190 THE PHYSICS OF VIRUSES 



illustrated in Fig. 8.1, where the changed virus is shown as 

 shaded. Since the mutation point is not si)ecially selected, any 

 number of mutants is as likely as any other. 



The third possibility is that reproduction by some kind of 

 growth and division takes place. In i)rinciple, division into n 

 units is possible; Luria considers division into two, as indicated 

 in Figs. 8.1b and 8.1c. The simplest method is that shown in 

 Fig. 8.1b, where each generation of the progeny occurs at the 

 same time. It is more likely that the actual process is the same, 

 but is not synchronized, and this is shown in Fig. 8.1c. The im- 

 portant point is that exponential growth follows each mutation, 

 so that the progeny of the mutant, which also consists of mu- 

 tants, develop as shown. 



To compute the number of mutants expected we can argue 

 thus. Designate the generation 0, 1, ^ . . . as indicated. Then a 

 mutation at the A'th generation jjroduces 2^" mutant i)hages. Call 

 this X. The total number of phage particles present at the A'th 

 generation is iV/2'^, where N is the total number present at the 

 end, the zeroth generation. If the chance of mutation per particle 

 at (or between) each generation is m, then the number of mu- 

 tants at the kih generation is mN/^''. This is mN/.r. Thus the 

 number of groups (clones) of mutants containing x ])articles per 

 group is inversely proportional to x. 



This assumes synchronism. If the generations are not syn- 

 chronized, then any particular value of .r can be derived from a 

 value of k occurring at a stage where division has been slow and 

 fewer individuals have l)een present, or it can corresi)ond to a 

 well populated generation. 'Ihese variable factors do not alter 

 the essential form of the distribution in which the pro])ortion of 

 clones »f size x, or greater, should be inversely as .r. 



Luria's data are tabulated l)elow. Two mutants were closely 

 observed. The figures are connected for the small number of 

 cases where the original infecting particle is itself a mutant. 



It can be seen that the proportion of clones with high values 

 of X is not extremely small, as required by the Poisson distribu- 

 tion for random mutation. This is thus experimentally ruled out. 

 Also, the proportion of clones does V^ecome less as x increases, 



