MUTATIONS OF BACTERIA 501 



mathematical difficulties. An approximation to the beginning of the distribu- 

 tion function — that is, to its values for small numbers of resistant bacteria — 

 may be obtained by grouping mutations according to the bacterial generation 

 during which they occurred. For instance, the probability of obtaining seven 

 resistant bacteria may be broken down into the sum of the following alterna- 

 tive events: (a) seven mutations during the last generation; (b) three mutations 

 during the last generation and two mutations one generation back; (c) three 

 mutations during the last generation and one mutation two generations back; 

 (d) one mutation during the last generation and three mutations one genera- 

 tion back; (e) one mutation during the last generation, one mutation one gen- 

 eration back and one mutation two generations back. 



The probability of each of these events depends only on the mutation rate 

 and on the final number of bacteria. 



The grouping of mutations according to the bacterial generation during 

 which they occurred, and the assumption that the bacteria increase in simple 

 geometric progression, simplify the calculation sufficiently to permit numerical 

 computation. On the other hand, the classes with two, four, eight, etc., mu- 

 tants are artificially favored by this procedure, so that a somewhat uneven 

 distribution results, with too high values for two, four, eight, etc., resistant 

 bacteria (see fig. 2). 



MATERIAL AND METHODS 



The material used for our experimental study consisted of a bacterial virus 

 a and of its host, Escherichia coli B (Delbruck and Luria 1942). Secondary 

 cultures after apparently complete lysis of B by virus a show up within a few 

 hours from the time of clearing. They consist of cells which are resistant to 

 the action of virus a, but sensitive to a series of other viruses active on B. 

 The resistant cells breed true and can be established easily as pure cultures. 

 No trace of virus could be found in any pure culture of the resistant bacteria 

 studied in this paper. The resistant strains are therefore to be considered as 

 non-lysogenic. 



Tests were made to see whether the resistance to virus a was a stable char- 

 acter of the resistant strains. In the first place, it was found that virus a is 

 not appreciably adsorbed by any of the resistant strains. In the second place, 

 when a certain amount of virus a is mixed with a growing culture of a resistant 

 strain, no measurable increase of the titer of virus a occurs over a period of 

 several hours. This is a very sensitive test for the occurrence of sensitive bac- 

 teria, and its negative result for all resistant strains shows that reversion to 

 sensitivity must be a very rare event. 



Morphologically at least two types of colonies of resistant bacteria may be 

 distinguished. The first type of colony is similar to the type produced by the 

 sensitive strain both in size and in the character of the surface and of the 

 edge. The second type of colony is much smaller and translucent. The differ- 

 ence in colony type is maintained in subcultures. Microscopically the bacteria 

 from these two types of colonies are indistinguishable. They also do not differ 



