452 HOWARD B. NEWCOMBE 



T5. These mutant categories are designated B/r/1 and B/r/1,5 respectively. 

 Within each there occurs a number of morphologically distinguishable colony 

 forms, and it is possible that these represent a number of mutations of dis- 

 similar origin; but in this study no attempt has been made to distinguish 

 between the various types of mutation that give rise to resistance to Tl. 



DISCREPANT ESTIMATES OF MUTATION RATE FROM NUMBERS OF RESISTANT 

 CLONES (METHOD 1) AND OF RESISTANT INDIVIDUALS (METHOD 2) 



In view of the possibility that B/r may differ from B in the rate with which it 

 mutates, rates for B/r were determined by each of the Luria and Delbruck 

 methods, using phage Tl. 



Eight separate experiments were carried out, and for each experiment 25 

 broth cultures of 0.2 cc were grown. Small inocula were used, and the cultures 

 were incubated for 18 hours, by which time growth had stopped. 



The inocula contained approximately ten bacteria per culture in four of the 

 experiments, and approximately 10 4 in the other four. These numbers were 

 small enough so that the chance carry-over of a mutant in the inoculum would 

 be readily detected. 



Method 1 was used to calculate mutation rate, a, from the proportion of 

 cultures having no resistant bacteria, Po, and the average number of bacteria 

 at the end of growth, N, using the formula: 



a = - (In 2) (In P )/N. (1) 



The above formula is derived from formulas (4) and (5) of Luria and Del- 

 bruck (1943), In being the natural logarithm. 



Method 2 was used to calculate mutation rate, a, from the average number 

 of resistant bacteria per culture, r, the average number of bacteria at the end 

 of growth, N, and the number of cultures, C, using the formula: 



r = (aN/ln 2) In (CaN/ln 2). (2) 



This is derived from formula (8) of Luria and Delbruck. 



The natural logarithm of 2 appears in these formulas because the mutation 

 rate refers to the rate per bacterium per division cycle, as distinct from the 

 rate per bacterial division. The significance of this distinction is best visualized 

 by using a concrete example. If a population of 10 8 bacteria passes through 

 one division cycle and one mutation takes place, the number of bacterial di- 

 visions is 10 8 and the mutation rate per bacterial division is 1 X 10~ 8 . The 

 mean population throughout the cycle, however, is 10 8 /ln 2, so that the rate 

 per bacterium per division cycle is In 2X10 -8 , which is .693 X10 -8 . 



The first of these two methods of expressing mutation rate would be appli- 

 cable if mutation took place only at the time of cell division, and affected 

 just one of the offspring. The second would be applicable if mutability were 

 continuous throughout the division cycle. In the absence of information on 

 this point the choice is arbitrary, and since the latter method has been used 

 by previous authors its use is continued in this paper to facilitate comparisons. 



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