title: 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.
authors.affiliation: Department of Bioinformatics, Friedrich Schiller University Jena, Ernst-Abbe-Platz 2, 07743 Jena, Germany stefan.schu@uni-jena.de.
authors.forename: Stefan
authors.initials: S
authors.lastname: Schuster
authors.affiliation: Computer Science & Engineering, University of Minnesota, Minneapolis, MN 55455, U.S.A.
authors.forename: Daniel
authors.initials: D
authors.lastname: Boley
authors.affiliation: Department of Bioinformatics, Friedrich Schiller University Jena, Ernst-Abbe-Platz 2, 07743 Jena, Germany.
authors.forename: Philip
authors.initials: P
authors.lastname: Möller
authors.affiliation: Department of Bioinformatics, Friedrich Schiller University Jena, Ernst-Abbe-Platz 2, 07743 Jena, Germany Institute of Systematic Zoology and Evolutionary Biology, Friedrich Schiller University Jena, Erbertstraße 1, 07737 Jena, Germany.
authors.forename: Heiko
authors.initials: H
authors.lastname: Stark
authors.affiliation: Research Group Medical Systems Biology, Christian-Albrechts-University Kiel, Brunswiker Straße 10, Kiel 24105, Germany.
authors.forename: Christoph
authors.initials: C
authors.lastname: Kaleta
mesh_terms: D000255:Adenosine Triphosphate / Q000378:metabolism*; D000465:Algorithms; D000818:Animals; D018533:Biomass; D004734:Energy Metabolism / Q000502:physiology; D005947:Glucose / Q000378:metabolism; D006019:Glycolysis / Q000502:physiology*; D006801:Humans; D008928:Mitochondria / Q000378:metabolism; D008962:Models, Theoretical
chemical_list: D000255:Adenosine Triphosphate; D005947:Glucose
keywords: Warburg effect; cancer metabolism; metabolic modelling; rate vs. yield; respirofermentation