10 MUTATIONS 



ability of a mutation occurring in each division is constant and inde- 

 pendent of what has gone on before. Then, the probabihty that the final 

 sperm is a mutation, if there are n divisions before, is one minus the 

 probability that a mutation does not occur, raised to the nth power, in 

 other words, it is a power function and not a straight mutation. 



Lederberg: Or the likelihood of double-mutant cells. That's a good 

 approximation. 



Steinberg: But this is a probability of a successive nonmutant. It 

 would probably come out the same. 



Lederberg: It is a very simple formulation of what I put on the 

 board before. I think I see what you're driving at, Kim, and I think, 

 probably, both of you are quite right. Let's take this formula. It is 

 intuitively obvious that this is the probability that in a given product 

 there is a mutant, and this is the proportion of mutants to totals, in 

 the case where we can take the linear approximation. That is equal 

 to the interval rate times the number of intervals at risk. Now, 

 how do we estimate these? Let me just say, too, you can multiply 

 this out and you get the formula that was given here. During clonal 

 growth, you estimate n as the "log" of N. Later on, there is a period 

 of equilibrium of stem cell production, and then n is proportional to 

 time, and N is not changed proportional to time; so you end up with 

 a formula, if you want to take N into account, the interval of clonal 

 growth — you take the number of intervals that have passed without 

 reference to the increase in the number of cells. This is your old 

 formula. 



If you want to write it out in the form you had before, this is for 

 the period of clonal growtli. The number of intervals can be counted 

 by seeing how many stems have been produced, and there is a subse- 

 quent interval of stem line growth where there is no increase in the 

 number of cells, so we take T period of stem lines, divided by X. 

 That should be a complete description of the probability of the final 

 population of mutants. Is that correct? 



Atwood: Yes. I was trying to diagram this situation as you had it. 

 Dr. Goldstein. This is the clone up to the time of establishment of 

 stem cell regime, and this leads to the establishment of a certain num- 

 ber of normal stem lines and a certain number of mutant stem lines. 

 From that time on, every mutant stem line gives off some mutant 

 gametes and every normal one gives off some normal gametes, with the 

 exception of the mutations that may occur in clones intervening be- 

 tween stem cell and gametes. 



The mutations occurring in these intervening clones will not show 



