344 SPECULATIONS ON CELLULAR ACTIONS 



titles required for the decisive state; and now regard h as the mean num- 

 ber of groups of decisive processes produced per cell per unit dose. The 

 dose-effect relationships can now be described mathematically by the 

 methods of conventional, formal target theory (1). 



When m/r and n/s are constant among the individual cells, the survival 

 curve in general is described by 



No 

 where 



^ = 1 - [1 - Yf (1) 



Y = e 



--1 



2 



2! 



/m \ 



(2) 



-hD (3) 



in which expression the first m/r terms are used in any particular case.* 

 When N/Nq, the fraction of cells not affected, is plotted against the dose 

 D, the shape of the resulting survival curve is determined by m/r and 

 n/s, and its slope by h. If m/r = 1 = n/s, the survival curve is a simple 



exponential : 



N _ 



If m/r, n/s, or both are greater than unity, the curve is sigmoid and its 

 precise shape is determined by m/r and n/s. Some examples are shown 

 in Fig. 4, along with the exponential of Eq. 3, the value of h being the 

 same in all cases. 



Analogies avith Target Theory 



At this point we can recognize analogies between some of our concepts 

 and those of conventional target theory. Our precursor is the "target"; 

 the group of r decisive processes is a "hit"; m is the number of individual 

 decisive processes necessary to alter the target, but it is possible that 

 these m processes may be delivered in only m/r "packets"; m/r ac- 

 cordingly is the "hit number" for the change of a single target (precursor) 

 to a decisive entity; n is the number of targets which must be altered to 

 guarantee the end effect (that is, produce the decisive state) ; if a group 



* Equation 1 presupposes the following conditions: (a) whenever m > 1, the in- 

 dividual decisive processes (M, Fig. 2) operating on an individual precursor occur 

 independently of each other and are equally probable; (6) the probability of irrele- 

 vant processes is large compared to that of relevant ones and is constant during ir- 

 radiation. 



