460 HOWARD B. NEWCOMBE 



its first appearance. This would be interpreted as indicating that the mutant 

 clone had its origin one or more divisions prior to its becoming phenotypically 

 detectable. 



One obvious alternative to this interpretation should be mentioned, namely 

 that the excess numbers of mutants are due to more r^pid division in these 

 than in the parent strain. This is rendered unlikely however by the evidence 

 of Demerec and Fano (1945) that these mutants do not divide more rapidly, 

 and in addition more critical evidence against the possibility has been obtained 

 from the experiments described under method 3. 



The experimental procedure was essentially that used by Demerec (1946) 

 in his work on mutation rates in E. coli following irradiation. Bacteria are grown 

 on agar for varying periods of time, sprayed with phage, and incubated until 

 colonies appear. Mutations occurring during growth, and gaining phenotypic 

 expression, will give rise to resistant clones. Since individual bacteria cannot 

 move about on the agar, the members of a clone are confined to a particular 

 locality. These resistant clones survive the application of phage, and eventually 

 form colonies of visible size. Thus each mutation which gives rise to phage 

 resistance is in the end represented by one colony. 



An estimate of mutation rate is obtained by dividing the number of resistant 

 clones appearing in a given period by the number of bacterial divisions times 

 1/ln 2. Thus, if Ri and R 2 are the numbers of resistant clones present at times 

 1 and 2, the number of resistant clones arising during the interval between 

 times 1 and 2 is R 2 — Ri. Similarly, if Ni and N 2 are the numbers of bacteria 

 present at times 1 and 2 respectively, the increase during the interval will be 

 N 2 — Ni. Since each division of a bacterium increases the total number by 

 one, this value is equal to the number of bacterial divisions during the period. 

 Mutation rate per bacterium per division cycle, a, will therefore be obtained 

 from the formula: 



a = (In 2)(R 2 - R,)/(N, - N x ). (4) 



Since the values of R 1? R 2 , Ni and N 2 represent viable cells only, an assump- 

 tion is involved, namely that all bacteria divide. It will be shown later that this 

 assumption is approximately correct for the early stages of logarithmic growth, 

 and it is assumed that no appreciable increase in the proportion of cells which 

 fail to divide, takes place until the phase of declining growth rate is approached. 

 In these experiments precautions were taken to ensure that growth is limited 

 to the period of exponential increase. 



It will also be shown that the effect of the presence of cells which do not di- 

 vide further, will be to increase the estimated rate of mutation. The present 

 experiments can therefore be considered critical if the estimates of mutation 

 rate obtained using method 4 are found to be low relative to those obtained 

 using methods 2 and 3. 



Estimates of the values of Ri, R 2 , Ni, and N 2 are obtained as follows. Four 

 plates are inoculated with a suitable number of bacteria, two being incubated 

 until time 1 and two until time 2. One plate from each incubation period is 

 sprayed with phage and then incubated further. The numbers of colonies 



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