450 HOWARD B. NEWCOMBE 



not constant throughout growth, and the possibility that phenotypic resistance 

 does not appear for one or more generations after mutation to resistance 

 has taken place, will now be considered. 



A striking and unexpected finding of the Luria and Delbruck experi- 

 ments was that the rates estimated by these two methods differed by a con- 

 siderable factor, that from method 1 (utilizing the number of resistant clones 

 developing in liquid cultures) being lower than that from method 2 (utilizing 

 the average number of resistant individuals per culture). The averages of their 

 estimates are .32X10 -8 and 2.4 X10~ 8 per bacterium per division cycle, re- 

 spectively. This difference has since been confirmed by Demerec and Fano 

 (1945), who have in addition shown that it is not peculiar to experiments 

 using Tl but is also true of rates of mutation to resistance to other phages 

 (T3, T4, T5, T6, and T7) when estimated by methods 1 and 2. 



A statistical bias in method 2 (which gives the high estimate) may contrib- 

 ute to the discrepancy, but the work of Luria and Delbruck suggests 

 that its contribution is small. (For a discussion of this point the reader is re- 

 ferred to the original publication. Also, a method of estimating mutation rate, 

 which avoids this source of error will be considered in a later section of the 

 present paper.) 



Since the two methods will give the same estimate if, and only if, (1) the 

 rate of mutation is constant throughout growth and (2) the occurrence of a 

 mutation gives rise to a phenotypic mutant without delay, it was concluded 

 that one of these two conditions did not obtain. There was no critical evidence 

 to indicate which one, however, since the discrepant estimates could be ex- 

 plained by assuming either a high mutation rate during the greater part of the 

 growth period, dropping during the last few divisions, or a delay of one or 

 more generations between mutation and phenotypic expression. 



Luria and Delbruck did not favor the latter interpretation, since a fixed 

 delay of one or more generations before the development of phenotypic re- 

 sistance would mean that mutant clones would number two or more individ- 

 uals at the time when phenotypic resistance appeared. It was therefore as- 

 sumed that cultures with just one resistant individual would be rare if there 

 were a delay; and these, instead of being rare, had been observed in consider- 

 able numbers (see Luria 1946). It has been pointed out, on the other hand, 

 that if some lines of descent within the clone were to develop resistance earlier 

 than others, mutation plus delay could give rise to cultures having only one 

 phenotypically resistant individual (Sonneborn 1946). Thus the assumption 

 of a delay is permissible provided it is also assumed that phenotypic expression 

 is earlier in some lines of descent than in others within the same mutant clone. 



Two alternative possibilities therefore exist: (1) that of a relatively high mu- 

 tation rate during all but the last few generations, and (2) that of a variable 

 delay in phenotypic expression. The possible significance of the second of these 

 two alternatives should be considered. If there is a delay in phenotypic expres- 

 sion, then some cultures which showed no phenotypically resistant bacteria 

 would contain mutants that could not be detected. Also, the end number of 

 resistant bacteria in a culture would represent only part of the genetic mutants 



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