Bulletin of Mathematical Biology

, Volume 80, Issue 5, pp 954–970 | Cite as

Adaptation to Stochastic Temporal Variations in Intratumoral Blood Flow: The Warburg Effect as a Bet Hedging Strategy

  • Curtis A. Gravenmier
  • Miriam Siddique
  • Robert A. Gatenby
Special Issue : Mathematical Oncology


While most cancers promote ingrowth of host blood vessels, the resulting vascular network usually fails to develop a mature organization, resulting in abnormal vascular dynamics with stochastic variations that include slowing, cessation, and even reversal of flow. Thus, substantial spatial and temporal variations in oxygen concentration are commonly observed in most cancers. Cancer cells, like all living systems, are subject to Darwinian dynamics such that their survival and proliferation are dependent on developing optimal phenotypic adaptations to local environmental conditions. Here, we consider the environmental stresses placed on tumors subject to profound, frequent, but stochastic variations in oxygen concentration as a result of temporal variations in blood flow. While vascular fluctuations will undoubtedly affect local concentrations of a wide range of molecules including growth factors (e.g., estrogen), substrate (oxygen, glucose, etc.), and metabolites (\(\hbox {H}^{+})\), we focus on the selection forces that result solely from stochastic fluctuations in oxygen concentration. The glucose metabolism of cancer cells has been investigated for decades following observations that malignant cells ferment glucose regardless of oxygen concentration, a condition termed the Warburg effect. In contrast, normal cells cease fermentation under aerobic conditions and this physiological response is termed the Pasteur effect. Fermentation is markedly inefficient compared to cellular respiration in terms of adenosine triphosphate (ATP) production, generating just 2 ATP/glucose, whereas respiration generates 38 ATP/glucose. This inefficiency requires cancer cells to increase glycolytic flux, which subsequently increases acid production and can significantly acidify local tissue. Hence, it initially appears that cancer cells adopt a disadvantageous metabolic phenotype. Indeed, this metabolic “hallmark” of cancer is termed “energy dysregulation.” However, if cancers arise through an evolutionary optimization process, any common observed property must confer an adaptive advantage. In the present work, we investigate the hypothesis that aerobic glycolysis represents an adaptation to stochastic variations in oxygen concentration stemming from disordered intratumoral blood flow. Using mathematical models, we demonstrate that the Warburg effect evolves as a conservative metabolic bet hedging strategy in response to stochastic fluctuations of oxygen. Specifically, the Warburg effect sacrifices fitness in physoxia by diverting resources from the more efficient process of respiration, but preemptively adapts cells to hypoxia because fermentation produces ATP anaerobically. An environment with sufficiently stochastic fluctuations of oxygen will select for the bet hedging (Warburg) phenotype since it is modestly successful irrespective of oxygen concentration.


Tumor metabolism Intermittent hypoxia Bet hedging Warburg effect 



This work was supported by a James S. McDonnell Foundation Grant, the V Foundation for Cancer Research, “Cancer Therapy: Perturbing a Complex Adaptive System,” NIH/National Cancer Institute (NCI) R01CA170595, Application of Evolutionary Principles to Maintain Cancer Control (PQ21), and NIH/NCI U54CA143970-05 [Physical Science Oncology Network (PSON)] “Cancer as a Complex Adaptive System.” CG was supported by an Alpha Omega Alpha Carolyn L. Kuckein Fellowship.


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Copyright information

© Society for Mathematical Biology 2017

Authors and Affiliations

  1. 1.University of South Florida School of MedicineTampaUSA
  2. 2.Cancer Biology and Evolution ProgramMoffitt Cancer CenterTampaUSA

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