FREQUENCY OF SPONTANEOUS BACTERIOPHAGE MUTANTS 



Synchronization is expressed by the requirement that for x ^ 2^, y^ = 0. 



The frequency distribution (1) is, of course, identical to that of bacterial 

 mutants in a series of similar populations (Luria and Delbriick, 1943; Lea and 

 Coulson, 1949). If we limit our observation to one intracellular cycle of phage 

 production, the maximum clone size will be the maximum "burst size." Each 

 phage burst with 2^ particles represents a population. For m » 2~^, there will 

 practically never be more than one mutation per bacterium; the frequency dis- 

 tribution (1) will then be that of the mutant clones among a large number of 

 bacterial yields, with limitations imposed by the inequality of burst size from 

 cell to cell. 



II. Independent Successive Replications 

 Let us suppose that each new replica of a gene is produced independently of 

 the preceding one, for example, by a series of successive acts of replication 

 controlled by the initial gene brought in by the infecting phage particle. 



(a) If one of the copies mutates (at the time of its formation or later) the 

 probability of mutation in other copies produced in the same cell should not be 

 affected. Assuming a uniform mutation probability m, the mutants will be 

 distributed at random among phage bursts (Poisson distribution). 



(b) If the initial gene, the pattern, mutates while turning out replicas, we may 

 assume that afterwards it produces only mutants. If the mutation rate is con- 

 stant in successive replications, there will occur as many cases of mutation just 

 before the production of the last viable gene copy as before the production of the 

 second last, the third last, and so on. The mutants will be in clones, and the 

 frequency of clones of different sizes will be uniform, at least up to the value of 

 the minimum burst size. 



Experimental Work 



Previous data on the number of host range mutants in individual phage 

 cultures (Luria, 1945a; Hershey, 1946a) did not allow the desired type of analy- 

 sis, because the quantitative detection of the mutants was uncertain and because 

 their low frequency made it necessary to look for them in mass cultures, where 

 more than one cycle of intrabacterial growth of some mutants could take place. 



The experiments here reported consisted in making single infection of Escheri- 

 chia coli B with phage T2L (Hershey, 1946a; for the experimental methods used, 

 see Adams, 1950) and counting the mutants r oyw produced in phage bursts from 

 individual bacteria. These mutant phenotypes (Hershey, 1946b) were chosen 

 because they occur with suitable frequency, can be recognized and scored 

 efficiently, and can be tested for genetic allelism or nonallelism (Hershey and 

 Rotman, 1948). Previous extensive tests by Dulbecco (1949) and other tests 

 made in the course of this work established the following technical points. 



1. Mutant plaques r and w can be detected and scored without difficulty after 

 six to eight hours of incubation at 37°C on nutrient agar plates under standard 

 conditions (plating in a 0.6% agar layer over 24 hour old 1% agar plates, with 

 about 2 X 10* young bacteria per plate). Over 100 single plaque isolations and 

 replatings confirmed the scorings made by plaque type. 



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