A Cellular Automaton Model of Early Tumor Growth and Invasion: The Effects of Native Tissue Vascularity and Increased Anaerobic Tumor Metabolism

Patel, Aalpen A.; Gawlinski, E. T.; Lemieux, Susan K.; Gatenby, Robert A.

doi:10.1006/jtbi.2001.2385

Cited by 234 publications

(176 citation statements)

References 58 publications

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“…Studying the dynamics of glycolysis in terms of collective interactions between cancer cells for the acidification of the extra-cellular environment solves a problem that previous models (Gatenby and Gawlinski, 1996;Patel et al, 2001;Smallbone et al, 2005Smallbone et al, , 2007Basanta et al, 2008Basanta et al, , 2011 of the acid-mediated tumor invasion hypothesis Gawlinski, 1996, 2003;Gatenby and Gillies, 2004 had left unsolved: why does the Warburg effect occur under normal oxygen concentrations? Considering the products of glycolysis as a diffusible public good with nonlinear (non-monotonic) benefits, therefore, enables us to fully explain the Warburg effect.…”

Section: Discussionmentioning

confidence: 99%

“…Models of this acid-mediated tumor invasion hypothesis (Gatenby and Gawlinski, 1996;Patel et al, 2001;Smallbone et al 2005Smallbone et al , 2007Basanta et al, 2008Basanta et al, , 2011Silva et al, 2010) show that cells with increased glycolysis will also evolve resistance to acidinduced toxicity, which can lead indeed to a significant proliferative advantage for the tumor. These models, however, make a crucial assumption: that resistance can only arise in cells with glycolysis (e.g.…”

Section: The Acid-mediated Tumor Invasion Hypothesismentioning

confidence: 99%

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Evolutionary dynamics of the Warburg effect: Glycolysis as a collective action problem among cancer cells

Archetti

2014

Journal of Theoretical Biology

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The upregulation of glycolysis in tumors is common even when oxygen is not limiting. The adaptive value of this "Warburg effect" is unclear. Glycolysis is costly for a cell but the ensuing acidity is beneficial for the tumor. A collective action problem among cancer cells arises. Game theory shows that the acidity induced by glycolysis can explain the Warburg effect. a r t i c l e i n f o a b s t r a c tThe upregulation of glycolysis in cancer cells (the "Warburg effect") is common and has implications for prognosis and treatment. As it is energetically inefficient under adequate oxygen supply, its adaptive value for a tumor remains unclear. It has been suggested that the acidity produced by glycolysis is beneficial for cancer cells because it promotes proliferation against normal cells. Current models of this acid-mediated tumor invasion hypothesis, however, do not account for increased glycolysis under nonlimiting oxygen concentrations and therefore do not fully explain the Warburg effect. Here I show that the Warburg effect can be explained as a form of cooperation among cancer cells, in which the products of glycolysis act as a public good, even when oxygen supply is high enough to make glycolysis energetically inefficient. A multiplayer game with non-linear, non-monotonic payoff functions that models the benefits of the acidity induced by glycolysis reveals that clonal selection can stabilize glycolysis even when energetically costly, that is, under non-limiting oxygen concentration. Characterizing the evolutionary dynamics of glycolysis reveals cases in which anti-cancer therapies that rely on the modification of acidity can be effective.

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Section: Discussionmentioning

confidence: 99%

Section: The Acid-mediated Tumor Invasion Hypothesismentioning

confidence: 99%

Evolutionary dynamics of the Warburg effect: Glycolysis as a collective action problem among cancer cells

Archetti

2014

Journal of Theoretical Biology

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“…A discussion of how cell-centered simulations like CPM can help to explain aspects of developmental biology can be found in Merks and Glazier (2005). Some models in this category (Hogeweg, 2000(Hogeweg, , 2002Tozeren et al, 2005) use cellular automata (Ilachinski, 2001;Wolfram, 1984) to model cell motility and differentiation in order to simulate tumor growth (Dormann and Deutsch, 2002;Patel et al, 2001) and embryogenesis (Longo et al, 2004).…”

Section: Previous Workmentioning

confidence: 99%

A computational model of chemotaxis-based cell aggregation

et al. 2008

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We present a computational model that successfully captures the cell behaviors that play important roles in 2-D cell aggregation. A virtual cell in our model is designed as an independent, discrete unit with a set of parameters and actions. Each cell is defined by its location, size, rates of chemoattractant emission and response, age, life cycle stage, proliferation rate and number of attached cells. All cells are capable of emitting and sensing a chemoattractant chemical, moving, attaching to other cells, dividing, aging and dying. We validated and fine-tuned our in silico model by comparing simulated 24-hour aggregation experiments with data derived from in vitro experiments using PC12 pheochromocytoma cells. Quantitative comparisons of the aggregate size distributions from the two experiments are produced using the Earth Mover's Distance (EMD) metric. We compared the two size distributions produced after 24 hours of in vitro cell aggregation and the corresponding computer simulated process. Iteratively modifying the model's parameter values and measuring the difference between the in silico and and in vitro results allow us to determine the optimal values that produce simulated aggregation outcomes closely matched to the PC12 experiments. Simulation results demonstrate the ability of the model to recreate large-scale aggregation behaviors seen in live cell experiments.

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“…In Patel et al (2001), a CA model of tumour growth in the presence of native vasculature was proposed 4 to analyse the role of host vascular density and tumour metabolism on tumour growth.…”

mentioning

confidence: 99%

“…This has been observed in experiments (Gatenby and Gawlinsky, 1996). The models formulated by Dormann and Deutsch (2002) and Patel et al (2001) are both hybrid CA models. Turner and Sherrat (2002) studied malignant invasion using the extended Potts model (Graner and Glazier, 1992).…”

mentioning

confidence: 99%

Towards whole-organ modelling of tumour growth

Alarcón

Byrne

Maini

2004

Progress in Biophysics and Molecular Biology

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Multiscale approaches to modelling biological phenomena are growing rapidly. We present here some recent results on the formulation of a theoretical framework which can be developed into a fully integrative model for cancer growth. The model takes account of vascular adaptation and cell-cycle dynamics. We explore the effects of spatial inhomogeneity induced by the blood flow through the vascular network and of the possible effects of p27 on the cell cycle. We show how the model may be used to investigate the efficiency of drug-delivery protocols. r

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A Cellular Automaton Model of Early Tumor Growth and Invasion: The Effects of Native Tissue Vascularity and Increased Anaerobic Tumor Metabolism

Cited by 234 publications

References 58 publications

Evolutionary dynamics of the Warburg effect: Glycolysis as a collective action problem among cancer cells

Evolutionary dynamics of the Warburg effect: Glycolysis as a collective action problem among cancer cells

A computational model of chemotaxis-based cell aggregation

Towards whole-organ modelling of tumour growth

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