Structural control of metabolic flux

Abstract

Organisms have to continuously adapt to changing environmental conditions or undergo developmental transitions. To meet the accompanying change in metabolic demands, the molecular mechanisms of adaptation involve concerted interactions which ultimately induce a modification of the metabolic state, which is characterized by reaction fluxes and metabolite concentrations. These state transitions are the effect of simultaneously manipulating fluxes through several reactions. While metabolic control analysis has provided a powerful framework for elucidating the principles governing this orchestrated action to understand metabolic control, its applications are restricted by the limited availability of kinetic information. Here, we introduce structural metabolic control as a framework to examine individual reactions' potential to control metabolic functions, such as biomass production, based on structural modeling. The capability to carry out a metabolic function is determined using flux balance analysis (FBA). We examine structural metabolic control on the example of the central carbon metabolism of Escherichia coli by the recently introduced framework of functional centrality (FC). This framework is based on the Shapley value from cooperative game theory and FBA, and we demonstrate its superior ability to assign "share of control" to individual reactions with respect to metabolic functions and environmental conditions. A comparative analysis of various scenarios illustrates the usefulness of FC and its relations to other structural approaches pertaining to metabolic control. We propose a Monte Carlo algorithm to estimate FCs for large networks, based on the enumeration of elementary flux modes. We further give detailed biological interpretation of FCs for production of lactate and ATP under various respiratory conditions.

Figure 1. Metabolic network of central carbon metabolism of E. coli.

Reactions and metabolites are listed in Supplementary Tables S11 and S12.

Figure 2. KO-reduced functionality of biomass production under conditions of aerobic respiration.

Errorbars are provided for all and indicate 95% confidence intervals. Results are only depicted for a relative standard error smaller than 10%.

Figure 3. KO-reduced functionality of biomass production under conditions of nitrate respiration.

Errorbars are provided for all and indicate 95% confidence intervals. Results are only depicted for a relative standard error smaller than 10%.

Figure 4. KO-reduced functionality of biomass production under conditions of fermentation.

Errorbars are provided for all and indicate 95% confidence intervals. Results are only depicted for a relative standard error smaller than 10%.

Figure 5. Prediction of gene expression patterns by control-effective fluxes (CEFs).

Calculated ratios between transcript levels during exponential growth on glucose (GLC) and growth on acetate (AC) under conditions of aerobic respiration based on CEFs versus experimentally determined transcript ratios. Lines indicate 95% confidence intervals for experimental data (horizontal lines), linear regression (solid line), perfect match (dashed line) and two-fold deviation (dotted line).

Figure 6. Prediction of gene expression patterns by functional centralities (FCs).

Calculated ratios between transcript levels during exponential growth on glucose (GLC) and growth on acetate (AC) under conditions of aerobic respiration based on FCs versus experimentally determined transcript ratios. Lines indicate 95% confidence intervals for experimental data (horizontal lines), linear regression (solid line), perfect match (dashed line) and two-fold deviation (dotted line).