180 MUTATIONS 



Let m be the total number of cell generations in the lineage of a given 

 sperm. This is to be segmented according to the 4 periods depicted in 

 Figure 25. Thus mi is the number of cell generations from zygote to 

 establishment of the stem cell population; m2 is the average number 

 of divisions of a stem cell during childhood; ms has the same meaning 

 from puberty through all of reproductive life ; m4 is the small number 

 of cell generations within the sperm clone itself from the unequal stem 

 cell division to the final spermatozoa. Let t be time, in days ; g be mean 

 generation time, in days ; n be an estimate of the total number of genes 

 in the human gamete. 



After continuous lifelong exposure to a mutagen, the probability that 

 a given sperm will be mutant with respect to a particular gene (which 

 is the same thing as the frequency of such mutants in a sperm popula- 

 tion) can be represented as the sum of four different terms, 



P = V2 (mi+m2 + m3 + m4) p. 



Now I am going to assume that we can speak of an average mutation 

 probability for all genes in man, so that by multiplying the above 

 expression by the total number of genes (assumed to be 10^) we can 

 obtain an estimate of the probability that a sperm is mutant in any 

 respect at all. It will also prove helpful to substitute for ms the 

 equivalent expression t.s/gs, where gs is the mean generation time (days) 

 in the line of stem cells during reproductive life. We then obtain 



P = y2 (mi+nio + t.s/ga+mj) np. 



The number of cell generations in the early establishment of the germ 

 line in the fetus, nii, is obviously a fixed quantity in man. I am going 

 to estimate that 30 may be the correct datum here, although I would 

 welcome correction based on actual data. This is a fairly important 

 figure because it determines the relative importance of fetal life and 

 later life with respect to mutagenic exposure. Dr. Atwood the other 

 day brought this out and suggested that the fetal period might be 

 equivalent to ten years of later exposure. 



As for m2, the ensuing period until puberty, this term and ms both 

 probably have the value zero in the female. In the male, if we assume 

 pubertal age 5 x 10^ days and stem cell mitosis every 12 days in child- 

 hood as after puberty, we obtain approximately 400 stem cell gen- 

 erations as the value of m2. In the subsequent term, ga will also be 

 given the value 12 days, which is probably the period of the seminifer- 



