106 S. E. LURIA AND R. DULBECCO 



which were found to have the same probability of reactivation as the respective 

 wild types. The results cover ranges of values of r from 2.5 to over 30, and of 

 X from 0.02 to 20. 



The individual values of w, and those of the variables, r and x, are obtained 

 from the following actual measurements: 1) titer of phage; 2) total number of 

 bacteria; 3) survival of phage; 4) survival of bacteria and/or assay of free 

 phage; 5) plaque count from the mixture. Each of these measurements involves 

 an error of estimation due to dilution and sampling errors. Several of these 

 determinations, however, are the same within each experiment. The results 

 from individual experiments are, therefore, more consistent than those from 

 different experiments, as shown in table 5. 



The only graphic representation that could show all values of w for each 

 phage and allow of comparison with the calculated values of y would be a 

 tri-dimensional plot of w as a function of r and of x. As second best choice, 

 we plotted the values of w as a function of r for several values of x taken as 

 constant, and as a function of x for several values of r taken as constant. 

 Individual values of w fluctuate rather widely, but the data as a whole make 

 it possible to draw curves, which represent averages and which can be consid- 

 ered as the curves for 2i> as a function of r and of x. A number of such plots 

 using all the experimental points for the corresponding values of the variables, 

 are presented in figures 2,3, and 4 (multiplicity of infection as variable) and 

 figures 5, 6, and 7 (dose of radiation as variable). 



The trend of these plots is similar to that of the theoretical curves for y^ 

 and it is possible to find for each phage a constant value of n (number of units) 

 such that the corresponding values of y become very similar to those of w for 

 low values of x and for any value of r. That is, it is possible for each phage to 

 determine a constant number of units for which the experimental probability 

 of reactivation equals the theoretical one for any dose of radiation provided 

 the multiplicity of infection is low. The corresponding theoretical curves for 

 y have been drawn in the plots of the values of w. For phage T2^ the best fit is 

 for w = 25; for T4, n=\S\ for T6, w = 30 (see especially figures 5, 6, and 7). 



The main feature emerging from the curves in figures 2, 3, and 4 is that the 

 values of w tend to unity for increasing multiplicity of infection. In several 

 cases, the number of cells that liberate phage actually reaches the number of 

 multiple-infected cells, but in no case does it go beyond it, proving that reacti- 

 vation does not occur in single-infected cells. 



The curves in figures 5, 6, 7, for w as a function of r, are of the multiple-hit 

 type, indicating that suppression of phage production depends on damage in a 

 number of elements. The values of w tend to unity for low doses, again showing 

 that reactivation potentially can take place in every multiple-infected cell. 



Comparison in figures 2-4 with the curves for y, chosen to fit the experi- 

 mental curves for low values of x, shows that the general similarity is limited 

 by a systematic deviation. As the multiplicity increases, both w and y tend 

 asymptotically to unity, but w increases more slowly. This means that, as the 

 number of phage particles per bacterium increases, the probability of reacti- 



260 



