DELAYED EXPRESSION OF MUTATIONS 453 



These considerations are of course based on the assumption that each bacterium 

 divides, an assumption which will be discussed later in the paper. 



Methods 1 and 2 have been used with strain B/r in order to determine (a) 

 whether, as with strain B, estimates obtained by method 1 are lower than 

 those obtained by method 2, and (b) whether the estimates from these two 

 methods are the same for B/r as for B. 



The data from these experiments and the estimated mutation rates are 

 given in table 1. Those obtained using method 1 average .40X10 -8 and, those 

 using method 2 average 3.6 X10~ 8 . 



It will be seen from table 9 — in which the results of previous workers, using 

 strain B, have been quoted — that the discrepancy between the estimates of 

 mutation rate given by the two methods as applied to B/r is similar to the 

 discrepancy using strain B. It is also evident that the estimate of mutation 

 rate for strains B/r and B are similar. 



THE ELIMINATION OF A POSSIBLE UPWARD BIAS IN METHOD 2 

 BY THE USE OF LARGE INOCULA (METHOD 3) 



The formula for calculating mutation rate from the average number of 

 mutants per culture (method 2) disregards the early divisions, when the popu- 

 lation is small and it is unlikely that a mutation will occur. The divisions 

 which enter into the calculation are those occurring after an arbitrary time, this 

 time being chosen so that on the average one mutation will occur prior to it 

 in the whole series of cultures. Luria and Delbruck point out that the chance 

 occurrence of this early mutation might account for part of the discrepancy 

 between the estimates of rate obtained with the two methods. For a detailed 

 discussion of this point the reader is referred to their paper. 



It was therefore necessary to arrive at an estimate which, like that obtained 

 by method 2, would utilize the number of resistant bacteria arising during 

 growth in liquid culture, but which would not be biased by the chance occur- 

 rence of early mutations. This was done by growing the test cultures from in- 

 ocula of sufficient size to ensure that an appreciable number of mutations would 

 take place during the first division. Since much of the statistical fluctuation in 

 end numbers of resistant bacteria is thus eliminated, mutation rates may be 

 estimated from single cultures. (An experiment similar to this has been pro- 

 posed by Shapiro 1946.) 



The method can be used only if the proportion of resistant bacteria in the 

 inoculum is small, since otherwise the relatively small increase due to mutation 

 during growth could not be accurately determined. To serve as inocula, there- 

 fore, cultures containing very small proportions of resistant bacteria were 

 chosen. 



Five 50 cc and five 300 cc aerated cultures were grown from inocula of 

 2.6 X10 9 and 2.1 X10 8 bacteria, respectively. Synthetic medium, the M-9 of 

 Anderson (1946), was used because the bacteria can be grown to a higher 

 number per unit volume in it than in broth. In two separate sets of experi- 

 ments growth resulted in increases in the numbers of individuals of approxi- 

 mately a hundredfold and three thousandfold, respectively. 



55 



