MUTATIONS OF BACTERIA 507 



number of cultures with one resistant bacterium very closely fits the expecta- 

 tion. The classes with two, four, eight, etc., resistant bacteria are bound to 

 be favored in the theoretical distribution, as explained in the theoretical part. 



The results shown in figure 2 also confirm the assumption that the dis- 

 crepancy between experimental and calculated standard deviations must be 

 due to an excess of cultures with large numbers of resistant bacteria. 



Summing up the evidence, we may say that the experiments show clearly 

 that the resistant bacteria appear in similar cultures not as random samples 

 but in groups of varying sizes, indicating a correlating cause for such grouping, 

 and that the assumption of genetic relatedness of the bacteria of such groups 

 offers the simplest explanation for them. 



Mutation Rate 



As pointed out in the theoretical part of this paper, mutation rates may be 

 estimated from the experiments by two essentially different methods. The 

 first method makes use of the fact that the number of mutations in a series of 

 similar cultures should be distributed in accordance with Poisson's law; the 

 average number of mutations per culture is calculated from the proportion 

 of cultures containing no resistant bacteria at the moment of the test, accord- 

 ing to equation (5). 



There are two technical difficulties involved in the application of this 

 method. In the first place, rather large numbers of cultures have to be handled 

 and conditions have to be chosen so that the proportion of resistant bacteria 

 is neither too small nor too large. In the second place, the entire cultures have 

 to be tested, which means, in our method of testing, that cultures of rather 

 small volume have to be used and great care must be taken to plate as nearly 

 as possible the entire culture. 



Experiment No. 23 (see table 3) permits an estimate of the mutation rate 

 by this method. Out of 87 cultures, no resistant bacteria were found in 29 

 cultures, a proportion of .33. From equation (5) we calculate therefore that the 

 average number of mutations per culture in this experiment was 1.10. Since 

 the total number of bacteria per culture was 2.4X10 8 , we obtain as the mu- 

 tation rate, from equation (4), 



a = .47 X io~ 8 mutations per bacterium per time unit 

 = .32 X io~ 8 mutations per bacterium per division cycle. 



This calculation makes use exclusively of the proportion of cultures contain- 

 ing no resistant bacteria. It is therefore inefficient in its use of the information 

 gathered in the experiment. 



The second method makes use of the average number of resistant bacteria 

 per culture. The relation of this average number with the mutation rate was 

 discussed in the theoretical part of this paper and was found to be expressed 

 by equation (8). The mutation rates calculated by this method for each experi- 

 ment are collected in table 4. 



