Abstract
BackgroundIn recent years, constrained optimization – usually referred to as flux balance analysis (FBA) – has become a widely applied method for the computation of stationary fluxes in large-scale metabolic networks. The striking advantage of FBA as compared to kinetic modeling is that it basically requires only knowledge of the stoichiometry of the network. On the other hand, results of FBA are to a large degree hypothetical because the method relies on plausible but hardly provable optimality principles that are thought to govern metabolic flux distributions.ResultsTo augment the reliability of FBA-based flux calculations we propose an additional side constraint which assures thermodynamic realizability, i.e. that the flux directions are consistent with the corresponding changes of Gibb's free energies. The latter depend on metabolite levels for which plausible ranges can be inferred from experimental data. Computationally, our method results in the solution of a mixed integer linear optimization problem with quadratic scoring function. An optimal flux distribution together with a metabolite profile is determined which assures thermodynamic realizability with minimal deviations of metabolite levels from their expected values. We applied our novel approach to two exemplary metabolic networks of different complexity, the metabolic core network of erythrocytes (30 reactions) and the metabolic network iJR904 of Escherichia coli (931 reactions). Our calculations show that increasing network complexity entails increasing sensitivity of predicted flux distributions to variations of standard Gibb's free energy changes and metabolite concentration ranges. We demonstrate the usefulness of our method for assessing critical concentrations of external metabolites preventing attainment of a metabolic steady state.ConclusionOur method incorporates the thermodynamic link between flux directions and metabolite concentrations into a practical computational algorithm. The weakness of conventional FBA to rely on intuitive assumptions about the reversibility of biochemical reactions is overcome. This enables the computation of reliable flux distributions even under extreme conditions of the network (e.g. enzyme inhibition, depletion of substrates or accumulation of end products) where metabolite concentrations may be drastically altered.
Highlights
In recent years, constrained optimization – usually referred to as flux balance analysis (FBA) – has become a widely applied method for the computation of stationary fluxes in large-scale metabolic networks
Whereas the maximization of biomass production appears to be a reasonable objective of the cellular metabolism of rapidly growing and replicating primitive cells such as bacteria, the flux distribution in complex eukaryotic cells is governed by a larger variety of cellular functions that have to be met simultaneously
Regarding flux distributions predicted by constrained optimization methods as FBA it is desirable to judge their feasibility post-hoc but to include thermodynamic constraints on flux directionalities directly into their calculation [21,22,23]
Summary
In recent years, constrained optimization – usually referred to as flux balance analysis (FBA) – has become a widely applied method for the computation of stationary fluxes in large-scale metabolic networks. Flux measurements – except for exchange reactions that deliver metabolites into the external space – are still difficult and costly to perform as they require determining labeled isotopomers in a time-dependent manner [11,12,13] Another possibility to increase the credibility of flux balance calculations is to include some basic thermodynamics of the reactions and transport processes constituting the network. The rationale behind this empirical weighting procedure is to impede reversing the direction of a reaction (such that the change of Gibb's free energy has the opposite sign than under standard conditions) with increasing value of the thermodynamic equilibrium constant This way of mixing the costs for the maintenance of metabolic fluxes with the thermodynamic 'costs' for reversing the direction of a reaction in one and the same objective function is questionable for two reasons. In the following we outline the method and provide applications to two different metabolic networks: (i) the energy- and redox metabolism of red blood cells for which a detailed kinetic model has been established [24] allowing to check the feasibility of our method and (ii) the large-scale genome-based metabolic network of Escherichia coli iJR904 [25] which has already been subjected to FBA in several studies [23,26,27]
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