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2012, 9(4): 843-876. doi: 10.3934/mbe.2012.9.843

Evolution of uncontrolled proliferation and the angiogenic switch in cancer

1. 

Department of Life Sciences, Scottsdale Community College, 9000 E. Chaparral Rd., Scottsdale, AZ 85256, United States

2. 

School of Mathematical and Statistical Sciences, Arizona State University, PO Box 874501, Tempe AZ, 85287-1804, United States

Received  February 2012 Revised  May 2012 Published  October 2012

The major goal of evolutionary oncology is to explain how malignant traits evolve to become cancer "hallmarks." One such hallmark---the angiogenic switch---is difficult to explain for the same reason altruism is difficult to explain. An angiogenic clone is vulnerable to "cheater" lineages that shunt energy from angiogenesis to proliferation, allowing the cheater to outcompete cooperative phenotypes in the environment built by the cooperators. Here we show that cell- or clone-level selection is sufficient to explain the angiogenic switch, but not because of direct selection on angiogenesis factor secretion---angiogenic potential evolves only as a pleiotropic afterthought. We study a multiscale mathematical model that includes an energy management system in an evolving angiogenic tumor. The energy management model makes the counterintuitive prediction that ATP concentration in resting cells increases with increasing ATP hydrolysis, as seen in other theoretical and empirical studies. As a result, increasing ATP hydrolysis for angiogenesis can increase proliferative potential, which is the trait directly under selection. Intriguingly, this energy dynamic allows an evolutionary stable angiogenesis strategy, but this strategy is an evolutionary repeller, leading to runaway selection for extreme vascular hypo- or hyperplasia. The former case yields a tumor-on-a-tumor, or hypertumor, as predicted in other studies, and the latter case may explain vascular hyperplasia evident in certain tumor types.
Citation: John D. Nagy, Dieter Armbruster. Evolution of uncontrolled proliferation and the angiogenic switch in cancer. Mathematical Biosciences & Engineering, 2012, 9 (4) : 843-876. doi: 10.3934/mbe.2012.9.843
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B. Kaur, C. Tan, D. J. Brat, D. E. Post and E. G. Van Meir, Gene and hypoxic regulation of angiogenesis in gliomas, J. Neuro-Oncol., 70 (2004), 229-243. doi: 10.1007/s11060-004-2752-5.

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J. D. Nagy, The ecology and evolutionary biology of cancer: A review of mathematical models of necrosis and tumor cell diversity, Math. Biosci. Eng., 2 (2005), 381-418.

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J. D. Nagy, E. M. Victor and J. H. Cropper, Why don't all whales have cancer? A novel hypothesis resolving Peto's paradox, Int. Comp. Biol., 47 (2007), 317-328. doi: 10.1093/icb/icm062.

[45]

N. Navin, J. Kendall, J. Troge, P. Andrews, L. Rodgers, J. McIndoo, K. Cook, A. Stapansky, D. Levy, D. Esposito, L. Muthuswamy, A. Krasnitz, W. R. McCombie, J. Hicks and M. Wiglerm, Tumour evolution inferred by single-cell sequencing, Nature, 472 (2011), 90-94. doi: 10.1038/nature09807.

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show all references

References:
[1]

B. Alberts, D. Bray, J. Lewis, M. Raff, K. Roberts and J. D. Watson, "Molecular Biology of the Cell," $3^{rd}$ edition, Garland, New York, 1994.

[2]

F. I. Ataullakhanov, S. V. Komarova, M. V. Martynov and V. M. Vitvitsky, A possible role of adenylate metabolism in human erythrocytes: 2. adenylate metabolism is able to improve the erythrocyte volume stabilization, J. Theor. Biol., 183 (1996), 307-316. doi: 10.1006/jtbi.1996.0222.

[3]

F. I. Ataullakhanov, S. V. Komarova and V. M. Vitvitsky, A possible role of adenylate metabolism in human erythrocytes: simple mathematical model, J. Theor. Biol., 179 (1996), 75-86. doi: 10.1006/jtbi.1996.0050.

[4]

F. I. Ataullakhanov and V. M. Vitvitsky, What determines the intracellular ATP concentration?, Biosci. Rep., 22 (2002), 501-511. doi: 10.1023/A:1022069718709.

[5]

F. I. Ataullakhanov, V. M. Vitvitsky, A. M. Zhabotinsky, A. V. Pichugin, O. V. Platonova, B. N. Kholodenko and L. I. Ehrlich, The regulation of glycolysis in human erythrocytes: the dependence of the glycolytic flux on the ATP concentration, Eur. J. Biochem., 115 (1981), 359-365. doi: 10.1111/j.1432-1033.1981.tb05246.x.

[6]

D. E. Atkinson, "Cellular Energy Metabolism and Its Regulation," Academic Press, New York, 1977.

[7]

L. E. Benjamin, I. Hemo and E. Keshet, A plasticity window for blood vessel remodelling is defined by pericyte coverage of the preformed endothelial network and is regulated by PDGF-B and VEGF, Development, 125 (1998), 1591-1598.

[8]

T. Bønsdorff, M. Gautier, W. Farstad, K. Rønningen, F. Lingaas and I. Olsaker, Mapping of the bovine genes of the de novo AMP synthesis pathway, Anim. Genet., 35 (2004), 438-444. doi: 10.1111/j.1365-2052.2004.01201.x.

[9]

J. J. Boza, D. Moënnoz, C. E. Bournot, S. Blum, I. Zbinden, P. A. Finot and O. Ballèvre, Role of glutamine on the de novo purine nucleotide synthesis in Caco-2 cells, Eur. J. Nutr., 39 (2000), 38-46.

[10]

D. J. Brat and E. G. Van Meir, Vaso-occlusive and prothrombotic mechanisms associated with tumor hypoxia, necrosis, and accelerated growth in glioblastoma, Lab. Invest., 84 (2004), 397-405. doi: 10.1038/labinvest.3700070.

[11]

J. P. Collins, "Evolutionary ecology" and the use of natural selection in ecological theory, J. Hist. Biol., 19 (1986), 257-288. doi: 10.1007/BF00138879.

[12]

J. de Grouchy and C. de Nava, A chromosomal theory of carcinogenesis, Ann. Intern. Med., 69 (1968), 381-391.

[13]

F. Du, X.-H. Zhu, Y. Zhang, M. Friedman, N. Zhang adn K. Uqurbil and W. Chen, Tightly coupled brain activity and cerebral ATP metabolic rate, Proc. Nat. Acad. Sci. USA, 105 (2008), 6409-6414. doi: 10.1073/pnas.0710766105.

[14]

I. F. Dunn, O. Heese and P. McL. Black, Growth factors in glioma angiogenesis: FGFs, PDGF, EGF, and TGFs, J. Neuro-Onco., 50 (2000), 121-137. doi: 10.1023/A:1006436624862.

[15]

D. Gammack, H. M. Byrne and C. E. Lewis, Estimating the selective advantage of mutant p53 tumour cells to repeated rounds of hypoxia, Bull. Math. Biol., 63 (2001), 135-166. doi: 10.1006/bulm.2000.0210.

[16]

S. A. H. Geritz, É. Kisdi, G. Meszéna and J. A. J. Metz, Evolutionarily singular stategies and the adaptive growth and branching of the evolutionary tree, Evol. Ecol., 12 (1998), 35-57. doi: 10.1023/A:1006554906681.

[17]

A. C. Giese, "Cell Physiology," $5^{th}$ edition, Saunders, Philadelphia, 1973.

[18]

M. Greaves, Darwinian medicine: A case for cancer, Nature Rev. Cancer, 7 (2007), 213-221.

[19]

M. Greaves and C. C. Maley, Clonal evolution in cancer, Nature, 481 (2012), 306-313. doi: 10.1038/nature10762.

[20]

D. Hanahan and J. Folkman, Patterns and emerging mechanisms of the angiogenic switch during tumorigenesis, Cell, 86 (1996), 353-364. doi: 10.1016/S0092-8674(00)80108-7.

[21]

D. Hanahan and R. A. Weinberg, The hallmarks of cancer, Cell, 100 (2000), 57-70. doi: 10.1016/S0092-8674(00)81683-9.

[22]

D. Hanahan and R. A. Weinberg, Hallmarks of cancer: The next generation, Cell, 144 (2011), 646-674. doi: 10.1016/j.cell.2011.02.013.

[23]

D. G. Hardie, D. Carling and M. Carlson, The AMP-activated/SNF1 protein kinase subfamily: Metabolic sensors of the eukaryotic cell?, Ann. Rev. Biochem., 67 (1998), 821-855. doi: 10.1146/annurev.biochem.67.1.821.

[24]

T. S. Hauschka, The chromosomes in ontogeny and oncogeny, Cancer Res., 21 (1961), 957-974.

[25]

J. Holash, P. C. Maisonpierre, D. Compton, P. Boland, C. R. Alexander, D. Zagzag, G. D. Yancopolous and S. J. Weigand, Vessel cooperation, regression and growth in tumors mediated by angiopoietins and VEGF, Science, 221 (1998), 1994-1998.

[26]

J. Maynard Smith, "Evolution and the Theory of Games," Cambridge University Press, Cambridge, 1982.

[27]

J. Maynard Smith and G. R. Price, The logic of animal conflict, Nature, 246 (1973), 15-18. doi: 10.1038/246015a0.

[28]

A. Joshi and B. O. Palsson, Metabolic dynamics in the human red cell. Parts 1-2, J. Theor. Biol., 141 (1989), 515-545. doi: 10.1016/S0022-5193(89)80233-4.

[29]

A. Joshi and B. O. Palsson, Metabolic dynamics in the human red cell. Parts 3-4, J. Theor. Biol., 142 (1990), 41-85. doi: 10.1016/S0022-5193(05)80012-8.

[30]

W. G. Kaelin and P. J. Ratcliffe, Oxygen sensiing by metazoans: The central role of the HIF hydroxylase pathway, Mol. Cell, 30 (2008), 393-402. doi: 10.1016/j.molcel.2008.04.009.

[31]

G. Karoubi, D. J. Stewart and D. W. Courtman, A population analysis of VEGF transgene expression and secretion, Biotech. Bioeng., 101 (2008), 1083-1093. doi: 10.1002/bit.21993.

[32]

B. Kaur, C. Tan, D. J. Brat, D. E. Post and E. G. Van Meir, Gene and hypoxic regulation of angiogenesis in gliomas, J. Neuro-Oncol., 70 (2004), 229-243. doi: 10.1007/s11060-004-2752-5.

[33]

D. G. Kilburn, M. D. Lilly and F. C. Webb, The energetics of mammalian cell growth, J. Cell Sci., 4 (1969), 645-654.

[34]

L. A. Lai, R. Kostadivov, M. T. Barrett, D. A. Peiffer, D. Pokholok, R. Odze, C. A. Sanchez, C. C. Maley, B. J. Reid, K. L. Gunderson and P. S. Rabinovitch, Deletion at fragile sites is a common and early event in Barrett's esophagus, Mol. Cancer Res., 8 (2010), 1084-1094.

[35]

L. W. Law, Origin of the resistance of leukaemic cells to folic acid antagonists, Nature, 169 (1952), 628-629. doi: 10.1038/169628a0.

[36]

A. M. Leroi, V. Koufopanou and A. Burt, Cancer selection, Nature Rev. Cancer, 3 (2003), 226-231.

[37]

A. Levan and J. J. Biesele, Role of chromosomes in cancerogenesis, as studied in serial tissue culture of mammalian cells, Ann. N. Y. Acad. Sci., 71 (1958), 1022-1053. doi: 10.1111/j.1749-6632.1958.tb46820.x.

[38]

M. V. Martinov, A. G. Plotnikov, V. M. Vitvitsky and F. I. Ataullakhanov, Deficiencies of glycolytic enzymes as a possible cause of hemolytic anemia, Biochim. Biophys. Acta, 1474 (2000), 75-87. doi: 10.1016/S0304-4165(99)00218-4.

[39]

L. M. Merlo, J. W. Pepper, B. J. Reid and C. C. Maley, Cancer as an evolutionary and ecological process, Nature Rev. Cancer, 6 (2006), 924-935.

[40]

L. M. Merlo, N. A. Shah, X. Li, P. L. Blount, T. L. Vaughan, B. J. Reid and C. C. Maley, A comprehensive survey of clonal diversity measures in Barrett's esophagus as biomarkers of progression to esophageal adenocarcinoma, Cancer Prev. Res., 3 (2010), 1388-1397.

[41]

J. A. J. Metz, R. Nesbit and S. A. H. Geritz, How should we define 'fitness' for general ecological scenarios?, Trends Ecol. Evol., 7 (1992), 198-202.

[42]

J. D. Nagy, Competition and natural selection in a mathematical model of cancer, Bull. Math. Biol., 66 (2004), 663-687. doi: 10.1016/j.bulm.2003.10.001.

[43]

J. D. Nagy, The ecology and evolutionary biology of cancer: A review of mathematical models of necrosis and tumor cell diversity, Math. Biosci. Eng., 2 (2005), 381-418.

[44]

J. D. Nagy, E. M. Victor and J. H. Cropper, Why don't all whales have cancer? A novel hypothesis resolving Peto's paradox, Int. Comp. Biol., 47 (2007), 317-328. doi: 10.1093/icb/icm062.

[45]

N. Navin, J. Kendall, J. Troge, P. Andrews, L. Rodgers, J. McIndoo, K. Cook, A. Stapansky, D. Levy, D. Esposito, L. Muthuswamy, A. Krasnitz, W. R. McCombie, J. Hicks and M. Wiglerm, Tumour evolution inferred by single-cell sequencing, Nature, 472 (2011), 90-94. doi: 10.1038/nature09807.

[46]

G. Neufeld, T. Cohen, S. Gengrinovitch and Z. Poltorak, Vascular endothelial growth factor and its receptors, FASEB J., 13 (1999), 9-22.

[47]

P. C. Nowell, The clonal evolution of tumor cell populations, Science, 194 (1976), 23-28. doi: 10.1126/science.959840.

[48]

K. Parvinen, Evolutionary suicide, Acta Biotheor., 53 (2005), 241-264. doi: 10.1007/s10441-005-2531-5.

[49]

K. Pavlov and C. C. Maley, New models of neoplastic progression in Barrett's esophagus, Biochem. Soc. Trans., 38 (2010), 331-336. doi: 10.1042/BST0380331.

[50]

C. M. Perrins, Survival of young swifts in relation to brood size, Nature, 201 (1964), 1147-1148. doi: 10.1038/2011147b0.

[51]

K. H. Plate, G. Breier, H. A. Weich and W. Risau, Vascular endothelial growth factor is a potent tumour angiogenesis factor in human gliomas in vivo, Nature, 359 (1992), 845-848. doi: 10.1038/359845a0.

[52]

C. M. Robbins, W. A. Tembe, A. Baker, S. Sinari, T. Y. Moses, S. Beckstrom-Sternberg, J. Beckstrom-Sternberg, M. Barrett, J. Long, A. Chinnaiyan, J. Lowey, E. Suh, J. V. Pearson, D. W. Craig, D. B. Angus, K. J. Pienta and J. D. Carpten, Copy number and targeted mutational analysis reveals novel somatic events in metastatic prostate tumors, Genome Res., 21 (2011), 47-55. doi: 10.1101/gr.107961.110.

[53]

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