472 



HOWARD B. NEWCOMBE 

 Table 11 



Averages of mutation rates for strains B and B/r to resistance to phage Tl obtained by methods 

 1 to 5. Summary of calculations using data, or mutation rates already calculated, from the present in- 

 vestigation, Luria and Delbruck (1943), Demerec and Fano {1945), and Beale (1948). 



MUTATION RATE, XI 0~ 8 

 METHOD FORMULA '" 



Present L. & D. D. & F. Beale 



Estimates based on numbers 

 of resistant clones 

 (1) Series of liquid cult., 



no resist . b. a = - (In 2) (In P ) /N 



(4) Solid medium, resist. 



clones a = (ln2)(R 2 -R 1 )/(N 2 -Ni) 



0.40 



0.32 0.68 



0.51 — 



0.49* 



Estimates based on numbers 

 of resistant individuals 



(2) Series of liquid cult., 



av. res. b. r = (aN/ln2) ln(CaN/ln2) 3.6 2.4 



(3) Liquid cult, from 



large inocula a = (ln2)(r 2 /N 2 — n/NO/g 3.1 — 



(5) Series of liquid cult., 



max. res. b. a = (ln 2)(h-r)/CN 2.2 1.5 



2.7 — 



Early growth 



(4a) Solid med., res. 



clones, first div. a=(ln 2)(R 2 -R 1 )/(N 2 -N 1 ) 8.3 — 



Symbols: 



a, mutation rate per bacterium per division cycle. 



r, average number of resistant bacteria per culture. 



h, highest number of resistant bacteria in any one culture of a series. 



N, average number of bacteria per culture; Ni and N 2 , average number at times 1 and 2 



respectively. 

 C, number of cultures. 

 R, average number of resistant clones per plate; Ri and R 2 , average numbers at times 1 and 



2 respectively, 

 g, number of cell generations. 



Po, proportion of test cultures in which there are no resistant mutants. 

 * Note: the value .7X10~ 8 bacterial divisions obtained by Beale has been converted to the 

 rate per bacterium per division cycle by multiplying by In 2 ( = .693). 



the growth period is long, and in which the majority of the resistant individuals 

 are from mutations occurring many generations previous to the cessation of 

 growth. 



The estimates of rate obtained by these methods are all considerably greater 

 than those which took into consideration only the numbers of resistant clones 

 and not the numbers of resistant individuals, and differ only slightly among 

 themselves. In the present experiments they average approximately 3X10 -8 . 



It is thus evident that the numbers of resistant individuals in a mutant 

 clone must be greater than would be expected on the basis of the time of pheno- 

 typic appearance of that clone. One simple interpretation of this — namely, 



74 



