S. E. LURIA 



A theory proposed by this writer (Luria, 1947) assumed independent repUcation 

 of these determinants (or groups of determinants) followed by their assembly 

 into mature virus particles. This theory originally aimed at accounting for the 

 reactivation of ultraviolet inactivated phage inside multiple-infected bacteria 

 (Luria and Dulbecco, 1949) and was extended to account for some features of 

 genetic recombination (Hershey and Rotman, 1949). The main ground for 

 proposing the theory, namely, the belief that the reactivation resulted from 

 genetic exchange, has been weakened by new evidence (Dulbecco, 1952), and the 

 theory has as little left to support it as to disprove it. 



Yet, all this concerns the organization of virus material during reproduction, 

 not the elementary process of replication. The latter cannot yet be attacked at 

 the chemical level by any tool except speculation. It can be attacked on a 

 limited front, however, by strictly genetic means. The experiments described 

 in this paper were done to investigate the rate of replication of individual genetic 

 determinants of the virus. They indicate that reproduction is exponential, each 

 replica acting as a source of new replicas. 



Theory 



Phage mutations occur only in the intracellular state, presumably during 

 replication. If a phage mutation occurs in a bacterium, that bacterium will 

 liberate one or more mutants (assuming that no loss occurs intracellularly). 

 Delbriick pointed out several years ago that the actual numbers of mutants 

 would depend on the mode of phage replication — more specifically, on the mode 

 of replications of the determinant or "gene" involved (see Luria, 1945b). We 

 shall analyze a few possible mechanisms; other mechanisms may be proposed, 

 but do not seem to lead to any simple picture. 



I. Exponential Reproduction 



One gene produces n genes, each of which in turn gives n genes, and so on. 

 After r generations, the number will be n^ For n = 2 (duplication mechanism), 

 the situation is analogous to bacterial reproduction. Let us assume this to be 

 the case. N gene copies will derive from one gene by N-1 acts of replication. 

 Let the last generation have the order number 0, the second last the order number 

 1, the third last 2, and so on. Suppose a mutation occurs at generation k, either 

 as an "error of replication" affecting one of the two products of duplication, or 

 as a change in one gene during interphase. If the replication process is com- 

 pletely synchronized (the consequences of nonsynchronization can, if necessary, 

 be analyzed), the resulting clone of mutants will at generation consist of 2^ 

 individuals. If the total number of individuals (at generation 0) in the popula- 

 tion is N, at generation k there were N/2'' individuals. Assuming a constant 

 probability m of mutation per individual, the number of mutations occurring 

 at generation k is mN/2''. The relation between the number x of mutants in 

 a clone and the frequency yx of such clones will then be obtained as follows: 



mN ^. mN /-1^ 



Yx = ^^; X = 2^; yx = ^1^ 



Z^ X 



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