MUTAGENS OF POTENTIAL SIGNIFICANCE 181 



ous cycle in man. Finally, m4 in man is a very small number, no greater 

 than 4 or 5, and in woman evidently only 2.* 



Atwood: The mutant frequency should be higlier at the end if you 

 have had clonal growth. 



Goldstein: We disagree on this, as we did the other day. There is no 

 formal difference between the growth here in the stem line and the 

 growth here in the sperm clone. This whole thing is one large clone 

 (see Fig. 2) , and the probability that a cell anywhere in it is mutant 

 is a function of the number of times it has been at risk. 



Novick: Kim, would you think it were correct if the population size 

 is very large? Wouldn't you think it is simply a question of population 

 size that is important? 



Atwood: I fail to understand you. 



Novick: I meant population size in number of cells, either sperm or 

 spermatogonia present. If the number of spermatogonia can be con- 

 sidered as very large, in fact, then he is correct. If the number of 

 sperm is very small, then one has to use some nondeterministic ex- 

 pressions. I think this is what you were concerned about. 



Atwood: It wasn't, but it should have been. 



Goldstein: It is a basic point. It was at issue the other day and it 

 seems to be at issue again. Let's see if we can agree about the analysis 

 of an ordinary clone. How do you analyze the probability for an 

 ordinary bacterial clone — what is the probability that a given member 

 of the final population will be mutant? I am saying that the prob- 

 ability that this cell is mutant is equal to the probability of mutation 

 per cell division times the number of cell divisions that have occurred 

 in the history of that bacterium. 



Neel: Instead of saying "per cell division," would you say "per cell 

 cycle," to keep Dr. Zamenhof happy, and me, too? It is per cell cycle. 



Goldstein: Yes, per cell cycle; all right. 



What I am trying to ascertain is the relative importance of the 



* The figures used here for mi, mo, g3, and m4 are the best I could obtain. 

 C. P. LeBlond (personal communication) supphed estimates based on work with 

 the rat and some suggestions as to the probable values of the several parameters 

 in man. The statement that stem cells divide regularly throughout childhood is 

 an extrapolation from findings of Clermont and Perey (15) in the rat. The estimate 

 of 12 days as the mean generation time in the stem line of man is derived from 

 LeBlond 's suggestion that one might be justified in assuming that cycle duration 

 in man is 10 to 12 days, since figures of this type have been observed in many 

 species. However, he points out that direct evidence in man is lacking. Comment- 

 ing on the difficulty of making reasonable guesses about man, he writes: "Our 

 knowledge of the human testis is pitiful." 



