Exact solution of a two-type branching process: Models of tumor progression

Journal of Statistical Mechanics: Theory and Experiment

Volumn 2011, Issue 8, 2011, Pages

  Antal, Tibor ^a   Krapivsky, P L ^b  

^a UNIVERSITY OF EDINBURGH   (United Kingdom)

^b Boston University   (United States)

Author keywords

exact results; mutational and evolutionary processes (theory); population dynamics (theory); stochastic processes (theory)

Indexed keywords

EID: 80053480439     PISSN: None     EISSN: 17425468     Source Type: Journal    
DOI: 10.1088/1742-5468/2011/08/P08018     Document Type: Article

References (37)

1. Frank S A 2007 Dynamics of Cancer: Incidence, Inheritance, and Evolution (Princeton, NJ: Princeton University Press)
2. Attolini C S O and Michor F 2009 Evolutionary theory of cancer Ann. NY Acad. Sci. 1168 23
3. Armitage P and Doll R 2004 The age distribution of cancer and a multi-stage theory of carcinogenesis 1954 Int. J. Epidemiol. 33 1174
4. Knudson A 1971 Mutation and cancer - statistical study of retinoblastoma Proc. Nat. Acad. Sci. 68 820
5. Kern S E 2002 Research philosopy - whose hypothesis? Ciphering, sectorials, d lesions, freckles and the operation of stigler's law Cancer Biol. Ther. 1 571
6. Weinberg R A 2007 The Biology of Cancer (New York: Garland Sciences, Taylor and Francis)
7. Vogelstein B and Kinzler K W 2002 The Genetic Basis of Human Cancer 2nd edn (New York: McGraw-Hill, Medical Pub. Division)
8. Nowak M A 2006 Evolutionary Dynamics: Exploring the Equations of Life (Cambridge, MA: Harvard University Press)
9. Harris T E 1963 The Theory of Branching Processes (New York: Dover)
10. Athreya K B and Ney P 1972 Branching Processes (Berlin: Springer)
11. Kimmel M and Axelrod D E 2002 Branching Processes in Biology (New York: Springer)
12. Haccou P, Jagers P and Vatutin V A 2005 Branching Processes: Variation, Growth, and Extinction of Populations (Cambridge: Cambridge University Press)
13. Bartlett M S 1955 An Introduction to Stochastic Processes: with Special Reference to Methods and Applications (Cambridge: University Press)
14. Zheng Q 1999 Progress of a half century in the study of the Luria-Delbruck distribution Math. Biosci. 162 1
15. Pharr P N, Nedelman J, Downs H P, Ogawa M and Gross A J 1985 A stochastic model for mast cell proliferation in culture J. Cell. Physiol. 125 379
16. Kendall D G 1960 Birth-and-death processes, and the theory of carcinogenesis Biometrika 47 13
17. Luebeck E and Moolgavkar S 2002 Multistage carcinogenesis and the incidence of colorectal cancer Proc. Nat. Acad. Sci. 99 15095
18. Iwasa Y, Nowak M and Michor F 2006 Evolution of resistance during clonal expansion Genetics 172 2557
19. Komarova N 2006 Stochastic modeling of drug resistance in cancer J. Theor. Biol. 239 351
20. Bozic I, Antal T, Ohtsuki H, Carter H, Kim D, Chen S, Karchin R, Kinzler K W, Vogelstein B and Nowak M A 2010 Accumulation of driver and passenger mutations during tumor progression Proc. Nat. Acad. Sci. 107 18545
21. Durrett R and Moseley S 2010 Evolution of resistance and progression to disease during clonal expansion of cancer Theor. Popul. Biol. 77 42-48
22. Clayton E, Doupe D P, Klein A M, Winton D J, Simons B D and Jones P H 2007 A single type of progenitor cell maintains normal epidermis Nature 446 185
23. Antal T and Krapivsky P L 2010 Exact solution of a two-type branching process: clone size distribution in cell division kinetics J. Stat. Mech. P07028
24. Michor F, Nowak M and Iwasa Y 2006 Stochastic dynamics of metastasis formation J. Theor. Biol. 240 521
25. Dingli D, Michor F, Antal T and Pacheco J M 2007 The emergence of tumor metastases Cancer Biol. Ther. 6 383
26. Yachida S et al 2010 Distant metastasis occurs late during the genetic evolution of pancreatic cancer Nature 467 1114
27. Fearon E R and Vogelstein B 1990 A genetic model for colorectal tumorigenesis Cell 61 759
28. Beerenwinkel N, Antal T, Dingli D, Traulsen A, Kinzler K W, Velculescu V E, Vogelstein B and Nowak M A 2007 Genetic progression and the waiting time to cancer PLoS Comput. Biol. 3 2239
29. Durrett R, Foo J, Leder K, Mayberry J and Michor F 2010 Evolutionary dynamics of tumor progression with random fitness values Theor. Popul. Biol. 78 54
30. Klein A M, Brash D E, Jones P H and Simons B D 2010 Stochastic fate of p53-mutant epidermal progenitor cells is tilted toward proliferation by uv b during preneoplasia Proc. Nat. Acad. Sci. 107 270
31. Klein A M, Doupe D P, Jones P H and Simons B D 2007 Kinetics of cell division in epidermal maintenance Phys. Rev. E 76 021910
32. Bender C M and Orszag S A 1978 Advanced Mathematical Methods for Scientists and Engineers (International Series in Pure and Applied Mathematics) (New York: McGraw-Hill)
33. Antal T and Krapivsky P L 2011 Multiple-type critical branching processes in preparation
34. Jones S et al 2008 Comparative lesion sequencing provides insights into tumor evolution Proc. Nat. Acad. Sci. 105 4283
35. Fearon E R, Hamilton S R and Vogelstein B 1987 Clonal analysis of human colorectal tumors Science 238 193
36. Gradshtein I S, Ryzhik I M and Jeffrey A 2000 Table of Integrals, Series, and Products (San Diego, CA: Academic)
37. Olver F W J 2010 NIST Handbook of Mathematical Functions (Cambridge: Cambridge University Press)