A Flux Balance of Glucose Metabolism Clarifies the Requirements of the Warburg Effect

Abstract

The Warburg effect, or aerobic glycolysis, is marked by the increased metabolism of glucose to lactate in the presence of oxygen. Despite its widespread prevalence in physiology and cancer biology, the causes and consequences remain incompletely understood. Here, we show that a simple balance of interacting fluxes in glycolysis creates constraints that impose the necessary conditions for glycolytic flux to generate lactate as opposed to entering into the mitochondria. These conditions are determined by cellular redox and energy demands. By analyzing the constraints and sampling the feasible region of the model, we further study how cell proliferation rate and mitochondria-associated NADH oxidizing and ATP producing fluxes are interlinked. Together this analysis illustrates the simplicity of the origins of the Warburg effect by identifying the flux distributions that are necessary for its instantiation.

Figure 1

The flux-balance model of glycolysis demonstrates how the Warburg effect is affected by fluxes in glucose metabolism. (A) Flux-balance model of glycolysis. (B) Equality constraints for balance of NADH, carbon, and ATP. (C) Expression of the extent of the Warburg effect by fluxes J_in, J_N, and J_A. (D) Analysis of the Warburg effect in healthy tissues. Negative values of W imply that carbon sources other than glucose are required to match cellular ATP demand. (E and F) Effects of increasing glucose uptake, increasing mitochondrial coupling or decreasing ATP turnover on the shift from oxidative phosphorylation to aerobic glycolysis. To see this figure in color, go online.

Figure 2

The interplay of redox balancing and proliferation in regulating aerobic glycolysis. (A and B) Correlation of PHGDH and malate-aspartate shuttle at single gene and pathway level among breast tumor samples in the Cancer Genome Atlas. Color in the scatter plot represents density of points. (C–E) Comparison of correlations shown in (A) and (B) between the expression of PHGDH, MDH1, and MAS and other metabolic genes involved in the KEGG pathway databased termed ‘Metabolic Pathways’. The false discovery rate (FDR) values were defined as the fraction of ‘background’ correlations larger than that between PHGDH and MDH1 or between PHGDH and MAS. (F) Two-dimensional box plot shows the distribution of JN and $\mu$ estimated from data reported in literature. (G) Distribution of W evaluated for NCI-60 cell lines from exchange flux rates. The W=1 line connecting the NADH oxidizing flux JN and the growth rate $\mu$. Different colors represent different values of $\alpha$. To see this figure in color, go online.

Figure 3

Landscape of balanced fluxes in central carbon metabolism. (A) Distribution of feasible flux configurations and their relative level of the Warburg effect defined as the rank of W among all sampled flux configurations. W increases as the color changes from blue to red. Mitochondrial coupling α=16 was used in the sampling. (B) Correlation of expression of malate-aspartate shuttle-associated genes and growth rate of NCI-60 cell lines. (C) Correlation of pyruvate dehydrogenase expression with growth rate in NCI-60 cell lines. (D) Interplay of proliferation and mitochondria-coupled NADH-oxidizing flux in determining the extent of aerobic glycolysis. (E) Relative strength of aerobic glycolysis of NCI-60 cell lines projected on growth rate and average expression level of MAS and PDH-related genes. (F) Distribution of W/(W+1) among 20,000 randomly sampled flux configurations. (G) Distribution of $\alpha J_{Ox}/J_A$ among 20,000 randomly sampled flux configurations. To see this figure in color, go online.

Figure 4

Maximization of biomass production may not lead to aerobic glycolysis. (A) Maximization of growth rate under different combinations of upper limits for J_N and J_in and the corresponding extent of the Warburg effect. W/(1+W) was used instead of W for continuity. (B) Maximal growth rate under different combinations of upper limits for J_N and J_in. (C) Distribution of W/(1+W) among 10000 randomly generated models maximizing growth rate under different combinations of the upper limits for all fluxes in the flux balance model with inclusion of a random solvent capacity constraint. To see this figure in color, go online.