Mathematical models for explaining the Warburg effect: a review focussed on ATP and biomass production

Abstract

For producing ATP, tumour cells rely on glycolysis leading to lactate to about the same extent as on respiration. Thus, the ATP synthesis flux from glycolysis is considerably higher than in the corresponding healthy cells. This is known as the Warburg effect (named after German biochemist Otto H. Warburg) and also applies to striated muscle cells, activated lymphocytes, microglia, endothelial cells and several other cell types. For similar phenomena in several yeasts and many bacteria, the terms Crabtree effect and overflow metabolism respectively, are used. The Warburg effect is paradoxical at first sight because the molar ATP yield of glycolysis is much lower than that of respiration. Although a straightforward explanation is that glycolysis allows a higher ATP production rate, the question arises why cells do not re-allocate protein to the high-yield pathway of respiration. Mathematical modelling can help explain this phenomenon. Here, we review several models at various scales proposed in the literature for explaining the Warburg effect. These models support the hypothesis that glycolysis allows for a higher proliferation rate due to increased ATP production and precursor supply rates.

MicroRNA-33b inhibits cell proliferation and glycolysis by targeting hypoxia-inducible factor-1α in malignant melanoma

“…Glycolysis serves a critical role in tumor cell proliferation (4,5). Therefore, the level of glycolysis in WM451 and SK-MEL-1 cells in each group was examined.…”

“…In tumors, the metabolism of glucose is largely fermentative with increased production of lactate, even when oxygen levels are adequate (3). Glycolysis provides tumor cells with energy and molecules, including ATP, fatty acids and nucleotides, thus ensuring the survival, rapid growth and proliferation of tumor cells under hypoxic and anoxic conditions (4,5). Furthermore, low levels of oxygen may induce the expression of hypoxia-inducible factor (HIF) during tumor progression, enhancing the glycolytic metabolism in cancer cells (6,7).…”

Metabolism of Preimplantation Embryo Development

“…A number of explanations have been proposed to explain this effect, including competition for ADP and inorganic phosphate (Pi) between glycolysis and OXPHOS, changes in intracellular pH and [Ca 2+ ], and metabolite (such as F1,6BP) suppression of complexes III and IV and/or modulation of mitochondrial unspecific channel (Diaz-Ruiz et al, 2008;Rodriguez-Enriquez, Juarez, RodriguezZavala, & Moreno-Sanchez, 2001; Rosas-Lemus, Uribe-Alvarez, Chiquete-Felix, & Uribe-Carvajal, 2014;Wojtczak, 1996). No matter the specific mechanism, it seems likely that when glucose is abundant, an overflow of EMP pathway by-products likely led to an evolution of a strategy that resulted in maximizing flux through the EMP pathway (via Warburg/ Crabtree effect) in order to increase biomass, and many higher eukaryotes, including humans, utilize a similar strategy (Schuster, Boley, Moller, Stark, & Kaleta, 2015;Vander Heiden et al, 2009).…”

From elementary flux modes to elementary flux vectors: Metabolic pathway analysis with arbitrary linear flux constraints

“…Although very simple, a similar network was recently used to model the Warburg and the Crabtree effect [21,22]. It consists of one internal metabolite (A), three external metabolites (S, P, Q), and three reactions, where reactions R1 and R3 are assumed to be irreversible.…”