Flux coupling analysis of genome-scale metabolic network reconstructions

Abstract

In this paper, we introduce the Flux Coupling Finder (FCF) framework for elucidating the topological and flux connectivity features of genome-scale metabolic networks. The framework is demonstrated on genome-scale metabolic reconstructions of Helicobacter pylori, Escherichia coli, and Saccharomyces cerevisiae. The analysis allows one to determine whether any two metabolic fluxes, v(1) and v(2), are (1) directionally coupled, if a non-zero flux for v(1) implies a non-zero flux for v(2) but not necessarily the reverse; (2) partially coupled, if a non-zero flux for v(1) implies a non-zero, though variable, flux for v(2) and vice versa; or (3) fully coupled, if a non-zero flux for v(1) implies not only a non-zero but also a fixed flux for v(2) and vice versa. Flux coupling analysis also enables the global identification of blocked reactions, which are all reactions incapable of carrying flux under a certain condition; equivalent knockouts, defined as the set of all possible reactions whose deletion forces the flux through a particular reaction to zero; and sets of affected reactions denoting all reactions whose fluxes are forced to zero if a particular reaction is deleted. The FCF approach thus provides a novel and versatile tool for aiding metabolic reconstructions and guiding genetic manipulations.

Figure 1

Two reaction fluxes are (1) directionally coupled if the activity of one flux implies the activity of the other without the converse necessarily holding true, (2) partially coupled if the activity of one flux implies the activity of the other and vice versa, or (3) fully coupled if activity of one flux fixes the activity of the other. Reactions in enzyme subsets as defined by Pfeiffer et al. (1999) are exclusively fully coupled. Various types of coupling are related to the flux ratio limits R_min and R_max as shown.

Figure 2

Examples of blocked reactions (dashed lines) and a fully coupled enzyme subset (heavy lines). Flux v₄ is blocked due to the absence of a reaction consuming metabolite H, whereas v₉ and v₁₀ are blocked because there are no reactions forming I or consuming K. Note, however, that v₄ can carry flux if metabolite H is allowed to accumulate (i.e., unsteady-state). Assuming that the biomass composition is prespecified, knowledge of any flux in the enzyme subset confers the values of all other fluxes in that subset. For example, if v₅ is fixed, then v₆ and v_bio are also fixed, as they are the only outlets for the flux towards metabolites C and F, respectively. Similarly, fluxes v₇ and v_E are fixed as a consequence of fixing v_bio and v₆.

Figure 3

Examples of affected reaction sets and equivalent knockouts for reaction v^*. Removing v^* from the network results in reaction fluxes v₁, v₂, and v₃ being forced equal to zero at steady-state, and thus they are referred to as affected by v^*. Removing any of v₄, v₅, or v₆ ensures that v^* cannot carry flux at steady-state, so they are said to be equivalent knockouts for v^*.

Figure 4

Total numbers and percentages of blocked reactions for the three networks under different growth conditions.

Figure 5

Percentage of reactions contained in coupled sets in the H. pylori, E. coli, and S. cerevisiae metabolic networks for growth on either a complex or glucose-minimal medium (with and without a biomass reaction).

Figure 6

Coupled reaction set identified for purine biosynthesis in E. coli on a glucose-minimal medium, assuming a constant biomass composition. The numbers indicate the relative values or range of values for each flux in any particular flux distribution for given growth condition. Secondary metabolites and cofactors are omitted for simplicity.

Figure 7

Reactions coupled to biomass formation for aerobic S. cerevisiae growth on a glucose-minimal medium. Secondary metabolites and cofactors are omitted for simplicity. All reactions are fully coupled, meaning that knowledge of one reaction flux is sufficient to specify the flux through all reactions at steady-state. Note that PAP is converted to AMP, which is a precursor to biomass. This enzyme subset is decomposed into numerous subsystems, indicated by different colored arrows, if the biomass reaction is replaced with drains on the various biomass precursors.

Figure 8

Comparison of the FCF-identified coupled reaction sets for H. pylori with the enzyme subsets identified by Schilling et al. (2002). The latter approach subdivides the network into six smaller subnetworks based on functional classification, and finds subsets for each one of them. The FCF procedure considers the network in its entirety. The reaction names in each row correspond to different coupled reaction sets. Underlined reactions highlight coupling relationships identified only using the FCF method, and the two arrows indicate the coupling of enzyme subsets across functional classifications. Reaction abbreviations can be found in the supplemental material of Schilling et al. (2002).

Figure 9

The complete reaction coupling relationships in E. coli central metabolism for aerobic growth on glucose. Reversible reactions are listed by the reaction name, followed by _F and _B to denote the forward and backward directions, respectively. The reaction names and stoichiometry corresponding to the reaction abbreviations are found in the Supplementary material.

Figure 10

The number of reactions N(k) implying k other reactions are plotted as a function of k for H. pylori, E. coli, and S. cerevisiae growth on a glucose-minimal medium.

Figure 11

Genome-wide metabolic coupling for E. coli growth on a glucose-minimal medium with (A) or without (B) the presence of a biomass reaction. The biomass reaction is located in the bottom left corner of (A).