PROBLEMS OF MEASUREMENT OF MUTATION RATES 



Atwood: It could be done without resorting to a laboratory method 

 of finding carriers, could it not? 



Neel: Yes, that is true; but the first approach was, as I stated, based 

 on unreliable laboratory tests (17, 36). 



Auerbach: I think, in Drosophila, the males have a higher rate. 



Atwood: Yes. Well, in any case, the mutant cells that will be found 

 at reproductive age are accumulating prior to that time. The number 

 of mutants has a different relation to the number of mutations, depend- 

 ing on whether we are in the clonal region of the growth curve or in 

 the steady state region. On the average, the number of mutant cells 

 produced during clonal growth will be greater than the number of muta- 

 tions by a factor of the log of the number of cells, whereas, in the 

 steady state, the number of mutants and mutations will be the same. 

 We can show this as follows: 



Let's imagine that we have N cells at the end of the time, and we 

 start out with No cells, which may be the number differentiated off to 

 form this tissue. We divide the time of growth from N„ to N into n 

 intervals. These intervals may be doubling times or any convenient 

 intervals. At the end, the number of cells present is NqX", where n is 

 the number of intervals and X is any base, which would depend for 

 convenience on the interval chosen. You might choose a base of 2 if 

 you wanted to have n doublings. Mutations occur in each interval at 

 a rate, a, per cell so that in the first interval we have aNo mutations 

 but each contributes X° mutants, because each grows through the n 

 intervals, or a total of aNoX° mutants. In the last interval, we would 

 have aNoX" mutations, and each contributes 1 mutant. Hence, we again 

 have aNoX° mutants. 



For any intervening interval, say n — 1, we have the same relation- 

 ship ; that is, these aNoX°"^ mutations form X mutants each if they are 

 one interval behind, or X^ mutants per mutation for the second in- 

 terval behind, and so on. Each generation contributes equally to the 

 final number of mutants, on the average, aNpX" mutants. The total 

 final number of mutants is the sum of those contributed for n intervals, 

 naNoX". 



If at the end of clonal growth we have lO^*' germ line cells, as I 

 think would be a reasonable conjecture for the human male, there are 

 about 30 times as many mutant cells at the end than there were 

 mutations that occurred during that period. 



Lederberg: That is based on how many generations? How many 

 doublings? 



Atwood: Well, 10^° is about 33 doublings. Now, thereafter, when 



