RADIOBIOLOGY OF BACTERIOPHAGE 355 



B. Target Theory 



Modifications of one basic experiment serve as the basis for most investi- 

 gations in the effects of irradiation on phage. This basic experiment is to 

 measure the survival of some property of the phage as a function of increasing 

 dose of radiation. The simplest such dose-response is well illustrated by the 

 loss of the ability of phage to make a complete cycle of infection, terminated 

 by the release of more infective phage. For both X-rays and suicide (and 

 sometimes for ultraviolet light) such responses are "one-hit." That is, in- 

 fectivity decreases exponentially as a function of dose, and this exponential 

 response holds over the entire dose range. Equation (1) characterizes such a 

 response. 



SfSo = e-''^^ (1) 



where So is the original number of infective particles, S is the number 

 remaining after some dose of radiation D, and kj^ is a constant which is char- 

 acteristic of the phage strain and the conditions under which it is irradiated. 

 In many cases the dose is applied at a constant rate so that we can write 



SfSo = e-'-^' (2) 



where t is a unit of time, and kz is a constant which depends on ki and on 

 the rate of appHcation of the dose. It is common practice to plot a "survival 

 curve" as log loiSISg) versus t (Fig, 1). The resulting plot is a straight line, 

 the slope of which is a measure of the "sensitivity" of the phage. When the 

 survival of infectivity has reached 0.37, ^2^ equals 1, and we say that on the 

 average there has been one "hit" per particle. On occasion we shall use the 

 survival equation in the form 



SISo = e-*- (3) 



where r is the number of hits per particle which inactivate the property of 

 infectivity. 



In so defining a "hit" we are adopting a form of "target theory" as a 

 framework for our subsequent thinking. In this model we imagine that darts 

 are flung at random at a number of targets of equal size. The darts corres- 

 pond to quanta of radiation, the targets to phage particles, A dart will 

 "stick" to a target which it strikes with a probability a; i.e., a quantum of 

 radiation impinging upon a phage particle will be effective with a probability 

 a called the "quantum efficiency." This regime leads to a Poisson distribution 

 of darts stuck into targets (or hits upon phage particles). For any average 

 number of hits r there will be a fraction of particles e~^ which are not hit at 

 all, a fraction re~^ which are hit once, a fraction r^e~^l2 which are hit twice, 

 and, in general, a fraction 



F = r'^e-'jx ! (4) 



which have been hit x times. 



