A Mathematical Solution to Peto's Paradox Using Polya's Urn Model: Implications for the Aetiology of Cancer in General

Overview

Journal Theory Biosci

Specialty Biology

Date 2019 Feb 17

PMID 30771154

Citations 3

Authors

Anastasio Salazar-Banuelos

Affiliations

Soon will be listed here.

Abstract

Ageing is the leading risk factor for the emergence of cancer in humans. Accumulation of pro-carcinogenic events throughout life is believed to explain this observation; however, the lack of direct correlation between the number of cells in an organism and cancer incidence, known as Peto's Paradox, is at odds with this assumption. Finding the events responsible for this discrepancy can unveil mechanisms with potential uses in prevention and treatment of cancer in humans. On the other hand, the immune system is important in preventing the development of clinically relevant tumours by maintaining a fine equilibrium between reactive and suppressive lymphocyte clones. It is suggested here that the loss of this equilibrium is what ultimately leads to increased risk of cancer and to propose a mechanism for the changes in clonal proportions based on decreased proliferative capacity of lymphocyte clones as a natural phenomenon of ageing. This mechanism, being a function of the number of cells, provides an explanation for Peto's Paradox.

Citing Articles

Revealing endogenous conditions for Peto's paradox via an ordinary differential equation model.

Kan H, Chen Y J Math Biol. 2024; 89(2):27.

PMID: 38970664 PMC: 11227477. DOI: 10.1007/s00285-024-02123-7.

The molecular evolution of cancer associated genes in mammals.

MacDonald N, Raven N, Diep W, Evans S, Pannipitiya S, Bramwell G Sci Rep. 2024; 14(1):11650.

PMID: 38773187 PMC: 11109183. DOI: 10.1038/s41598-024-62425-0.

TERT promoter alterations could provide a solution for Peto's paradox in rodents.

Vedelek B, Maddali A, Davenova N, Vedelek V, Boros I Sci Rep. 2020; 10(1):20815.

PMID: 33257697 PMC: 7704627. DOI: 10.1038/s41598-020-77648-0.

References

Ebbesen P . Cancer and normal ageing. Mech Ageing Dev. 1984; 25(3):269-83. DOI: 10.1016/0047-6374(84)90001-0. View

Vaz N, Varela F . Self and non-sense: an organism-centered approach to immunology. Med Hypotheses. 1978; 4(3):231-67. DOI: 10.1016/0306-9877(78)90005-1. View

Rozhok A, Salstrom J, DeGregori J . Stochastic modeling indicates that aging and somatic evolution in the hematopoetic system are driven by non-cell-autonomous processes. Aging (Albany NY). 2015; 6(12):1033-48. PMC: 4298364. DOI: 10.18632/aging.100707. View

Myers K, Bleesing J, Davies S, Zhang X, Martin L, Mueller R . Impaired immune function in children with Fanconi anaemia. Br J Haematol. 2011; 154(2):234-40. PMC: 5922775. DOI: 10.1111/j.1365-2141.2011.08721.x. View

Burnet M . Cancer: a biological approach. III. Viruses associated with neoplastic conditions. IV. Practical applications. Br Med J. 1957; 1(5023):841-7. PMC: 1973618. DOI: 10.1136/bmj.1.5023.841. View

Smyth M, Dunn G, Schreiber R . Cancer immunosurveillance and immunoediting: the roles of immunity in suppressing tumor development and shaping tumor immunogenicity. Adv Immunol. 2006; 90:1-50. DOI: 10.1016/S0065-2776(06)90001-7. View

Nagy J, Victor E, Cropper J . Why don't all whales have cancer? A novel hypothesis resolving Peto's paradox. Integr Comp Biol. 2011; 47(2):317-28. DOI: 10.1093/icb/icm062. View

Khatami M . Inflammation, aging, and cancer: tumoricidal versus tumorigenesis of immunity: a common denominator mapping chronic diseases. Cell Biochem Biophys. 2009; 55(2):55-79. DOI: 10.1007/s12013-009-9059-2. View

Koebel C, Vermi W, Swann J, Zerafa N, Rodig S, Old L . Adaptive immunity maintains occult cancer in an equilibrium state. Nature. 2007; 450(7171):903-7. DOI: 10.1038/nature06309. View

10.

Poutahidis T, Kleinewietfeld M, Erdman S . Gut microbiota and the paradox of cancer immunotherapy. Front Immunol. 2014; 5:157. PMC: 3985000. DOI: 10.3389/fimmu.2014.00157. View

11.

Freitas A, Rocha B, COUTINHO A . Lymphocyte population kinetics in the mouse. Immunol Rev. 1986; 91:5-37. DOI: 10.1111/j.1600-065x.1986.tb01482.x. View

12.

Kodama K, Ozasa K, Okubo T . Radiation and cancer risk in atomic-bomb survivors. J Radiol Prot. 2012; 32(1):N51-4. DOI: 10.1088/0952-4746/32/1/N51. View

13.

Cosette J, Moussy A, Onodi F, Auffret-Cariou A, Neildez-Nguyen T, Paldi A . Single Cell Dynamics Causes Pareto-Like Effect in Stimulated T Cell Populations. Sci Rep. 2015; 5:17756. PMC: 4673432. DOI: 10.1038/srep17756. View

14.

Rocha B, Penit C, Baron C, Vasseur F, Dautigny N, Freitas A . Accumulation of bromodeoxyuridine-labeled cells in central and peripheral lymphoid organs: minimal estimates of production and turnover rates of mature lymphocytes. Eur J Immunol. 1990; 20(8):1697-708. DOI: 10.1002/eji.1830200812. View

15.

Burnet M . Cancer; a biological approach. I. The processes of control. Br Med J. 1957; 1(5022):779-86. PMC: 1973174. DOI: 10.1136/bmj.1.5022.779. View

16.

Henry C, Marusyk A, DeGregori J . Aging-associated changes in hematopoiesis and leukemogenesis: what's the connection?. Aging (Albany NY). 2011; 3(6):643-56. PMC: 3164372. DOI: 10.18632/aging.100351. View

17.

Evans C, Ho Y, Daveson B, Hall S, Higginson I, Gao W . Place and cause of death in centenarians: a population-based observational study in England, 2001 to 2010. PLoS Med. 2014; 11(6):e1001653. PMC: 4043499. DOI: 10.1371/journal.pmed.1001653. View

18.

Dunn G, Bruce A, Ikeda H, Old L, Schreiber R . Cancer immunoediting: from immunosurveillance to tumor escape. Nat Immunol. 2002; 3(11):991-8. DOI: 10.1038/ni1102-991. View

19.

Day N . The Armitage-Doll multistage model of carcinogenesis. Stat Med. 1990; 9(6):677-9. DOI: 10.1002/sim.4780090614. View

20.

Kihara K, Fujita S, Ohshiro T, Yamamoto S, Sekine S . Spontaneous regression of colon cancer. Jpn J Clin Oncol. 2014; 45(1):111-4. DOI: 10.1093/jjco/hyu170. View