Linear programming model can explain respiration of fermentation products

Philip Möller, Xiaochen Liu, Stefan Schuster, Daniel Boley

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


Many differentiated cells rely primarily on mitochondrial oxidative phosphorylation for generating energy in the form of ATP needed for cellular metabolism. In contrast most tumor cells instead rely on aerobic glycolysis leading to lactate to about the same extent as on respiration. Warburg found that cancer cells to support oxidative phosphorylation, tend to ferment glucose or other energy source into lactate even in the presence of sufficient oxygen, which is an inefficient way to generate ATP. This effect also occurs in striated muscle cells, activated lymphocytes and microglia, endothelial cells and several mammalian cell types, a phenomenon termed the “Warburg effect”. The effect is paradoxical at first glance because the ATP production rate of aerobic glycolysis is much slower than that of respiration and the energy demands are better to be met by pure oxidative phosphorylation. We tackle this question by building a minimal model including three combined reactions. The new aspect in extension to earlier models is that we take into account the possible uptake and oxidation of the fermentation products. We examine the case where the cell can allocate protein on several enzymes in a varying distribution and model this by a linear programming problem in which the objective is to maximize the ATP production rate under different combinations of constraints on enzymes. Depending on the cost of reactions and limitation of the substrates, this leads to pure respiration, pure fermentation, and a mixture of respiration and fermentation. The model predicts that fermentation products are only oxidized when glucose is scarce or its uptake is severely limited.

Original languageEnglish (US)
Article numbere0191803
JournalPloS one
Issue number2
StatePublished - Feb 2018

Bibliographical note

Funding Information:
This work was supported by grant 1319749 from the U.S. National Science Foundation to D.B., by the Deutsche Forschungsgemeinschaft (RTG 1715) to P.M. and S.S. and by a University of Jena fellowship to P.M. No other external funding was received for this study. The contents of this paper are solely the responsibility of the authors and do not necessarily represent the official views of any funding agency.

Publisher Copyright:
Copyright: © 2018 Möller et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.


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