72 M. DEMEREC [VOL. 56 



ponential. This means that the effect of two or more mutants together is con- 

 siderably greater than would be expected from the added values of the effects of 

 single mutants. 



No attempt has been made to determine the frequency with which genes affect- 

 ing resistance to penicillin mutate. It may be estimated from survival curves, 

 however, that the mutation rate is low, in the neighborhood of 1 X 10 -8 . With 

 such a low mutation rate, it is evident that the increase in resistance must occur 

 in successive steps, and that the chance that one step will be skipped is very 

 slight, the chance that two steps will be skipped practically nil. (A step would 

 be skipped when mutations in two genes occurred simultaneously in the same 

 bacterium; and two steps would be skipped if three mutations occurred simul- 

 taneously in a single cell. The chance of two simultaneous mutations is 10 -8 X 

 10-s = 1 q-i6 ) an( j f three simultaneous mutations, 10" 8 X 10~ 8 X 10~ 8 = 10~ 24 . 

 Since the volume of an S. aureus cell is about one cubic micron, it would be ex- 

 pected that one double mutant, on the average, would be found in ten liters of 

 bacteria, and one triple mutant in one million cubic meters.) 



The observed behavior of resistance to streptomycin also can be explained by 

 assuming the existence of several genes determining such resistance. Unlike the 

 genes for penicillin resistance, however, these differ greatly from one another in 

 potency. If a gene of low potency mutates, the first-step resistant strain will 

 have a low degree of resistance, but if mutation occurs in a highly potent gene, 

 the first-step resistant strain will be highly resistant. Consequently, consider- 

 able variation in degree of resistance is to be expected between first-step strains; 

 and for the same reason a highly resistant strain may be obtained either in one 

 step, by selection of a highly resistant first-step mutant, or in several steps, by 

 selection of mutants of low resistance values. 



CLINICAL CONSIDERATIONS 



A major consideration in the clinical use of antibiotics is how to avoid the 

 development of resistant strains, since the usefulness of an antibiotic is closely 

 related to the number of resistant pathogens and to their incidence in infections. 

 For this reason, analysis of the mechanism of origin of resistance to penicillin and 

 streptomycin has an important bearing on the clinical application of these 

 antibiotics. 



From the clinical standpoint, the situation in regard to penicillin is relatively 

 simple and well defined. Since resistance develops in steps, and it is very un- 

 likely that a step will be skipped in the process, the clinician can avoid develop- 

 ment of resistant pathogens by using initial doses that are adequate for the 

 elimination of first-step resistant individuals. Fortunately, most of the common 

 pathogenic strains that have been investigated (North and Christie, 1945; Meads 

 et al., 1945) are very sensitive to penicillin, so that large doses are not required in 

 clinical use. It is equally important for the clinician to maintain the effective con- 

 centration in treatment as long as the infection persists, because decrease of the 

 concentration below the effective level will permit the accumulation of first-step 

 resistant bacteria, which may increase to a point that will allow the occurrence of 



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