype. Even with extra constraints FBA still aims to compute a single flux distribution; in most cases there are a large number of solutions, which are missed through the additional assumptions made in order to force the system to a single solution
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