By contrast the cells responsible for osteosarcomas

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By contrast, the cells responsible for osteosarcomas are present in much greater numbers during adolescence, when their proliferation is required to increase the size of the skeleton, than they are in young children or adults. In this case, it is the number of cells at risk that is the most important deter- minant of the frequency of cancer. Reference: Knudson AG (2001) Two genetic hits (more or less) to cancer. Nat. Rev. Cancer 1, 157–162. 20–17 The time at which the death rates due to breast and cervical cancer slow cor- responds to the menopause, at which time the production of estrogen declines. Estrogen normally promotes the proliferation of cells in the breast and uterus. Thus, the decline in estrogen would reduce the population of proliferating cells, thereby reducing the risk of cancer in these tissues. Reference: Armitage R & Doll R (1954) The age distribution of cancer and a multi-stage theory of carcinogenesis. Reprinted in (2004) Br. J. Cancer 91, 1983–1989. CALCULATIONS 20–18 A tumor that arose from 50 cell doublings would contain 2 50 cells, which is 1.1 ¥ 10 15 cells. If 10 8 cells is 1 gram, then the tumor would weigh 1.1 ¥ 10 7 g, which is 24,000 pounds. Thus, a limit of 50 cell divisions, by itself, does not provide much protection against cancer. Even in a 40-year-old, whose fibroblasts divide about 40 times in culture, a tumor arising from 40 cell divi- sions would weigh more than 20 pounds. This calculation assumes that all cells survive. It is likely, however, that many cells die by apoptosis, especially at early stages in the evolution of can- cer. In combination with extensive cell death, a limit of 50 cell divisions could protect against cancer. 20–19 A. The cell-cluster model for cancer formation predicts an exponential rela- tionship between carcinogen concentration and cancer formation. In the equation, Nx n , the concentration of mutagen, would influence the probabil- ity of mutation, x , so that 1, 2, and 4 times the carcinogen concentration would give 1 x , 2 x , and 4 x probabilities of mutation, respectively. The num- bers of cancers should then be N (1 x ) n , N (2 x ) n , and N (4 x ) n , respectively. To illustrate this with numbers, let N = 10 9 , x = 10 –2 , and n = 5, as they are in the body of the problem. Substituting these numbers gives 0.1, 3.2, and 102.4
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THE PREVENTABLE CAUSES OF CANCER A459 cancer clusters for 1, 2, and 4 times the carcinogen concentration. This pre- dicted exponential dependence on carcinogen concentration does not match the linear dependence observed experimentally. B. The tumor-progression model for cancer formation predicts a linear rela- tionship between carcinogen concentration and cancer formation, so long as the frequency of mutation is low. A slowly progressing tumor presents a moving target for mutation. At an early time, say when it has one mutation, carcinogen treatment can stimulate the acquisition of a second mutation in one of its cells, allowing that cell to progress to the next stage. It is unlikely, however, to introduce two mutations into one cell in the small population of cells that constitutes the early tumor. At a later stage, when the tumor cells
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