102 S. E. LURIA AND R. DULBECCO 



2^ [l _ (1 _ Q-rlny^n 



, k=2 kl 



y = z/m = , n -X • (^^ 



1 — (a; + l)e ^ 



The expression y thus obtained is a function of x (average number of phage 

 particles adsorbed per bacterium), of r (average number of lethal hits per par- 

 ticle), and of n (number of units per particle). 



We shall call w the ratio between the nuniber of bacteria that actually liber- 

 ate active phage (plaque count) and the number of multiple-infected bacteria. 

 For each mixture of bacteria and irradiated phage, we can determine experi- 

 mentally r, X, and the placjue count, and obtain from these the values of m and 

 w. We can then compare the experimental values of w with the calculated 

 values of y for several different values of n.^ 



The function y = F {r, x, n) was tabulated numerically for a range of values 

 of r (between 3 and 50), of x (between 0.05 and 20), and of n (between 10 and 

 60). We used for k those ranges of values for which the contributions of the 

 corresponding classes were relevant. The corresponding curves were drawn 

 iox y = F (r) {x and n constant), and for y = F (x) (r and n constant). 



Before comparing the experimental results with the curves, it is useful to 

 discuss briefly what we may expect from the comparison. If reactivation only 

 occurs in bacteria with more than one inactive particle, w should never be 

 greater than unity. If among the requirements for reactivation there are those 

 stated in the assumptions of our theory, the ratio w/y should never be greater 

 than unity. Finally, if the requirements stated in our assumptions are necessary 

 and sufficient for reactivation, the ratio w/y should be unity, that is, active 

 phage should be produced in all those bacteria that receive a full complement 

 of the hypothetical units in non-lethal form. Should this obtain, it would then 

 be possible to calculate the value of n for each phage from the experimental 

 values of w. 



It is important to keep in mind that the assumptions of our theory, up to 

 this point, do not contain any implication as to the nature, properties, or 

 mechanism of transfer of the postulated units. They only assert that each unjt 

 has genetic individuality and can be made lethal by radiation as a result of one 

 photochemical reaction, which is of the "all or none" type and independent of 

 other reactions of the same type in other units of either the same or other phage 

 particles. Production of active phage is conditioned by the presence in one 

 bacterium of one active copy of each unit, this copy not being replaceable by 

 any number of inactive copies. 



The theory does not imply that all phage particles receive the same number 

 of lethal hits, but that the lethal hits are distributed at random among the 

 units of all phage particles. 



' In preliminary reports (Luria 1947, 1948) we used the symbol y both for the theoretical and 

 experimental probabilities of reactivation. We also gave values of l/y instead of y(or w). The 

 present notation, while consistent with the previous one, makes the presentation mere logical. 



256 



