The thermodynamic meaning of metabolic exchange fluxes

Abstract

Metabolic flux analysis (MFA) deals with the experimental determination of steady-state fluxes in metabolic networks. An important feature of the (13)C MFA method is its capability to generate information on both directions of bidirectional reaction steps given by exchange fluxes. The biological interpretation of these exchange fluxes and their relation to thermodynamic properties of the respective reaction steps has never been systematically investigated. As a central result, it is shown here that for a general class of enzyme reaction mechanisms the quotients of net and exchange fluxes measured by (13)C MFA are coupled to Gibbs energies of the reaction steps. To establish this relation the concept of apparent flux ratios of enzymatic isotope-labeling networks is introduced and some computing rules for these flux ratios are given. Application of these rules reveals a conceptional pitfall of (13)C MFA, which is the inherent dependency of measured exchange fluxes on the chosen tracer atom. However, it is shown that this effect can be neglected for typical biochemical reaction steps under physiological conditions. In this situation, the central result can be formulated as a two-sided inequality relating fluxes, pool sizes, and standard Gibbs energies. This relation has far-reaching consequences for metabolic flux analysis, quantitative metabolomics, and network thermodynamics.

FIGURE 1

Reaction mechanism examples of increasing complexity used to demonstrate the application of the three computational rules for apparent forward/backward flux quotients: (a) General bidirectional multistep Michaelis-Menten mechanism for a unimolecular reaction S → P. (b) Sequential mechanism for a unimolecular reaction S → P with two cofactors T, Q not taken into account for isotopic labeling. (c) Sequential binding mechanism for a bimolecular reaction S + T → P. (d) Random binding mechanism for a bimolecular reaction S + T → P. (e) Random bi-bi reaction mechanism with multiple substrates and products S + T → P + Q. S, T are substrates, P, Q are products, E is free enzyme, and M_i, ES, ET, EST, and ESPQ are enzyme complexes. Shaded circles indicate the potentially labeled substrates and products.

FIGURE 2

Isotope-labeling networks for the reaction mechanism from Fig. 1 d. (a) Tracing an S atom to P. (b) Tracing a T atom to P. Dashed arrows indicate substances which enter or leave the network but are not considered for isotope tracing.