Robustness of glycolysis in yeast to internal and external noise

Glycolysis is one of the most essential intracellular networks, found in a wide range of organisms. Due to its importance and due to its wide industrial applications, many experimental studies on all details of this process have been performed. Until now, however, to the best of our knowledge, there has been no comprehensive investigation of the robustness of this important process with respect to internal and external noise. To close this gap, we applied two complementary and mutually supporting approaches to a full-scale model of glycolysis in yeast: (a) a linear stability analysis based on a generalized modeling that deals only with those effective parameters of the system that are relevant for its stability, and (b) a numerical integration of the rate equations in the presence of noise, which accounts for imperfect mixing. The results suggest that the occurrence of metabolite oscillations in part of the parameter space is a side effect of the optimization of the system for maintaining a constant adenosine triphosphate level in the face of a varying energy demand and of fluctuations in the parameters and metabolite concentrations.

Figure 1

Metabolic reaction network of glycolysis in yeast, adopted from Hynne et al. [20]. $x=\text{extern}$, $\text{out}=\text{species}$ to be export from the cellular volume, $\text{in}=\text{cellular}$ intake.

Figure 2

Dependency of the occurrence of oscillations on the metabolic concentrations. Shown is the natural logarithm of the ratio of the mean concentrations for oscillating systems $S_{\text{oscillating}}^0$ to their value the operation point $S_{\text{total}}^0$.

Figure 3

Dependency of the occurrence of oscillations on the saturation parameters. Shown is the natural logarithm of the ratio of their values for oscillating systems ${\Theta }_{\text{oscillating}}^{\text{kin}}$ to their values at the operation point ${\Theta }_{\text{total}}^{\text{kin}}$.

Figure 4

Elementary flux modes of glycolysis, adopted from Hynne et al. [20], and the dependency of the occurrence of oscillations on linear combinations of elementary flux modes.

Figure 5

ATP concentration in the stable (left-hand column) or oscillating (right-hand column) system with ATP consumption rate $k_{23}$ being doubled (first row) or halved (second row) after 30 min.

Figure 6

(a) Oscillations in the deterministic system and (b) the system under the influence of noise.

Figure 7

Correlations of metabolites’ mean values.

Figure 8

Proportion of oscillating systems of the 844 simulations.

Figure 9

Influence of individual parameters in the system with noise on the occurrence of oscillations.

Figure 10

Mean and standard deviation of all metabolites analyzed for the 844 simulations. Top: Mean concentrations and the original mean values from Hynne et al. [20] are shown. Error bars are standard deviations from sampling of the 844 different replica. Bottom: Standard deviation in the time series of metabolic concentrations. Again, error bars are standard deviations from the sampling over the 844 parameter choices. For reference, we show also the corresponding $5\%$ noise level imposed on the metabolites’ concentrations (horizontal line).