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

Abstract

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 ([Formula: see text], 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.

A mathematical dissection of the adaptation of cell populations to fluctuating oxygen levels

“…Previous empirical and theoretical work has suggested that cycling hypoxia makes it necessary for cancer cells to adapt to fluctuating environmental conditions (Gillies et al, 2018;Amend et al, 2018) and impacts on tumour growth by increasing clonal diversity, promoting metastasis and supporting more plastic phenotypic variants (Cairns et al, 2001;Cairns and Hill, 2004;Louie et al, 2010;Verduzco et al, 2015;Chen et al, 2018;Saxena and Jolly, 2019). In particular, it has been hypothesised that -by analogy with bacterial populations facing unpredictable environmental changes (Kussell and Leibler, 2005;Smits et al, 2006;Veening et al, 2008;Acar et al, 2008;Beaumont et al, 2009;Nichol et al, 2016) -cancer cell populations could utilise risk spreading through stochastic phenotype switching, which is also known as bet-hedging (Philippi and Seger, 1989), as an adaptive strategy to survive in the harsh, constantly changing environmental conditions associated with cycling hypoxia (Gravenmier et al, 2018;Gillies et al, 2018).…”

Applications of mechanistic modelling to clinical and experimental immunology: an emerging technology to accelerate immunotherapeutic discovery and development

“…These hypotheses have been subsequently supported by experimental studies [20,21]. A more recent model [22] proposed a mechanism for the Warburg effect to arise even in oxygenated tumours, despite the apparent loss of fitness (Fig. 3b).…”

“…Models have enhanced mechanistic insight into tumour progression and metastasis, providing unexpected insights into the role of pH in the microenvironment to facilitate invasion of surrounding tissue (Fig. A more recent model [22] proposed a mechanism for the Warburg effect to arise even in oxygenated tumours, despite the apparent loss of fitness (Fig. The mathematical equations of one such model [20] predicted the existence of a pH gradient from the tumour periphery into healthy tissue, which was hypothesised to induce an acellular gap around the tumour and the remodelling of tissue to facilitate tumour invasion.…”

“…One such model was used to explore whether chemokines could attract T cells to antigen-expressing dendritic cells [31] (Fig. [20] (b) provided an evolutionary basis for the Warburg effect, as neoplastic cells that outcompete other cells in low oxygen concentrations (green shaded region) have a fitness advantage in an environment with variable oxygen concentrations (shown by the black line) and take over the tumour population (background of plot) [22]; (c) showed how moderate therapy improves patient survival over intensive therapy, that may select for resistant cells [23]; (d) showed that a less intense, more frequent therapy schedule improves survival in a dynamic model of resistance [24]; (e) predicted patient survival in a phase III clinical trial of a drug by parameterising tumour and survival models [2]. These authors found that an optimum search strategy cannot include such an effect, as although it increases the number of T cell-dendritic cell contacts per unit time, it sharply reduces the number of unique contacts due to crowding around dendritic cells.…”

“…Another model was used to determine whether the 'runand-tumble' motion exhibited by T cells (as opposed to diffusion) is due to an intrinsic, stochastic process, or whether it can be explained by the lymph node environment [32], and was developed in parallel with 4D multiphoton imaging experiments to validate model predictions. [20] (b) provided an evolutionary basis for the Warburg effect, as neoplastic cells that outcompete other cells in low oxygen concentrations (green shaded region) have a fitness advantage in an environment with variable oxygen concentrations (shown by the black line) and take over the tumour population (background of plot) [22]; (c) showed how moderate therapy improves patient survival over intensive therapy, that may select for resistant cells [23]; (d) showed that a less intense, more frequent therapy schedule improves survival in a dynamic model of resistance [24]; (e) predicted patient survival in a phase III clinical trial of a drug by parameterising tumour and survival models [2].…”