THE DISTRIBUTION OF THE NUMBERS OF MUTANTS 

 IN BACTERIAL POPULATIONS 



By D. E. LEA,* Department of Radiotherapeutics and Strangeivays Laboratory, Cambridge 

 and C. A. COULSON, Wheatstone Physics Laboratory, King's College, London 



Introduction 

 Luria & Delbruck (1943) have shown that if a culture of some hundreds or thousands of 

 millions of Bacterium coli, grown from a single cell, is plated out on a nutrient medium 

 impregnated with a bacteriophage to which the strain of coli is sensitive, the vast majority 

 of the bacteria are lysed, but a few give rise to colonies. These colonies contain only 

 bacteria resistant to the bacteriophage, and give rise only to resistant bacteria on further 

 subcultivation. Evidently hereditary variations or mutations can occur in bacteria. 

 Numerous other examples are known of mutations in bacteria, affecting fermentation 

 reactions (e.g. Lewis, 1934), resistance to chemicals (e.g. Stewart, 1947), to antibiotics 

 (e.g. Demerec, 1945), or to radiation (Witkin, 1946). 



The demonstration of phage-resistant mutants necessarily involves the exposing of the 

 bacteria to the phage, and it is not immediately obvious whether the mutation to phage 

 resistance occurs spontaneously during the growth of the culture, and is merely made 

 apparent by subsequently testing with phage, or whether the mutation is induced by the 

 phage and does not occur until the bacteria are brought into contact with phage. Most 

 experiments on bacterial variation have left open the two alternatives of spontaneous 

 mutation on the one hand, and induced mutation or adaptation on the other, and the 

 interpretation adopted has usually been determined by the previous training of the 

 individual worker rather than by any compelling evidence provided by the experiments. 



Luria and Delbruck, however, in their paper, described a method by which a decision 

 between the two alternative explanations may be reached, and concluded that the 

 acquirement of resistance to phage is a spontaneous mutation which occurs during the 

 growth of the culture and prior to its treatment with phage. Demerec (1945) and Witkin 

 (1946) have applied the same method to mutants resistant to penicillin and to X-rays 

 respectively, and have concluded that these changes also are spontaneous mutations 

 occurring independently of the penicillin or of the radiation respectively. 



The principle of Luria and Delbruck's test is as follows. A culture of (say) 10 9 bacteria 

 is divided into (say) ten equal portions which are separately tested for phage-resistant 

 organisms by plating out on a phage-impregnated medium. A small number is found in 

 each of the ten portions, and the numbers are found experimentally to be distributed with 

 a variance approximately equal to the mean. This result is not surprising on either hypo- 

 thesis. On the spontaneous mutation theory, we suppose that mutations to phage 

 resistance occurred from time to time during the growth of the culture. All the bacteria 

 produced by subsequent divisions of a mutant bacterium were similarly phage resistant. 

 Thus the culture of 10 9 bacteria contained a certain number of phage-resistant bacteria, 



* [Note by C. A. C. A few days before Dr Lea's untimely death in June 1947, the manuscript and the calcula- 

 tions reported here had just been completed. It was Dr Lea's intention to make further experiments more 

 suitable to a test of the theory outlined in this paper. These experiments cannot now be made, but it has been 

 thought wise to publish the theory and numerical tables because of their value to other investigators.] 



[Reprinted l>y permission of the Cambridge University Press from Journal of Genetics 

 49 : (3) 264-285, December, 1949] 



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