Figure 1.
Overview of procedure to identify thermodynamically feasible EFMs.
We use a metabolic network model of S. cerevisiae together with physiological data (e.g., growth rate, glucose uptake, ethanol production) in flux variability analysis (FVA) to determine reaction reversibilities and reaction activities for the specific conditions. Subsequently, we apply NET analysis to determine additional reaction direction constraints based on the activities of reactions that are active for all flux distributions. With the resulting condition specific reaction directionalities, we calculate all the EFMs for the metabolic network. Finally, we use quantitative metabolite data to test the reaction activities of each EFM for thermodynamic feasibility.
Figure 2.
Overview of the main reactions in the metabolic model of S. cerevisiae.
The shaded area indicates the mitochondrion. The colors of the directed arrows indicate from which information a constraint was added. The blue cross indicates the oxaloacetate transported that is predicted to be inactive after analyzing the thermodynamically feasible EFMs. For a list of metabolite names see Dataset S2.
Figure 3.
Principal component analysis on normalized EFMs represented in a matrix with each EFM as a sample and each reaction as a variable.
All reaction rates are normalized to the glucose uptake rate of the respective EFM. The projection of the data (dots) for principal components one and two (PC 1 and PC 2), and the coefficients of the highest loadings in component 2 (labeled vectors) are shown. The reactions with highest loadings in PC 2 are likely to be involved in the causes for infeasibility of EFMs. One million EFMs were sampled to perform the PCA, multiple repeats with random sampling gave similar results.
Figure 4.
Ranges of possible flux values for eight reactions for which a reduction in the feasible flux range was found, during growth on glucose.
The dark shaded bars show the possible flux range obtained from all EFMs, while the light shaded bars show the ranges that are obtained from the feasible EFMs. In the reaction formulas the [c] and [m] indicate that the metabolite or overall reaction occur in the cytosol or mitochondrion, respectively. Abbreviations: acald (acetaldehyde), etoh (ethanol), mal-L (malic acid), pi (phosphate), h (proton), nad (), nadh (NADH), oaa (oxaloacetic acid).
Figure 5.
Overview of the six reaction patterns that cause thermodynamic infeasibility of EFMs.
The number above each pattern indicates in how many EFMs the respective pattern occurs, and the number in bracket shows the percentage of the infeasible EFMs that contains the pattern.
Figure 6.
Cytosolic NADH oxidation rates of specific reactions versus the total cytosolic NADH oxidation rate for EFMs.
The reaction name is shown on each plot, with the reaction name in the metabolic model in brackets. Every dot represents one or more EFMs at the respective combination of oxidation rates. A grey shade represents a combination where both feasible and infeasible EFMs are present. The rates are normalized to the glucose uptake rate of each EFM.