Metabolic pathways analysis 2015 1187 Mathematical models for explaining the Warburg effect: a review focussed on ATP and biomass production Stefan Schuster* 1 , Daniel Boley†, Philip M ¨ oller*, Heiko Stark*‡ and Christoph Kaleta§ *Department of Bioinformatics, Friedrich Schiller University Jena, Ernst-Abbe-Platz 2, 07743 Jena, Germany †Computer Science & Engineering, University of Minnesota, Minneapolis, MN 55455, U.S.A. ‡Institute of Systematic Zoology and Evolutionary Biology, Friedrich Schiller University Jena, Erbertstraße 1, 07737 Jena, Germany §Research Group Medical Systems Biology, Christian-Albrechts-University Kiel, Brunswiker Straße 10, Kiel 24105, Germany 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. Introduction For producing ATP, tumour cells in mammalian tissues rely much more on glycolysis leading to lactate (in comparison with respiration) than the healthy cells from which the tumour cells originated. This is known as the Warburg effect, named after German biochemist Otto H. Warburg [1–3]. He published these observations in several German papers in the 1920s [4] and in 1956 in English [5]. Warburg himself explained the effect by impaired function of mitochondria in tumour cells [4,5]. Similar phenomena are observed in many other cell types. Examples are provided by Saccharomyces cerevisiae and several other yeasts (Crabtree effect) [6], and also by Escherichia coli and many other bacteria (overflow metabolism) [7,8]. An example of mammalian cells that have immediate access to oxygen in the blood but are, nevertheless, highly glycolytic, is provided by endothelial cells. These cells generate up to 85% of their ATP via glycolysis [9]. Lymphocytes show a metabolic shift upon activation. Although they mainly use respiration (oxidative phosphorylation) in the quiescent state, glycolysis is up- regulated during activation, even in the presence of oxygen Key words: cancer metabolism, metabolic modelling, rate vs. yield, respirofermentation, Warburg effect. Abbreviations: FBA, flux balance analysis; FBAwmc, FBA with macromolecular crowding; LP, linear programme; TCA, tricarboxylic acid. 1 To whom correspondence should be addressed (email stefan.schu@uni-jena.de). [10,11]. In the case of lymphocytes, the term Warburg effect is explicitly used as well [10]. Kupffer cells are ontogenetically related to lymphocytes and are resident macrophages in the liver. They also enhance glucose utilization after activation (e.g. by endotoxins) [12]. Microglia cells are the resident macrophages in the brain [13]. These cells suppress their mitochondrial function and up-regulate glycolysis upon activation, for example, by lipopolysaccharides [14]. The major consumers of glucose in the body are the muscular system and brain. Skeletal muscles consist of two types of fibres: slow- and fast-twitch fibres [15]. Fast-twitch fibres are predominant in muscles capable of short bursts of fast movement and only contain a few mitochondria. These fibres obtain most ATP by glycolysis and increase their glycolytic rate at heavy exercise [16]. Slow-twitch fibres, in contrast, predominate in muscles contracting slowly and steadily. They contain many mitochondria. Astrocytes are a special type of glial cells. They show an interesting metabolic interaction with neurons in the brain. Although both cell types are capable of respiring, astrocytes tend to convert glucose into lactate whereas activated neurons can take up the resulting lactate and degrade it to carbon dioxide and water [17]. The term glycolysis is used in the literature with slightly different meanings; it may refer to the conversion of glucose into pyruvate, being a pre-requisite of respiration. Alternatively, it may denote the conversion of glucose into Biochem. Soc. Trans. (2015) 43, 1187–1194; doi:10.1042/BST20150153 C  2015 Authors; published by Portland Press Limited