164 the physics of viruses 



Multiplicity Reactivation after Ultraviolet Treatment 



It was discovered by Luria (1947) that T-2, T-4, T-5, and 

 T-6 phages, when inactivated by ultraviolet light and then 

 caused to infect bacteria, multiply and show a much higher 

 yield of still active phage than is the case if single infections 

 alone are allowed. This shows that the virus is apparently partly 

 inactivated, so that the single infection cannot quite achieve 

 the process of multiplication, but yet has viral potency in some 

 degree. If two viruses are used to infect a bacterium, there is now 

 a chance that the residual potencies can combine to supplement 

 each other in such a way that a whole virus results, with the 

 usual consequences. This is spoken of as multiplicity reactiva- 

 tion and was originally analyzed in terms of a genetic recom- 

 bination process (Luria, 1947; Luria and Dulbecco, 1949). 

 This analysis depended rather critically on the one-hit nature of 

 phage inactivation, and, since this does not necessarily hold, 

 the precise conclusions may not be valid. Nevertheless, the 

 numerical considerations are sufficiently interesting to be worth 

 mentioning here in simplified form (following Luria, 1947). 



Suppose a number, //, of essential units (not necessarily 

 genetic) exist in each virus particle, and suppose r of these have 

 been inactivated. Then the average "hits" per unit is r/72, and 

 the probability of no inactivation is e"^^''^ per unit. The proba- 

 bility of at least one hit is 1 — e'^^'^'K If k ])articles are used to 

 infect, the chance that a ])articular unit has been hit in every 

 one of k particles is 



(1 - e- '■''')'' 



and the chance that one has not been hit is 



1 - (1 - e-'-^'^y- 



The chance that a bacteriiun receives active representatives of 

 all n units is ?/, where 



yy = {1 - (1 - e~'"''")^l" 



This reasoning ignores the possibility that two hits may occur 

 on one unit, and so has to be modified somewhat. This modifica- 



