A carcinogenesis model describing mutational events at the DNA adduct level

Mathematical Biosciences

Volumn 144, Issue 1, 1997, Pages 23-45

  Zheng, Qi ^a   Lutz, Werner K ^b   Gaylor, David W ^a  

^a NATIONAL CENTER FOR TOXICOLOGICAL RESEARCH   (United States)

^b UNIVERSITY OF WÜRZBURG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ADENINE; CARCINOGEN; CYTOSINE; DNA; GUANINE; THYMINE;

ANIMAL CELL; APOPTOSIS; ARTICLE; CARCINOGENESIS; CELL PROLIFERATION; DNA ADDUCT; LIVER CELL; MATHEMATICAL ANALYSIS; MUTATION; NONHUMAN; NUCLEIC ACID BASE SUBSTITUTION; RAT; STOCHASTIC MODEL;

ANIMALIA;

EID: 0030771695     PISSN: 00255564     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0025-5564(97)00005-9     Document Type: Article

References (50)

1. P. Armitage and R. Doll, The age distribution of cancer and a multistage theory of cancer. Br. J. Cancer 8:1-12 (1954).
2. P. Armitage and R. Doll, A two-stage theory of carcinogenesis in relation to the age distribution of human cancer. Br. J. Cancer 11:161-169 (1957).
3. J. D. Kalbfleisch, D. R. Krewski, and J. Van Ryzin, Dose-resposne models for time-to-response toxicity data. Can. J. Stat. 11:25-49 (1983).
4. D. Krewski, M. J. Goddard, and J. M. Zielinski, Dose-response relationships in carcinogenesis. In Mechanisms of Carcinogenesis in Risk Identification, H. Vaninio, P. N. Magee, D. B. McGregor, and A. J. McMichael, ed., IARC, Lyon, 1992, pp. 579-599.
5. S. M. Cohen and L. B. Ellwein, Cell proliferation in carcinogenesis. Science 249:1007-1011 (1990).
6. L. M. Schwartz and B. A. Osborne, Programmed cell death, apoptosis and killer genes. Immunol. Today 14:582-590 (1993).
7. G. T. Williams, Programmed cell death: apoptosis and oncogenesis. Cell 65:1097-1098 (1991).
8. D. G. Kendall, Birth-and-death process, and the theory of carcinogenesis. Biometrika 47:13-21 (1960).
9. J. Neyman, A two-step mutation theory of carcinogenesis. Bull. Inst. Int. Stat. 38:123-135 (1961).
10. J. Neyman and E. Scott, Statistical aspect of the problem of carcinogenesis. Proceedings of the Fifth Symposium on Mathematical Statistics and Probability, vol. 4, pp. 745-776, University of California Press, Berkeley, 1967.
11. S. H. Moolgavkar and D. J. Venzon, Two-event models for carcinogenesis: incidence curves for childhood and adult tumors. Math. Biosci. 47:55-77 (1979).
12. S. H. Moolgavkar and A. G. Knudson, Mutation and cancer: a model for human carcinogenesis. J. Natl. Cancer Inst. 66:1037-1052 (1981).
13. S. H. Moolgavkar and G. Luebeck, Two-event model for carcinogenesis: biological, mathematical and statistical considerations. Risk Anal. 10:323-341 (1990).
14. W. Y. Tan, Stochastic Models of Carcinogenesis. Marcel Dekker, New York, 1991.
15. A. Dewanji, S. H. Moolgavkar, and E. G. Luebeck, Two-mutation model for carcinogenesis: joint analysis of premalignant and malignant lesions. Math. Biosci. 104:97-109 (1991).
16. M. C. M. De Gunst and E. G. Luebeck, Quantitative analysis of two-dimensional observations of premalignant clones in the presence or absence of malignant tumors. Math. Biosci. 119:5-34 (1994).
17. A. Kopp-Schneider, C. J. Portier, and C. D. Sherman, The exact formula for tumor incidence in the two-stage model. Risk Anal. 14:1079-1080 (1994).
18. Q. Zheng, On the exact hazard and survival functions of the MVK stochastic carcinogenesis model. Risk Anal. 14:1081-1084 (1994).
19. W. K. Lutz, Endogenous genotoxic agents and processes as a basis of spontaneous carcinogenesis. Mutat. Res. 238:287-295 (1990).
20. C. J. Portier and A. Kopp-Schneider, A multistage model of carcinogenesis incorporating DNA damage and repair. Risk Anal. 11:535-543 (1991).
21. A. Kopp-Schneider, C. J. Portier, and F. Rippmann, The application of a multistage model that incorporates DNA damage and repair to the analysis of initiation/promotion experiments. Math. Biosci. 105:139-166 (1991).
22. W. K. Lutz, Inducible repair of DNA methylated by carcinogens. Trends Pharmac. Sci. 3:398-399 (1982).
23. C. C. Harris, K. Vahakangas, M. J. Newman, G. E. Trivers, A. K. M. Sinopoli, N. T. Mann, and W. E. Wright, Detection of benzo[a]pyrene diol epoxide-DNA adducts in peripheral blood lymphocytes and antibodies to the adducts in serum from coke oven workers. Proc. Natl. Acad. Sci. USA 82:6672-6676 (1985).
24. K. Hemminki, A. Dipple, D. E. G. Shuker, F. F. Kadlubar, D. Segerbäck, and H. Bartsch, eds., DNA Adducts: Identification and Biological Significance. IARC Scientific Publication No. 125 (1994).
25. D. H. Phillips, M. Castegnaro, and H. Bartsch, eds., Postlabelling Methods for Detection of DNA Adducts. IRAC Scientific Publication No. 124 (1993).
26. P. Toniolo, P. Boffetta, D. Shuker, N. Rothman, B. Hulka, and N. Pearce, eds., Application of Biomarkers to Cancer Epidemiology. IRAC Scientific Publication No. 142 (1996).
27. W. K. Lutz, Quantitative evaluation of DNA binding data for risk estimation and for classification of direct and indirect carcinogens. J. Cancer Res. Clin. Oncol. 112:85-91 (1986).
28. W. K. Lutz, Dose-response relationship and low dose extrapolation in chemical carcinogenesis. Carcinogenesis 11:1243-1247 (1990).
29. J. A. Swenberg, F. C. Richardson, J. A. Boucheron, and M. J. Dyroff, Relationships between DNA adduct formation and carcinogenesis. Environ. Health Perspect. 62:177-183 (1985).
30. C. C. Harris, Chemical and physical carcinogenesis: advances and perspectives for the 1990s. Cancer Res. 51(Suppl.):5023-5044 (1991).
31. W. K. Lutz, In vivo covalent binding of organic chemicals to DNA as quantitative indicator in the process of chemical carcinogenesis. Mutat. Res. 65:289-356 (1979).
32. M. Hollstein, D. Sidransky, B. Vogelstein, and C. C. Harris, P53 mutation in human cancers. Science 253:49-53 (1991).
33. M. S. Greenblatt, W. P. Bennett, M. Hollstein, and C. C. Harris, Mutations in the p53 tumor suppressor gene: clues to cancer etiology and molecular pathogenesis. Cancer Res. 54:4855-4878 (1994).
34. Q. Zheng, On the MVK stochastic carcinogenesis model with Erlang distributed cell life lengths. Risk Anal. 15:495-502 (1995).
35. N. T. J. Bailey, The Elements of Stochastic Processes with Application to the Natural Sciences. Wiley, New York, 1964.
36. C. L. Chiang. An Introduction to Stochastic Processes and Their Applications. Krieger, New York, 1980.
37. J. H. Matis, Q. Zheng, and T. R. Kiffe, Describing the spread of biological populations using stochastic compartmental models with births. Math. Biosci. 126:215-247 (1995).
38. S. Wolfram, Mathematica: A System for Doing Mathematics by Computer. 2d ed., Addison-Wesley, Reading, MA, 1991.
39. Q. Zheng, Combining symbolic and numerical computing in carcinogenesis modeling. (Proc. Tenth Int. Conf. on Mathematical and Computer Modelling and Scientific Computing), Mathematical Modelling and Scientific Computing. (1997) in press.
40. Q. Zheng and J. H. Matis, Some applications, properties and conjectures for higher order cumulants of a Markovian stepping-stone model. Commun. Stat. Theory Methods 22:3305-3319 (1993).
41. E. Renshaw, Interconnected population processes. J. Appl. Probab. 10:1-14 (1973).
42. H. G. Tucker, A stochastic model for a two-stage theory of carcinogenesis. Proc. Fourth Berkeley Symp. on Mathematical Statistics and Probability, pp. 387-403 (1966).
43. R. W. Whitmore and J. H. Matis, Compartmental analysis of carcinogenic experiments: formulation of a stochastic model. J. Math. Biol. 12:31-43 (1981).
44. M. J. Faddy, Stochastic compartmental models as approximation to more general stochastic systems with the general stochastic epidemic as an example. Adv. Appl. Probab. 9:448-461 (1977).
45. J. F. C. Kingman, Markov population processes. J. Appl. Probab. 6:1-18 (1969).
46. Q. Zheng, On a compartmental analysis result. Math. Biosci. 130:203-206 (1995).
47. F. John, Partial Differential Equations. Springer, New York, 1971.
48. D. W. Quinn, Calculating the hazard and probability of tumor for cancer risk assessment when the parameters are time-dependent. Risk Anal. 9:407-413 (1989).
49. Q. Zheng, MathSource item no. 0207-942, archived by Wolfram Research, Inc., available on CD-ROM and Internet http://www/wri.com(1995).
50. M. Kac, Some mathematical models in science. Science 166:695-699 (1969).